{"id":76713,"date":"2026-02-23T07:11:22","date_gmt":"2026-02-22T23:11:22","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/76713.html"},"modified":"2026-02-23T07:11:22","modified_gmt":"2026-02-22T23:11:22","slug":"%ef%bc%88%e5%ad%a6%e4%b9%a0%e7%ac%94%e8%ae%b0%ef%bc%892-2-%e6%95%b4%e6%95%b0%e8%a1%a8%e7%a4%ba%ef%bc%882-2-7-%e6%88%aa%e6%96%ad%e6%95%b0%e5%ad%97%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/76713.html","title":{"rendered":"\uff08\u5b66\u4e60\u7b14\u8bb0\uff092.2 \u6574\u6570\u8868\u793a\uff082.2.7 \u622a\u65ad\u6570\u5b57\uff09"},"content":{"rendered":"<\/p>\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>\u7ebf\u7d22\u680f<\/li>\n<li>\u7b14\u8bb0\u680f<\/li>\n<li>\n<ul>\n<li>1. \u622a\u65ad\u7684\u57fa\u672c\u6982\u5ff5\u4e0e\u793a\u4f8b<\/li>\n<li>2. \u622a\u65ad\u65e0\u7b26\u53f7\u6570\u7684\u539f\u7406\u4e0e\u516c\u5f0f<\/li>\n<li>\n<ul>\n<li>1&#xff09;\u539f\u7406<\/li>\n<li>2&#xff09;\u6570\u5b66\u76f4\u89c9<\/li>\n<li>3&#xff09;\u516c\u5f0f&#xff08;\u7b49\u5f0f2.9&#xff09;<\/li>\n<li>4&#xff09;\u63a8\u5bfc\u8fc7\u7a0b<\/li>\n<\/ul>\n<\/li>\n<li>3. \u622a\u65ad\u8865\u7801\u6570\u7684\u539f\u7406\u4e0e\u516c\u5f0f<\/li>\n<li>\n<ul>\n<li>1&#xff09;\u539f\u7406<\/li>\n<li>2&#xff09;\u516c\u5f0f&#xff08;\u7b49\u5f0f2.10&#xff09;<\/li>\n<li>3&#xff09;\u63a8\u5bfc\u8fc7\u7a0b<\/li>\n<\/ul>\n<\/li>\n<li>4.\u7ec3\u4e60\u98982.24<\/li>\n<\/ul>\n<\/li>\n<li>\u603b\u7ed3\u680f<\/li>\n<\/ul>\n<hr \/>\n<h2>\u7ebf\u7d22\u680f<\/h2>\n<li>\u622a\u65ad\u64cd\u4f5c\u7684\u5b9a\u4e49\u662f\u4ec0\u4e48&#xff1f;\u5b83\u4e3a\u4f55\u662f\u6ea2\u51fa\u7684\u4e00\u79cd\u5f62\u5f0f&#xff1f;<\/li>\n<li>\u622a\u65ad\u4e00\u4e2a w \u4f4d\u65e0\u7b26\u53f7\u6570\u200b \u5230 k \u4f4d\u200b \u7684\u6570\u5b66\u539f\u7406\u548c\u7ed3\u679c\u662f\u4ec0\u4e48&#xff1f;&#xff08;\u516c\u5f0f&#xff09;<\/li>\n<li>\u622a\u65ad\u4e00\u4e2a w\u4f4d\u8865\u7801\u6570\u200b \u5230 k \u4f4d\u200b \u7684\u6570\u5b66\u539f\u7406\u548c\u7ed3\u679c\u662f\u4ec0\u4e48&#xff1f;&#xff08;\u516c\u5f0f&#xff09;\u5b83\u4e0e\u65e0\u7b26\u53f7\u6570\u622a\u65ad\u6709\u4f55\u8054\u7cfb&#xff1f;<\/li>\n<li>\u7ec3\u4e60\u98982.24\u4e2d\u7684\u8868\u683c\u5e94\u5982\u4f55\u586b\u5199&#xff1f;\u5982\u4f55\u5e94\u7528\u76f8\u5e94\u7684\u539f\u7406&#xff08;\u516c\u5f0f&#xff09;\u6765\u89e3\u91ca&#xff1f;<\/li>\n<hr \/>\n<h2>\u7b14\u8bb0\u680f<\/h2>\n<h3>1. \u622a\u65ad\u7684\u57fa\u672c\u6982\u5ff5\u4e0e\u793a\u4f8b<\/h3>\n<p>&#xff08;1&#xff09;\u5b9a\u4e49&#xff1a;\u5f53\u7528\u4f4d\u6570\u66f4\u5c11&#xff08;k\u4f4d&#xff09;\u7684\u6570\u636e\u7c7b\u578b\u6765\u8868\u793a\u4e00\u4e2a\u4f4d\u6570\u8f83\u591a&#xff08;w\u4f4d&#xff0c; k &lt; w&#xff09;\u7684\u6570\u503c\u65f6&#xff0c;\u4f1a\u53d1\u751f\u622a\u65ad\u3002\u5177\u4f53\u64cd\u4f5c\u662f\u76f4\u63a5\u4e22\u5f03\u539f\u59cb\u6570\u636e\u7684\u9ad8 w-k\u4f4d\u3002 &#xff08;2&#xff09;\u672c\u8d28&#xff1a;\u8fd9\u662f\u4e00\u79cd\u4e0d\u6539\u53d8\u4f4d\u5bbd&#xff0c;\u800c\u5f3a\u884c\u538b\u7f29\u8868\u793a\u8303\u56f4\u7684\u6ea2\u51fa\u3002 &#xff08;3&#xff09;\u4ee3\u7801\u793a\u4f8b&#xff1a;<\/p>\n<p><span class=\"token keyword\">int<\/span> x <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">53191<\/span><span class=\"token punctuation\">;<\/span>           <span class=\"token comment\">\/\/ 32\u4f4d\u8865\u7801\u503c<\/span><br \/>\n<span class=\"token keyword\">short<\/span> sx <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">short<\/span><span class=\"token punctuation\">)<\/span>x<span class=\"token punctuation\">;<\/span>     <span class=\"token comment\">\/\/ \u622a\u65ad\u4e3a16\u4f4d&#xff0c;\u4f4d\u6a21\u5f0f\u4e3a0xCFC7<\/span><br \/>\n<span class=\"token comment\">\/\/ sx\u73b0\u5728\u88ab\u89e3\u91ca\u4e3a -12345&#xff08;\u8865\u7801&#xff09;<\/span><br \/>\n<span class=\"token keyword\">int<\/span> y <span class=\"token operator\">&#061;<\/span> sx<span class=\"token punctuation\">;<\/span>              <span class=\"token comment\">\/\/ \u901a\u8fc7\u7b26\u53f7\u6269\u5c55\u6062\u590d\u4e3a32\u4f4d&#xff0c;y &#061; -12345<\/span><\/p>\n<h3>2. \u622a\u65ad\u65e0\u7b26\u53f7\u6570\u7684\u539f\u7406\u4e0e\u516c\u5f0f<\/h3>\n<h4>1&#xff09;\u539f\u7406<\/h4>\n<p>\u622a\u65ad\u540e\u7684\u503c x\u2032\u7b49\u4e8e\u539f\u59cb\u503c x\u5bf9 2<sup>k<\/sup>\u53d6\u6a21\u3002<\/p>\n<h4>2&#xff09;\u6570\u5b66\u76f4\u89c9<\/h4>\n<p>\u6240\u6709\u88ab\u4e22\u5f03\u7684\u9ad8\u4f4d\u6743\u91cd\u90fd\u662f 2<sup>k<\/sup>\u7684\u500d\u6570&#xff08;\u5373\u5f62\u5982 2i&#xff0c;i\u2265k&#xff09;&#xff0c;\u56e0\u6b64\u5728\u6a21 2k\u8fd0\u7b97\u4e0b&#xff0c;\u5b83\u4eec\u7684\u8d21\u732e\u5747\u4e3a0\u3002<\/p>\n<h4>3&#xff09;\u516c\u5f0f&#xff08;\u7b49\u5f0f2.9&#xff09;<\/h4>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         B<\/p>\n<p>         2<\/p>\n<p>          U<\/p>\n<p>          k<\/p>\n<p>         (<\/p>\n<p>         [<\/p>\n<p>          x<\/p>\n<p>           k<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         ,<\/p>\n<p>         \u22ef<br \/>\n        \u2009<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>          0<\/p>\n<p>         ]<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         B<\/p>\n<p>         2<\/p>\n<p>          U<\/p>\n<p>          w<\/p>\n<p>         (<\/p>\n<p>         [<\/p>\n<p>          x<\/p>\n<p>           w<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         ,<\/p>\n<p>         \u22ef<br \/>\n        \u2009<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>          0<\/p>\n<p>         ]<\/p>\n<p>         )<br \/>\n        \u200a<\/p>\n<p>           m<\/p>\n<p>           o<\/p>\n<p>           d<\/p>\n<p>        \u200a<\/p>\n<p>          2<\/p>\n<p>          k<\/p>\n<p>        B2U_k([x_{k-1}, \\\\cdots, x_0]) &#061; B2U_w([x_{w-1}, \\\\cdots, x_0]) \\\\bmod 2^k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">([<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">])<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">([<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">])<\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8991em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>4&#xff09;\u63a8\u5bfc\u8fc7\u7a0b<\/h4>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         B<\/p>\n<p>         2<\/p>\n<p>          U<\/p>\n<p>          w<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          \u20d7<\/p>\n<p>         )<br \/>\n        \u200a<\/p>\n<p>           m<\/p>\n<p>           o<\/p>\n<p>           d<\/p>\n<p>        \u200a<\/p>\n<p>          2<\/p>\n<p>          k<\/p>\n<p>         B2U_w(\\\\vec{x})\\\\bmod 2^k <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.714em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2077em\"><span class=\"overlay\" style=\"height: 0.714em;width: 0.471em\"><\/p>\n<p>             <\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8991em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         &#061;<\/p>\n<p>          [<\/p>\n<p>           \u2211<\/p>\n<p>            i<\/p>\n<p>            &#061;<\/p>\n<p>            0<\/p>\n<p>            w<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>           x<\/p>\n<p>           i<\/p>\n<p>          \u22c5<\/p>\n<p>           2<\/p>\n<p>           i<\/p>\n<p>          ]<\/p>\n<p>        \u200a<\/p>\n<p>           m<\/p>\n<p>           o<\/p>\n<p>           d<\/p>\n<p>        \u200a<\/p>\n<p>          2<\/p>\n<p>          k<\/p>\n<p>         &#061;\\\\left[\\\\sum_{i&#061;0}^{w-1} x_i\\\\cdot 2^i\\\\right]\\\\bmod 2^k <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.3669em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.0788em;vertical-align: -1.2777em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">[<\/span><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8011em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8747em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8991em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         &#061;<\/p>\n<p>          [<\/p>\n<p>           \u2211<\/p>\n<p>            i<\/p>\n<p>            &#061;<\/p>\n<p>            0<\/p>\n<p>            k<\/p>\n<p>            \u2212<\/p>\n<p>            1<\/p>\n<p>           x<\/p>\n<p>           i<\/p>\n<p>          \u22c5<\/p>\n<p>           2<\/p>\n<p>           i<\/p>\n<p>          ]<\/p>\n<p>        \u200a<\/p>\n<p>           m<\/p>\n<p>           o<\/p>\n<p>           d<\/p>\n<p>        \u200a<\/p>\n<p>          2<\/p>\n<p>          k<\/p>\n<p>         (<\/p>\n<p>         \u56e0\u4e3a\u5f53\u00a0<\/p>\n<p>         i<\/p>\n<p>         \u2265<\/p>\n<p>         k<\/p>\n<p>         \u65f6&#xff0c;\u00a0<\/p>\n<p>          2<\/p>\n<p>          i<\/p>\n<p>        \u200a<\/p>\n<p>           m<\/p>\n<p>           o<\/p>\n<p>           d<\/p>\n<p>        \u200a<\/p>\n<p>          2<\/p>\n<p>          k<\/p>\n<p>         &#061;<\/p>\n<p>         0<\/p>\n<p>         )<\/p>\n<p>         &#061;\\\\left[\\\\sum_{i&#061;0}^{k-1} x_i\\\\cdot 2^i\\\\right]\\\\bmod 2^k\\\\quad(\\\\text{\u56e0\u4e3a\u5f53 }i\\\\geq k\\\\text{\u65f6&#xff0c; }2^i\\\\bmod 2^k&#061;0) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.3669em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.1138em;vertical-align: -1.2777em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">[<\/span><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8361em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8747em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1491em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u56e0\u4e3a\u5f53<\/span><span class=\"mord\">\u00a0<\/span><\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8747em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u65f6&#xff0c;<\/span><span class=\"mord\">\u00a0<\/span><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8747em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8991em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         &#061;<\/p>\n<p>          \u2211<\/p>\n<p>           i<\/p>\n<p>           &#061;<\/p>\n<p>           0<\/p>\n<p>           k<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>          x<\/p>\n<p>          i<\/p>\n<p>         \u22c5<\/p>\n<p>          2<\/p>\n<p>          i<\/p>\n<p>         &#061;\\\\sum_{i&#061;0}^{k-1} x_i\\\\cdot 2^i <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.3669em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.1138em;vertical-align: -1.2777em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8361em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8747em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8747em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         &#061;<\/p>\n<p>         B<\/p>\n<p>         2<\/p>\n<p>          U<\/p>\n<p>          k<\/p>\n<p>         (<\/p>\n<p>         [<\/p>\n<p>          x<\/p>\n<p>           k<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         ,<\/p>\n<p>         \u22ef<br \/>\n        \u2009<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>          0<\/p>\n<p>         ]<\/p>\n<p>         )<\/p>\n<p>         &#061;B2U_k([x_{k-1},\\\\cdots,x_0]) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.3669em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">([<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">])<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>3. \u622a\u65ad\u8865\u7801\u6570\u7684\u539f\u7406\u4e0e\u516c\u5f0f<\/h3>\n<h4>1&#xff09;\u539f\u7406<\/h4>\n<p>\u8865\u7801\u6570\u7684\u622a\u65ad\u662f\u4e24\u4e2a\u6b65\u9aa4\u7684\u7ec4\u5408&#xff1a; &#xff08;1&#xff09;\u4e0e\u65e0\u7b26\u53f7\u6570\u4e00\u6837\u622a\u65ad&#xff1a;\u8ba1\u7b97\u539f\u59cb\u503c&#xff08;\u65e0\u8bba\u88ab\u89e3\u91ca\u4e3a\u6709\u7b26\u53f7\u8fd8\u662f\u65e0\u7b26\u53f7&#xff09;\u5bf92<sup>k<\/sup>\u53d6\u6a21&#xff0c;\u5f97\u5230\u4e00\u4e2a\u8303\u56f4\u5728 [0,2<sup>k<\/sup>\u22121]\u5185\u7684\u4e2d\u95f4\u65e0\u7b26\u53f7\u6570\u3002\u8fd9\u4e2a\u6570\u7684\u4f4d\u6a21\u5f0f\u662f\u4fdd\u7559\u7684\u4f4e k\u4f4d\u3002 &#xff08;2&#xff09;\u91cd\u65b0\u89e3\u91ca\u4e3a\u8865\u7801&#xff1a;\u5c06\u5f97\u5230\u7684\u8fd9\u4e2a k\u4f4d\u65e0\u7b26\u53f7\u6570&#xff0c;\u901a\u8fc7\u51fd\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        U<\/p>\n<p>        2<\/p>\n<p>         T<\/p>\n<p>         k<\/p>\n<p>       U2T_k<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u91cd\u65b0\u89e3\u91ca\u4e3ak\u4f4d\u8865\u7801\u6570&#xff08;\u5373\u5224\u65ad\u5176\u6700\u9ad8\u4f4d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>          k<\/p>\n<p>          \u2212<\/p>\n<p>          1<\/p>\n<p>       x_{k\u22121}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6389em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u200b&#xff0c;\u82e5\u4e3a1&#xff0c;\u5219\u503c &#061; \u4e2d\u95f4\u503c &#8211; 2<sup>k<\/sup>&#xff09;\u3002<\/p>\n<h4>2&#xff09;\u516c\u5f0f&#xff08;\u7b49\u5f0f2.10&#xff09;<\/h4>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         B<\/p>\n<p>         2<\/p>\n<p>          T<\/p>\n<p>          k<\/p>\n<p>         (<\/p>\n<p>         [<\/p>\n<p>          x<\/p>\n<p>           k<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         ,<\/p>\n<p>         \u22ef<br \/>\n        \u2009<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>          0<\/p>\n<p>         ]<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         U<\/p>\n<p>         2<\/p>\n<p>          T<\/p>\n<p>          k<\/p>\n<p>         (<\/p>\n<p>         B<\/p>\n<p>         2<\/p>\n<p>          U<\/p>\n<p>          w<\/p>\n<p>         (<\/p>\n<p>         [<\/p>\n<p>          x<\/p>\n<p>           w<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>         ,<\/p>\n<p>         \u22ef<br \/>\n        \u2009<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>          0<\/p>\n<p>         ]<\/p>\n<p>         )<br \/>\n        \u200a<\/p>\n<p>           m<\/p>\n<p>           o<\/p>\n<p>           d<\/p>\n<p>        \u200a<\/p>\n<p>          2<\/p>\n<p>          k<\/p>\n<p>         )<\/p>\n<p>        B2T_k([x_{k-1}, \\\\cdots, x_0]) &#061; U2T_k \\\\big( B2U_w([x_{w-1}, \\\\cdots, x_0]) \\\\bmod 2^k \\\\big)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">([<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">])<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2em;vertical-align: -0.35em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">([<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">])<\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.0556em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2491em;vertical-align: -0.35em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>3&#xff09;\u63a8\u5bfc\u8fc7\u7a0b<\/h4>\n<p>\u9996\u5148\u901a\u8fc7\u63a8\u5bfc\u8bc1\u660e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        B<\/p>\n<p>        2<\/p>\n<p>         U<\/p>\n<p>         w<\/p>\n<p>        \u200b<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         \u20d7<\/p>\n<p>        )<\/p>\n<p>        m<\/p>\n<p>        o<\/p>\n<p>        d<\/p>\n<p>         2<\/p>\n<p>         k<\/p>\n<p>        &#061;<\/p>\n<p>        B<\/p>\n<p>        2<\/p>\n<p>         U<\/p>\n<p>         k<\/p>\n<p>        \u200b<\/p>\n<p>        (<\/p>\n<p>        [<\/p>\n<p>         x<\/p>\n<p>          k<\/p>\n<p>          \u2212<\/p>\n<p>          1<\/p>\n<p>        \u200b<\/p>\n<p>        ,<\/p>\n<p>        \u22ef<\/p>\n<p>        ,<\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>        \u200b<\/p>\n<p>        ]<\/p>\n<p>        )<\/p>\n<p>       B2U_w \u200b(\\\\vec{x})mod2^k&#061;B2U_k \u200b([x_{k\u22121} \u200b,\u22ef,x_0 \u200b])<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0991em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u200b<\/span><span class=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.714em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2077em\"><span class=\"overlay\" style=\"height: 0.714em;width: 0.471em\"><\/p>\n<p>            <\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u200b<\/span><span class=\"mopen\">([<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u200b<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u200b<\/span><span class=\"mclose\">])<\/span><\/span><\/span><\/span><\/span>\u3002\u7136\u540e&#xff0c;\u7531\u4e8e\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u8865\u7801\u89e3\u91ca\u7684\u7ed3\u679c&#xff0c;\u53ea\u9700\u8981\u5c06\u8fd9\u4e2a\u65e0\u7b26\u53f7\u7ed3\u679c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        U<\/p>\n<p>        2<\/p>\n<p>         T<\/p>\n<p>         k<\/p>\n<p>       U2T_k<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u200b\u5373\u53ef&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>        \u2032<\/p>\n<p>        &#061;<\/p>\n<p>        U<\/p>\n<p>        2<\/p>\n<p>         T<\/p>\n<p>         k<\/p>\n<p>        \u200b<\/p>\n<p>        (<\/p>\n<p>        x<\/p>\n<p>        m<\/p>\n<p>        o<\/p>\n<p>        d<\/p>\n<p>         2<\/p>\n<p>         k<\/p>\n<p>        )<\/p>\n<p>       x\u2032&#061;U2T_k \u200b(xmod2^k)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5556em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">\u2032<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0991em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u200b<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<h3>4.\u7ec3\u4e60\u98982.24<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222231120-699b8d183e0cc.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<li>\u65e0\u7b26\u53f7\u5217&#xff1a;\u76f4\u63a5\u5e94\u7528\u516c\u5f0f(2.9)\u3002\u4f8b\u5982 9 mod 8 &#061; 1\u3002<\/li>\n<li>\u8865\u7801\u5217&#xff1a;\u5e94\u7528\u516c\u5f0f(2.10)&#xff0c;\u5206\u4e24\u6b65\u3002 &#xff08;1&#xff09;\u5c06\u539f\u59cb\u503c\u89c6\u4e3a\u65e0\u7b26\u53f7\u6570&#xff08;\u6216\u76f4\u63a5\u53d6\u5176\u4f4d\u5411\u91cf&#xff09;&#xff0c;\u8ba1\u7b97 \u539f\u59cb\u503cmod8\u3002\u4f8b\u5982&#xff0c;0xB&#xff08;\u65e0\u8bba\u89e3\u91ca\u4e3a11\u8fd8\u662f-5&#xff09;\u7684\u4f4d\u6a21\u5f0f1011&#xff0c;1011\u8868\u793a\u7684\u65e0\u7b26\u53f7\u6570\u662f11&#xff0c;11 mod 8 &#061; 3\u3002 &#xff08;2&#xff09;\u5c06\u7ed3\u679c(3)\u89e3\u91ca\u4e3a3\u4f4d\u8865\u7801\u30023\u76843\u4f4d\u4e8c\u8fdb\u5236\u4e3a011&#xff0c;\u6700\u9ad8\u4f4d\u4e3a0&#xff0c;\u6240\u4ee5\u503c\u4e3a\u6b633\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260222231120-699b8d18a74c8.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/li>\n<h2>\u603b\u7ed3\u680f<\/h2>\n<p>\u672c\u8282\u6838\u5fc3\u662f\u7406\u89e3\u6574\u6570\u622a\u65ad\u7684\u539f\u7406\u4e0e\u6570\u5b66\u672c\u8d28\u3002<\/p>\n<li>\u64cd\u4f5c\u5b9a\u4e49&#xff1a;\u4e22\u5f03\u9ad8\u4f4d&#xff0c;\u5f3a\u5236\u51cf\u5c11\u8868\u793a\u4f4d\u5bbd\u3002\u8fd9\u662f\u4e00\u79cd\u6ea2\u51fa\u3002<\/li>\n<li>\u65e0\u7b26\u53f7\u6570\u622a\u65ad&#xff1a;\u7ed3\u679c\u662f\u539f\u59cb\u503c\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          2<\/p>\n<p>          k<\/p>\n<p>        2^k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53d6\u6a21&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         m<\/p>\n<p>         o<\/p>\n<p>         d<\/p>\n<p>        mod<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u6570\u5b66\u4e0a\u7b49\u4ef7\u4e8e\u53ea\u4fdd\u7559\u4f4ek\u4f4d\u3002 \u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         \u2032<\/p>\n<p>         &#061;<\/p>\n<p>         x<\/p>\n<p>         m<\/p>\n<p>         o<\/p>\n<p>         d<\/p>\n<p>          2<\/p>\n<p>          k<\/p>\n<p>        x\u2032&#061;xmod2^k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5556em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">\u2032<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u8865\u7801\u6570\u622a\u65ad&#xff1a;\u8fc7\u7a0b\u5206\u4e3a\u4e24\u6b65\u3002\u9996\u5148&#xff0c;\u50cf\u65e0\u7b26\u53f7\u6570\u4e00\u6837\u53d6\u6a21&#xff0c;\u5f97\u5230\u4e00\u4e2a\u4e2d\u95f4\u65e0\u7b26\u53f7\u503c\u3002\u7136\u540e&#xff0c;\u5173\u952e\u7684\u4e00\u6b65\u662f\u5c06\u8fd9\u4e2a\u4e2d\u95f4\u503c\u91cd\u65b0\u89e3\u91ca&#xff08;\u5e94\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         U<\/p>\n<p>         2<\/p>\n<p>          T<\/p>\n<p>          k<\/p>\n<p>        U2T_k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b\u51fd\u6570&#xff09;\u4e3a\u8865\u7801\u6570\u3002\u8fd9\u53ef\u80fd\u5bfc\u81f4\u6709\u7b26\u53f7\u89e3\u91ca\u4e0b\u7684\u503c\u53d1\u751f\u201c\u7b26\u53f7\u6539\u53d8\u201d&#xff08;\u5982\u4e00\u4e2a\u8d1f\u6570\u622a\u65ad\u540e\u53ef\u80fd\u53d8\u6210\u6b63\u6570&#xff0c;\u5982\u8865\u7801-5(0xB)\u622a\u65ad\u540e\u53d8\u4e3a3&#xff09;\u3002 \u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         \u2032<\/p>\n<p>         &#061;<\/p>\n<p>         U<\/p>\n<p>         2<\/p>\n<p>          T<\/p>\n<p>          k<\/p>\n<p>         \u200b<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         m<\/p>\n<p>         o<\/p>\n<p>         d<\/p>\n<p>          2<\/p>\n<p>          k<\/p>\n<p>         )<\/p>\n<p>        x\u2032&#061;U2T_k \u200b(xmod2^k)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5556em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">\u2032<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0991em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u200b<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u6838\u5fc3\u8054\u7cfb&#xff1a;\u622a\u65ad\u64cd\u4f5c\u76f4\u63a5\u4f5c\u7528\u4e8e\u4f4d\u6a21\u5f0f\u672c\u8eab\u3002\u5bf9\u4e8e\u65e0\u7b26\u53f7\u6570&#xff0c;\u622a\u65ad\u540e\u7684\u4f4d\u6a21\u5f0f\u76f4\u63a5\u6309\u65e0\u89e3\u91ca\u89e3\u8bfb\u3002\u5bf9\u4e8e\u8865\u7801\u6570&#xff0c;\u540c\u4e00\u5957\u622a\u65ad\u540e\u7684\u4f4d\u6a21\u5f0f&#xff0c;\u9700\u8981\u6309\u8865\u7801\u89c4\u5219\u91cd\u65b0\u89e3\u8bfb\u3002<\/li>\n<li>\u5173\u952e\u542f\u793a&#xff1a;\u622a\u65ad\u4f1a\u4e22\u5931\u4fe1\u606f&#xff0c;\u5e76\u53ef\u80fd\u5b8c\u5168\u6539\u53d8\u4e00\u4e2a\u6570\u7684\u8bed\u4e49&#xff08;\u5c24\u5176\u5bf9\u4e8e\u8865\u7801\u6570&#xff09;\u3002\u5728\u6d89\u53ca\u5f3a\u5236\u7c7b\u578b\u8f6c\u6362&#xff08;\u5927\u8f6c\u5c0f&#xff09;\u7684\u7f16\u7a0b\u4e2d&#xff0c;\u5fc5\u987b\u6e05\u695a\u5176\u622a\u65ad\u6548\u5e94&#xff0c;\u5c24\u5176\u662f\u7b26\u53f7\u4f4d\u88ab\u4e22\u5f03\u540e\u53ef\u80fd\u5f15\u53d1\u7684\u903b\u8f91\u9519\u8bef\u3002<\/li>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u76ee\u5f55\u7ebf\u7d22\u680f\u7b14\u8bb0\u680f1. 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