{"id":60166,"date":"2026-01-15T02:32:58","date_gmt":"2026-01-14T18:32:58","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/60166.html"},"modified":"2026-01-15T02:32:58","modified_gmt":"2026-01-14T18:32:58","slug":"%e6%8f%ad%e7%a7%98c%e7%9a%84%e6%a0%91%e7%8a%b6%e6%95%b0%e7%bb%84%e6%b7%b1%e5%ba%a6%e8%a7%a3%e6%9e%90%ef%bc%9a%e4%bb%8e%e5%8e%9f%e7%90%86%e5%88%b0%e9%ab%98%e6%95%88%e5%b0%81%e8%a3%85%e5%ae%9e","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/60166.html","title":{"rendered":"\u63ed\u79d8C++\u7684\u6811\u72b6\u6570\u7ec4\u6df1\u5ea6\u89e3\u6790\uff1a\u4ece\u539f\u7406\u5230\u9ad8\u6548\u5c01\u88c5\u5b9e\u8df5"},"content":{"rendered":"<p>\u6811\u72b6\u6570\u7ec4&#xff08;Binary Indexed Tree&#xff0c;BIT&#xff09;\u4f5c\u4e3a\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u5904\u7406\u52a8\u6001\u524d\u7f00\u548c\u95ee\u9898\u7684\u7ecf\u5178\u6570\u636e\u7ed3\u6784&#xff0c;\u51ed\u501f\u5176O(log n)\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u5355\u70b9\u66f4\u65b0\u4e0e\u533a\u95f4\u67e5\u8be2\u80fd\u529b&#xff0c;\u5728\u7b97\u6cd5\u7ade\u8d5b\u3001\u91d1\u878d\u6570\u636e\u5206\u6790\u53ca\u5927\u89c4\u6a21\u6570\u636e\u5904\u7406\u7b49\u9886\u57df\u5c55\u73b0\u51fa\u72ec\u7279\u4f18\u52bf\u3002\u672c\u6587\u901a\u8fc7\u4e8c\u8fdb\u5236\u4f4d\u8fd0\u7b97\u539f\u7406\u5256\u6790\u3001\u6a21\u677f\u7c7b\u5c01\u88c5\u5b9e\u73b0\u53ca\u591a\u573a\u666f\u5e94\u7528\u6848\u4f8b&#xff0c;\u7cfb\u7edf\u9610\u8ff0\u6811\u72b6\u6570\u7ec4\u7684\u6838\u5fc3\u673a\u5236\u4e0e\u5de5\u7a0b\u5b9e\u8df5\u65b9\u6cd5\u3002<\/p>\n<h3>\u4e00\u3001\u6811\u72b6\u6570\u7ec4\u7684\u4e8c\u8fdb\u5236\u4f4d\u8fd0\u7b97\u5185\u6838<\/h3>\n<h4>1.1 \u4f4e\u4f4d\u63a9\u7801&#xff08;lowbit&#xff09;\u7684\u6570\u5b66\u672c\u8d28<\/h4>\n<p>\u6811\u72b6\u6570\u7ec4\u7684\u6838\u5fc3\u64cd\u4f5c\u57fa\u4e8e\u00a0lowbit(x)&#061;x&amp;(-x)www.gov.cn.dongguan.manct.cn\u8fd0\u7b97&#xff0c;\u8be5\u64cd\u4f5c\u901a\u8fc7\u8865\u7801\u7279\u6027\u63d0\u53d6\u6574\u6570x\u7684\u4e8c\u8fdb\u5236\u6700\u4f4e\u6709\u6548\u4f4d\u3002\u4f8b\u5982&#xff1a;<\/p>\n<ul>\n<li>lowbit(6)&#061;2&#xff08;\u4e8c\u8fdb\u5236110\u2192010&#xff09;<\/li>\n<li>lowbit(12)&#061;4&#xff08;\u4e8c\u8fdb\u52361100\u21920100&#xff09;<\/li>\n<\/ul>\n<p>\u8fd9\u79cd\u4f4d\u8fd0\u7b97\u5c06\u6570\u7ec4\u7d22\u5f15\u5206\u89e3\u4e3a\u5c42\u7ea7\u7ed3\u6784&#xff0c;\u4f7f\u5f97\u6bcf\u4e2a\u8282\u70b9\u00a0C[i]\u8d1f\u8d23\u5b58\u50a8\u00a0A[i-lowbit(i)&#043;1&#8230;i]\u7684\u533a\u95f4\u548c\u3002\u4f8b\u5982&#xff0c;\u5f53i&#061;6\u65f6&#xff1a;<\/p>\n<p>cpp1int\u00a0lowbit(int\u00a0x)\u00a0{\u00a0return\u00a0x\u00a0&amp;\u00a0(-x);\u00a0}\u00a0\u00a0\/\/\u00a0\u63d0\u53d6\u6700\u4f4e\u4f4d1 <\/p>\n<h4>1.2 \u5206\u5c42\u5b58\u50a8\u7684\u6811\u5f62\u7ed3\u6784<\/h4>\n<p>\u6811\u72b6\u6570\u7ec4\u901a\u8fc7\u52a8\u6001\u8c03\u6574\u8282\u70b9\u8986\u76d6\u8303\u56f4\u5b9e\u73b0\u9ad8\u6548\u66f4\u65b0\u3002\u4ee5\u957f\u5ea6\u4e3a8\u7684\u6570\u7ec4\u4e3a\u4f8b&#xff1a;<\/p>\n<ul>\n<li>C[1]&#061;A[1]&#xff08;lowbit&#061;1&#xff09;<\/li>\n<li>C[2]&#061;A[1]&#043;A[2]&#xff08;lowbit&#061;2&#xff09;<\/li>\n<li>C[4]&#061;A[1]&#043;A[2]&#043;A[3]&#043;A[4]&#xff08;lowbit&#061;4&#xff09;<\/li>\n<li>C[8]&#061;A[1]&#043;&#8230;&#043;A[8]&#xff08;lowbit&#061;8&#xff09;<\/li>\n<\/ul>\n<p>\u8fd9\u79cd\u5206\u5c42\u5b58\u50a8\u4f7f\u5f97\u5355\u70b9\u66f4\u65b0\u65f6\u53ea\u9700\u4fee\u6539\u00a0log n\u00a0www.gov.cn.xiamen.manct.cn\u4e2a\u8282\u70b9&#xff0c;\u67e5\u8be2\u524d\u7f00\u548c\u65f6\u4e5f\u4ec5\u9700\u8bbf\u95ee\u00a0log n\u4e2a\u8282\u70b9\u3002<\/p>\n<h3>\u4e8c\u3001\u6811\u72b6\u6570\u7ec4\u7684\u6a21\u677f\u7c7b\u5c01\u88c5\u5b9e\u73b0<\/h3>\n<h4>2.1 \u57fa\u7840\u6a21\u677f\u7c7b\u8bbe\u8ba1<\/h4>\n<p>cpp1template&lt;typename\u00a0T\u00a0&#061;\u00a0int&gt;2class\u00a0FenwickTree\u00a0{3private:4\u00a0\u00a0\u00a0\u00a0std::vector&lt;T&gt;\u00a0data;5\u00a0\u00a0\u00a0\u00a0int\u00a0size;6\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a0int\u00a0lowbit(int\u00a0x)\u00a0{\u00a0return\u00a0x\u00a0&amp;\u00a0(-x);\u00a0}8\u00a0\u00a0\u00a0\u00a09public:10\u00a0\u00a0\u00a0\u00a0FenwickTree(int\u00a0n)\u00a0:\u00a0size(n),\u00a0data(n\u00a0&#043;\u00a01,\u00a00)\u00a0{}11\u00a0\u00a0\u00a0\u00a012\u00a0\u00a0\u00a0\u00a0\/\/\u00a0\u5355\u70b9\u66f4\u65b0&#xff1a;\u5728\u4f4d\u7f6ei\u589e\u52a0val13\u00a0\u00a0\u00a0\u00a0void\u00a0update(int\u00a0i,\u00a0T\u00a0val)\u00a0{14\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0while\u00a0(i\u00a0&lt;&#061;\u00a0size)\u00a0{15\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0data[i]\u00a0&#043;&#061;\u00a0val;16\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0i\u00a0&#043;&#061;\u00a0lowbit(i);17\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}18\u00a0\u00a0\u00a0\u00a0}19\u00a0\u00a0\u00a0\u00a020\u00a0\u00a0\u00a0\u00a0\/\/\u00a0\u524d\u7f00\u548c\u67e5\u8be2&#xff1a;[1&#8230;i]\u7684\u548c21\u00a0\u00a0\u00a0\u00a0T\u00a0query(int\u00a0i)\u00a0{22\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0T\u00a0sum\u00a0&#061;\u00a00;23\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0while\u00a0(i\u00a0&gt;\u00a00)\u00a0{24\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0sum\u00a0&#043;&#061;\u00a0data[i];25\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0i\u00a0-&#061;\u00a0lowbit(i);26\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}27\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return\u00a0sum;28\u00a0\u00a0\u00a0\u00a0}29\u00a0\u00a0\u00a0\u00a030\u00a0\u00a0\u00a0\u00a0\/\/\u00a0\u533a\u95f4\u67e5\u8be2&#xff1a;[l&#8230;r]\u7684\u548c31\u00a0\u00a0\u00a0\u00a0T\u00a0rangeQuery(int\u00a0l,\u00a0int\u00a0r)\u00a0{32\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return\u00a0query(r)\u00a0&#8211;\u00a0query(l\u00a0&#8211;\u00a01);33\u00a0\u00a0\u00a0\u00a0}34}; <\/p>\n<h4>2.2 \u6269\u5c55\u529f\u80fd&#xff1a;\u533a\u95f4\u4fee\u6539\u4e0e\u5355\u70b9\u67e5\u8be2<\/h4>\n<p>\u901a\u8fc7\u5dee\u5206\u6570\u7ec4\u6280\u672f\u5b9e\u73b0\u533a\u95f4\u6279\u91cf\u66f4\u65b0&#xff1a;<\/p>\n<p>cpp1template&lt;typename\u00a0T\u00a0&#061;\u00a0int&gt;2class\u00a0RangeFenwickTree\u00a0{3private:4\u00a0\u00a0\u00a0\u00a0FenwickTree&lt;T&gt;\u00a0tree1,\u00a0tree2;5\u00a0\u00a0\u00a0\u00a06public:7\u00a0\u00a0\u00a0\u00a0RangeFenwickTree(int\u00a0n)\u00a0:\u00a0tree1(n),\u00a0tree2(n)\u00a0{}8\u00a0\u00a0\u00a0\u00a09\u00a0\u00a0\u00a0\u00a0\/\/\u00a0\u533a\u95f4[l,r]\u589e\u52a0val10\u00a0\u00a0\u00a0\u00a0void\u00a0rangeUpdate(int\u00a0l,\u00a0int\u00a0r,\u00a0T\u00a0val)\u00a0{11\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0tree1.update(l,\u00a0val);12\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0tree1.update(r\u00a0&#043;\u00a01,\u00a0-val);13\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0tree2.update(l,\u00a0val\u00a0*\u00a0(l\u00a0&#8211;\u00a01));14\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0tree2.update(r\u00a0&#043;\u00a01,\u00a0-val\u00a0*\u00a0r);15\u00a0\u00a0\u00a0\u00a0}16\u00a0\u00a0\u00a0\u00a017\u00a0\u00a0\u00a0\u00a0\/\/\u00a0\u5355\u70b9\u67e5\u8be2&#xff1a;\u4f4d\u7f6ei\u7684\u503c18\u00a0\u00a0\u00a0\u00a0T\u00a0pointQuery(int\u00a0i)\u00a0{19\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return\u00a0tree1.query(i)\u00a0*\u00a0i\u00a0&#8211;\u00a0tree2.query(i);20\u00a0\u00a0\u00a0\u00a0}21}; <\/p>\n<h3>\u4e09\u3001\u5178\u578b\u5e94\u7528\u573a\u666f\u4e0e\u6027\u80fd\u4f18\u5316<\/h3>\n<h4>3.1 \u52a8\u6001\u9006\u5e8f\u5bf9\u7edf\u8ba1<\/h4>\n<p>\u5728\u7b97\u6cd5\u7ade\u8d5b\u4e2d&#xff0c;\u6811\u72b6\u6570\u7ec4\u53ef\u9ad8\u6548\u7edf\u8ba1\u6570\u7ec4\u9006\u5e8f\u5bf9\u6570\u91cf&#xff1a;<\/p>\n<p>cpp1int\u00a0countInversions(std::vector&lt;int&gt;&amp;\u00a0nums)\u00a0{2\u00a0\u00a0\u00a0\u00a0int\u00a0n\u00a0&#061;\u00a0nums.size();3\u00a0\u00a0\u00a0\u00a0FenwickTree&lt;int&gt;\u00a0tree(n);4\u00a0\u00a0\u00a0\u00a0std::vector&lt;int&gt;\u00a0sorted\u00a0&#061;\u00a0nums;5\u00a0\u00a0\u00a0\u00a0std::sort(sorted.begin(),\u00a0sorted.end());6\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a0\/\/\u00a0\u79bb\u6563\u5316\u5904\u74068\u00a0\u00a0\u00a0\u00a0std::unordered_map&lt;int,\u00a0int&gt;\u00a0rank;9\u00a0\u00a0\u00a0\u00a0for\u00a0(int\u00a0i\u00a0&#061;\u00a00;\u00a0i\u00a0&lt;\u00a0n;\u00a0&#043;&#043;i)\u00a0{10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0rank[sorted[i]]\u00a0&#061;\u00a0i\u00a0&#043;\u00a01;\u00a0\u00a0\/\/\u00a0\u6620\u5c04\u52301-based11\u00a0\u00a0\u00a0\u00a0}12\u00a0\u00a0\u00a0\u00a013\u00a0\u00a0\u00a0\u00a0int\u00a0res\u00a0&#061;\u00a00;14\u00a0\u00a0\u00a0\u00a0for\u00a0(int\u00a0i\u00a0&#061;\u00a0n\u00a0&#8211;\u00a01;\u00a0i\u00a0&gt;&#061;\u00a00;\u00a0&#8211;i)\u00a0{15\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0res\u00a0&#043;&#061;\u00a0tree.query(rank[nums[i]]\u00a0&#8211;\u00a01);16\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0tree.update(rank[nums[i]],\u00a01);17\u00a0\u00a0\u00a0\u00a0}18\u00a0\u00a0\u00a0\u00a0return\u00a0res;19} <\/p>\n<p>\u8be5\u7b97\u6cd5\u901a\u8fc7\u79bb\u6563\u5316\u5c06\u6570\u503c\u8303\u56f4\u538b\u7f29&#xff0c;\u5229\u7528\u6811\u72b6\u6570\u7ec4\u7edf\u8ba1\u5df2\u5904\u7406\u5143\u7d20\u4e2d\u5c0f\u4e8e\u5f53\u524d\u5143\u7d20\u7684\u6570\u91cf&#xff0c;\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n log n)\u3002<\/p>\n<h4>3.2 \u4e8c\u7ef4\u6811\u72b6\u6570\u7ec4\u5b9e\u73b0<\/h4>\n<p>\u5bf9\u4e8e\u77e9\u9635\u524d\u7f00\u548c\u95ee\u9898&#xff0c;\u53ef\u8bbe\u8ba1\u4e8c\u7ef4\u6811\u72b6\u6570\u7ec4&#xff1a;<\/p>\n<p>cpp1template&lt;typename\u00a0T\u00a0&#061;\u00a0int&gt;2class\u00a0FenwickTree2D\u00a0{3private:4\u00a0\u00a0\u00a0\u00a0std::vector&lt;std::vector&lt;T&gt;&gt;\u00a0data;5\u00a0\u00a0\u00a0\u00a0int\u00a0rows,\u00a0cols;6\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a0int\u00a0lowbit(int\u00a0x)\u00a0{\u00a0return\u00a0x\u00a0&amp;\u00a0(-x);\u00a0}8\u00a0\u00a0\u00a0\u00a09public:10\u00a0\u00a0\u00a0\u00a0FenwickTree2D(int\u00a0r,\u00a0int\u00a0c)\u00a0:\u00a0rows(r),\u00a0cols(c),\u00a0data(r\u00a0&#043;\u00a01,\u00a0std::vector&lt;T&gt;(c\u00a0&#043;\u00a01,\u00a00))\u00a0{}11\u00a0\u00a0\u00a0\u00a012\u00a0\u00a0\u00a0\u00a0void\u00a0update(int\u00a0x,\u00a0int\u00a0y,\u00a0T\u00a0val)\u00a0{13\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0for\u00a0(int\u00a0i\u00a0&#061;\u00a0x;\u00a0i\u00a0&lt;&#061;\u00a0rows;\u00a0i\u00a0&#043;&#061;\u00a0lowbit(i))\u00a0{14\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0for\u00a0(int\u00a0j\u00a0&#061;\u00a0y;\u00a0j\u00a0&lt;&#061;\u00a0cols;\u00a0j\u00a0&#043;&#061;\u00a0lowbit(j))\u00a0{15\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0data[i][j]\u00a0&#043;&#061;\u00a0val;16\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}17\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}18\u00a0\u00a0\u00a0\u00a0}19\u00a0\u00a0\u00a0\u00a020\u00a0\u00a0\u00a0\u00a0T\u00a0query(int\u00a0x,\u00a0int\u00a0y)\u00a0{21\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0T\u00a0sum\u00a0&#061;\u00a00;22\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0for\u00a0(int\u00a0i\u00a0&#061;\u00a0x;\u00a0i\u00a0&gt;\u00a00;\u00a0i\u00a0-&#061;\u00a0lowbit(i))\u00a0{23\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0for\u00a0(int\u00a0j\u00a0&#061;\u00a0y;\u00a0j\u00a0&gt;\u00a00;\u00a0j\u00a0-&#061;\u00a0lowbit(j))\u00a0{24\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0sum\u00a0&#043;&#061;\u00a0data[i][j];25\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}26\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}27\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return\u00a0sum;28\u00a0\u00a0\u00a0\u00a0}29\u00a0\u00a0\u00a0\u00a030\u00a0\u00a0\u00a0\u00a0T\u00a0rangeQuery(int\u00a0x1,\u00a0int\u00a0y1,\u00a0int\u00a0x2,\u00a0int\u00a0y2)\u00a0{31\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return\u00a0query(x2,\u00a0y2)\u00a0&#8211;\u00a0query(x1\u00a0&#8211;\u00a01,\u00a0y2)\u00a0&#8211;\u00a0query(x2,\u00a0y1\u00a0&#8211;\u00a01)\u00a0&#043;\u00a0query(x1\u00a0&#8211;\u00a01,\u00a0y1\u00a0&#8211;\u00a01);32\u00a0\u00a0\u00a0\u00a0}33}; <\/p>\n<h3>\u56db\u3001\u6027\u80fd\u5bf9\u6bd4\u4e0e\u5de5\u7a0b\u4f18\u5316<\/h3>\n<h4>4.1 \u4e0e\u7ebf\u6bb5\u6811\u7684\u5bf9\u6bd4\u5206\u6790<\/h4>\n<table style=\"width:NaN\">\n<tr>\u7279\u6027\u6811\u72b6\u6570\u7ec4\u7ebf\u6bb5\u6811<\/tr>\n<tbody>\n<tr>\n<td>\u7a7a\u95f4\u590d\u6742\u5ea6<\/td>\n<td>O(n)<\/td>\n<td>O(4n)<\/td>\n<\/tr>\n<tr>\n<td>\u66f4\u65b0\u65f6\u95f4<\/td>\n<td>O(log n)<\/td>\n<td>O(log n)<\/td>\n<\/tr>\n<tr>\n<td>\u67e5\u8be2\u65f6\u95f4<\/td>\n<td>O(log n)<\/td>\n<td>O(log n)<\/td>\n<\/tr>\n<tr>\n<td>\u5b9e\u73b0\u590d\u6742\u5ea6<\/td>\n<td>100-200\u884c\u4ee3\u7801<\/td>\n<td>300-500\u884c\u4ee3\u7801<\/td>\n<\/tr>\n<tr>\n<td>\u9002\u7528\u573a\u666f<\/td>\n<td>\u524d\u7f00\u548c\u3001\u9006\u5e8f\u5bf9\u7b49\u7b80\u5355\u64cd\u4f5c<\/td>\n<td>\u590d\u6742\u533a\u95f4\u4fee\u6539\u3001\u7ebf\u6bb5\u6811\u5408\u5e76\u7b49<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>4.2 \u5185\u5b58\u4f18\u5316\u6280\u5de7<\/h4>\n<p>\u5bf9\u4e8e\u8d85\u5927\u8303\u56f4\u6570\u636e&#xff08;\u59821e9\u7ea7\u522b&#xff09;&#xff0c;\u53ef\u91c7\u7528\u52a8\u6001\u5f00\u70b9\u6280\u672f&#xff1a;<\/p>\n<p>cpp1template&lt;typename\u00a0T\u00a0&#061;\u00a0int&gt;2class\u00a0SparseFenwickTree\u00a0{3private:4\u00a0\u00a0\u00a0\u00a0std::unordered_map&lt;int,\u00a0T&gt;\u00a0data;5\u00a0\u00a0\u00a0\u00a0int\u00a0min_val,\u00a0max_val;6\u00a0\u00a0\u00a0\u00a07\u00a0\u00a0\u00a0\u00a0int\u00a0lowbit(int\u00a0x)\u00a0{\u00a0return\u00a0x\u00a0&amp;\u00a0(-x);\u00a0}8\u00a0\u00a0\u00a0\u00a09public:10\u00a0\u00a0\u00a0\u00a0SparseFenwickTree(int\u00a0min_v,\u00a0int\u00a0max_v)\u00a0:\u00a0min_val(min_v),\u00a0max_val(max_v)\u00a0{}11\u00a0\u00a0\u00a0\u00a012\u00a0\u00a0\u00a0\u00a0void\u00a0update(int\u00a0x,\u00a0T\u00a0val)\u00a0{13\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if\u00a0(x\u00a0&lt;\u00a0min_val\u00a0||\u00a0x\u00a0&gt;\u00a0max_val)\u00a0return;14\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0x\u00a0-&#061;\u00a0min_val\u00a0&#8211;\u00a01;\u00a0\u00a0\/\/\u00a0\u6620\u5c04\u52301-based15\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0while\u00a0(x\u00a0&lt;&#061;\u00a0max_val\u00a0&#8211;\u00a0min_val\u00a0&#043;\u00a01)\u00a0{16\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0data[x]\u00a0&#043;&#061;\u00a0val;17\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0x\u00a0&#043;&#061;\u00a0lowbit(x);18\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}19\u00a0\u00a0\u00a0\u00a0}20\u00a0\u00a0\u00a0\u00a021\u00a0\u00a0\u00a0\u00a0T\u00a0query(int\u00a0x)\u00a0{22\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if\u00a0(x\u00a0&lt;\u00a0min_val)\u00a0return\u00a00;23\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0x\u00a0&#061;\u00a0std::min(x,\u00a0max_val);24\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0x\u00a0-&#061;\u00a0min_val\u00a0&#8211;\u00a01;25\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0T\u00a0sum\u00a0&#061;\u00a00;26\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0while\u00a0(x\u00a0&gt;\u00a00)\u00a0{27\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0sum\u00a0&#043;&#061;\u00a0data[x];28\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0x\u00a0-&#061;\u00a0lowbit(x);29\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}30\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0return\u00a0sum;31\u00a0\u00a0\u00a0\u00a0}32}; <\/p>\n<p>https:\/\/avg.163.com\/topic\/detail\/8790318 https:\/\/avg.163.com\/topic\/detail\/8790314 https:\/\/avg.163.com\/topic\/detail\/8790312 https:\/\/avg.163.com\/topic\/detail\/8790307 https:\/\/avg.163.com\/topic\/detail\/8790303 https:\/\/avg.163.com\/topic\/detail\/8790299 https:\/\/avg.163.com\/topic\/detail\/8790298 https:\/\/avg.163.com\/topic\/detail\/8790294 https:\/\/avg.163.com\/topic\/detail\/8790289 https:\/\/avg.163.com\/topic\/detail\/8790284 https:\/\/avg.163.com\/topic\/detail\/8790281 https:\/\/avg.163.com\/topic\/detail\/8790272 https:\/\/avg.163.com\/topic\/detail\/8790230 https:\/\/avg.163.com\/topic\/detail\/8790208 https:\/\/avg.163.com\/topic\/detail\/8790187 https:\/\/avg.163.com\/topic\/detail\/8790100 https:\/\/avg.163.com\/topic\/detail\/8790047 https:\/\/avg.163.com\/topic\/detail\/8789896 https:\/\/avg.163.com\/topic\/detail\/8789694 https:\/\/avg.163.com\/topic\/detail\/8789334 https:\/\/avg.163.com\/topic\/detail\/8789286 https:\/\/avg.163.com\/topic\/detail\/8789153 https:\/\/avg.163.com\/topic\/detail\/8788949 https:\/\/avg.163.com\/topic\/detail\/8788730 https:\/\/avg.163.com\/topic\/detail\/8787796 https:\/\/avg.163.com\/topic\/detail\/8787668 https:\/\/avg.163.com\/topic\/detail\/8787574 https:\/\/avg.163.com\/topic\/detail\/8787525 https:\/\/avg.163.com\/topic\/detail\/8787477 https:\/\/avg.163.com\/topic\/detail\/8787421 https:\/\/avg.163.com\/topic\/detail\/8787383 https:\/\/avg.163.com\/topic\/detail\/8787311 https:\/\/avg.163.com\/topic\/detail\/8787128 https:\/\/avg.163.com\/topic\/detail\/8787009 https:\/\/avg.163.com\/topic\/detail\/8786983 https:\/\/avg.163.com\/topic\/detail\/8786971 https:\/\/avg.163.com\/topic\/detail\/8786921 https:\/\/avg.163.com\/topic\/detail\/8786901 https:\/\/avg.163.com\/topic\/detail\/8786888 https:\/\/avg.163.com\/topic\/detail\/8786869 https:\/\/avg.163.com\/topic\/detail\/8786863 https:\/\/avg.163.com\/topic\/detail\/8786851 https:\/\/avg.163.com\/topic\/detail\/8786838 https:\/\/avg.163.com\/topic\/detail\/8786827 https:\/\/avg.163.com\/topic\/detail\/8786705 https:\/\/avg.163.com\/topic\/detail\/8786639 https:\/\/avg.163.com\/topic\/detail\/8786624 https:\/\/avg.163.com\/topic\/detail\/8786617 https:\/\/avg.163.com\/topic\/detail\/8786602 https:\/\/avg.163.com\/topic\/detail\/8786591 https:\/\/avg.163.com\/topic\/detail\/8786527 https:\/\/avg.163.com\/topic\/detail\/8786483 https:\/\/avg.163.com\/topic\/detail\/8786474 https:\/\/avg.163.com\/topic\/detail\/8786466 \u00a0<\/p>\n<h3>\u4e94\u3001\u7ed3\u8bed<\/h3>\n<p>\u6811\u72b6\u6570\u7ec4\u901a\u8fc7\u7cbe\u5999\u7684\u4e8c\u8fdb\u5236\u4f4d\u8fd0\u7b97\u8bbe\u8ba1&#xff0c;\u5728\u52a8\u6001\u6570\u636e\u7ef4\u62a4\u9886\u57df\u5c55\u73b0\u51fa\u5353\u8d8a\u7684\u6548\u7387\u4f18\u52bf\u3002\u4ece\u57fa\u7840\u7684\u5355\u70b9\u66f4\u65b0\u5230\u590d\u6742\u7684\u4e8c\u7ef4\u533a\u95f4\u67e5\u8be2&#xff0c;\u4ece\u9759\u6001\u6570\u636e\u7edf\u8ba1\u5230\u52a8\u6001\u6d41\u5904\u7406&#xff0c;\u5176\u6a21\u5757\u5316\u5c01\u88c5\u4e0e\u6269\u5c55\u80fd\u529b\u4e3a\u7b97\u6cd5\u5de5\u7a0b\u5e08\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u5de5\u5177\u3002\u5728\u5b9e\u9645\u5de5\u7a0b\u4e2d&#xff0c;\u7ed3\u5408\u5177\u4f53\u573a\u666f\u9009\u62e9\u6811\u72b6\u6570\u7ec4\u6216\u5176\u53d8\u79cd\u7ed3\u6784&#xff0c;\u53ef\u5728\u4fdd\u8bc1\u6027\u80fd\u7684\u540c\u65f6\u663e\u8457\u964d\u4f4e\u5f00\u53d1\u590d\u6742\u5ea6&#xff0c;\u8fd9\u79cd\u5e73\u8861\u827a\u672f\u6b63\u662f\u9ad8\u7ea7\u6570\u636e\u7ed3\u6784\u8bbe\u8ba1\u7684\u7cbe\u9ad3\u6240\u5728\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6811\u72b6\u6570\u7ec4&#xff08;Binary Indexed Tree&#xff0c;BIT&#xff09;\u4f5c\u4e3a\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u5904\u7406\u52a8\u6001\u524d\u7f00\u548c\u95ee\u9898\u7684\u7ecf\u5178\u6570\u636e\u7ed3\u6784&#xff0c;\u51ed\u501f\u5176O(log n)\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u5355\u70b9\u66f4\u65b0\u4e0e\u533a\u95f4\u67e5\u8be2\u80fd\u529b&#xff0c;\u5728\u7b97\u6cd5\u7ade\u8d5b\u3001\u91d1\u878d\u6570\u636e\u5206\u6790\u53ca\u5927\u89c4\u6a21\u6570\u636e\u5904\u7406\u7b49\u9886\u57df\u5c55\u73b0\u51fa\u72ec\u7279\u4f18\u52bf\u3002\u672c\u6587\u901a\u8fc7\u4e8c\u8fdb\u5236\u4f4d\u8fd0\u7b97\u539f\u7406\u5256\u6790\u3001\u6a21\u677f\u7c7b\u5c01\u88c5\u5b9e\u73b0\u53ca\u591a\u573a\u666f\u5e94\u7528\u6848\u4f8b&#xff0c;\u7cfb\u7edf\u9610\u8ff0\u6811\u72b6\u6570\u7ec4\u7684\u6838\u5fc3\u673a\u5236\u4e0e\u5de5\u7a0b\u5b9e\u8df5\u65b9\u6cd5\u3002<br \/>\n\u4e00\u3001\u6811\u72b6\u6570\u7ec4\u7684\u4e8c\u8fdb\u5236\u4f4d\u8fd0\u7b97\u5185\u6838<br \/>\n1.1 \u4f4e\u4f4d\u63a9\u7801&amp;#xff<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[55,99,427],"topic":[],"class_list":["post-60166","post","type-post","status-publish","format-standard","hentry","category-server","tag-c","tag-java","tag-427"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u63ed\u79d8C++\u7684\u6811\u72b6\u6570\u7ec4\u6df1\u5ea6\u89e3\u6790\uff1a\u4ece\u539f\u7406\u5230\u9ad8\u6548\u5c01\u88c5\u5b9e\u8df5 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/60166.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u63ed\u79d8C++\u7684\u6811\u72b6\u6570\u7ec4\u6df1\u5ea6\u89e3\u6790\uff1a\u4ece\u539f\u7406\u5230\u9ad8\u6548\u5c01\u88c5\u5b9e\u8df5 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u6811\u72b6\u6570\u7ec4&#xff08;Binary Indexed Tree&#xff0c;BIT&#xff09;\u4f5c\u4e3a\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u5904\u7406\u52a8\u6001\u524d\u7f00\u548c\u95ee\u9898\u7684\u7ecf\u5178\u6570\u636e\u7ed3\u6784&#xff0c;\u51ed\u501f\u5176O(log n)\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u5355\u70b9\u66f4\u65b0\u4e0e\u533a\u95f4\u67e5\u8be2\u80fd\u529b&#xff0c;\u5728\u7b97\u6cd5\u7ade\u8d5b\u3001\u91d1\u878d\u6570\u636e\u5206\u6790\u53ca\u5927\u89c4\u6a21\u6570\u636e\u5904\u7406\u7b49\u9886\u57df\u5c55\u73b0\u51fa\u72ec\u7279\u4f18\u52bf\u3002\u672c\u6587\u901a\u8fc7\u4e8c\u8fdb\u5236\u4f4d\u8fd0\u7b97\u539f\u7406\u5256\u6790\u3001\u6a21\u677f\u7c7b\u5c01\u88c5\u5b9e\u73b0\u53ca\u591a\u573a\u666f\u5e94\u7528\u6848\u4f8b&#xff0c;\u7cfb\u7edf\u9610\u8ff0\u6811\u72b6\u6570\u7ec4\u7684\u6838\u5fc3\u673a\u5236\u4e0e\u5de5\u7a0b\u5b9e\u8df5\u65b9\u6cd5\u3002 \u4e00\u3001\u6811\u72b6\u6570\u7ec4\u7684\u4e8c\u8fdb\u5236\u4f4d\u8fd0\u7b97\u5185\u6838 1.1 \u4f4e\u4f4d\u63a9\u7801&amp;#xff\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/60166.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-01-14T18:32:58+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/60166.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/60166.html\",\"name\":\"\u63ed\u79d8C++\u7684\u6811\u72b6\u6570\u7ec4\u6df1\u5ea6\u89e3\u6790\uff1a\u4ece\u539f\u7406\u5230\u9ad8\u6548\u5c01\u88c5\u5b9e\u8df5 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2026-01-14T18:32:58+00:00\",\"dateModified\":\"2026-01-14T18:32:58+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/60166.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/60166.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/60166.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u63ed\u79d8C++\u7684\u6811\u72b6\u6570\u7ec4\u6df1\u5ea6\u89e3\u6790\uff1a\u4ece\u539f\u7406\u5230\u9ad8\u6548\u5c01\u88c5\u5b9e\u8df5\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u63ed\u79d8C++\u7684\u6811\u72b6\u6570\u7ec4\u6df1\u5ea6\u89e3\u6790\uff1a\u4ece\u539f\u7406\u5230\u9ad8\u6548\u5c01\u88c5\u5b9e\u8df5 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/60166.html","og_locale":"zh_CN","og_type":"article","og_title":"\u63ed\u79d8C++\u7684\u6811\u72b6\u6570\u7ec4\u6df1\u5ea6\u89e3\u6790\uff1a\u4ece\u539f\u7406\u5230\u9ad8\u6548\u5c01\u88c5\u5b9e\u8df5 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"\u6811\u72b6\u6570\u7ec4&#xff08;Binary Indexed Tree&#xff0c;BIT&#xff09;\u4f5c\u4e3a\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u5904\u7406\u52a8\u6001\u524d\u7f00\u548c\u95ee\u9898\u7684\u7ecf\u5178\u6570\u636e\u7ed3\u6784&#xff0c;\u51ed\u501f\u5176O(log n)\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u5355\u70b9\u66f4\u65b0\u4e0e\u533a\u95f4\u67e5\u8be2\u80fd\u529b&#xff0c;\u5728\u7b97\u6cd5\u7ade\u8d5b\u3001\u91d1\u878d\u6570\u636e\u5206\u6790\u53ca\u5927\u89c4\u6a21\u6570\u636e\u5904\u7406\u7b49\u9886\u57df\u5c55\u73b0\u51fa\u72ec\u7279\u4f18\u52bf\u3002\u672c\u6587\u901a\u8fc7\u4e8c\u8fdb\u5236\u4f4d\u8fd0\u7b97\u539f\u7406\u5256\u6790\u3001\u6a21\u677f\u7c7b\u5c01\u88c5\u5b9e\u73b0\u53ca\u591a\u573a\u666f\u5e94\u7528\u6848\u4f8b&#xff0c;\u7cfb\u7edf\u9610\u8ff0\u6811\u72b6\u6570\u7ec4\u7684\u6838\u5fc3\u673a\u5236\u4e0e\u5de5\u7a0b\u5b9e\u8df5\u65b9\u6cd5\u3002 \u4e00\u3001\u6811\u72b6\u6570\u7ec4\u7684\u4e8c\u8fdb\u5236\u4f4d\u8fd0\u7b97\u5185\u6838 1.1 \u4f4e\u4f4d\u63a9\u7801&amp;#xff","og_url":"https:\/\/www.wsisp.com\/helps\/60166.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2026-01-14T18:32:58+00:00","author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"5 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/60166.html","url":"https:\/\/www.wsisp.com\/helps\/60166.html","name":"\u63ed\u79d8C++\u7684\u6811\u72b6\u6570\u7ec4\u6df1\u5ea6\u89e3\u6790\uff1a\u4ece\u539f\u7406\u5230\u9ad8\u6548\u5c01\u88c5\u5b9e\u8df5 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2026-01-14T18:32:58+00:00","dateModified":"2026-01-14T18:32:58+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/60166.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/60166.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/60166.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"\u63ed\u79d8C++\u7684\u6811\u72b6\u6570\u7ec4\u6df1\u5ea6\u89e3\u6790\uff1a\u4ece\u539f\u7406\u5230\u9ad8\u6548\u5c01\u88c5\u5b9e\u8df5"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/60166","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=60166"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/60166\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=60166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=60166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=60166"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=60166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}