{"id":98207,"date":"2026-08-31T12:32:50","date_gmt":"2026-08-31T04:32:50","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/98207.html"},"modified":"2026-08-31T12:32:50","modified_gmt":"2026-08-31T04:32:50","slug":"uva-11802-all-your-bases-belong-to-us","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/98207.html","title":{"rendered":"UVa 11802 All Your Bases Belong to Us"},"content":{"rendered":"

\u9898\u76ee\u63cf\u8ff0<\/h3>\n

\u7ed9\u5b9a\u4e24\u4e2a\u975e\u8d1f\u6574\u6570 nn<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u548c kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>，\u6c42\u6709\u591a\u5c11\u4e2a\u4e0d\u540c\u7684\u8fdb\u5236 bb<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>（b\u22652b \\\\ge 2<\/span><\/span>b<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>），\u4f7f\u5f97 n!n!<\/span><\/span>n<\/span>!<\/span><\/span><\/span><\/span><\/span> \u5728 bb<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span> \u8fdb\u5236\u4e0b\u672b\u5c3e\u6070\u597d\u6709 kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u4e2a\u96f6\u3002<\/p>\n

\u8f93\u5165\u683c\u5f0f<\/h3>\n

\u8f93\u5165\u7b2c\u4e00\u884c\u5305\u542b\u4e00\u4e2a\u6b63\u6574\u6570 TT<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span>（T\u226410000T \\\\le 10000<\/span><\/span>T<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>10000<\/span><\/span><\/span><\/span><\/span>），\u8868\u793a\u6d4b\u8bd5\u7528\u4f8b\u6570\u3002
\n\u63a5\u4e0b\u6765 TT<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span> \u884c，\u6bcf\u884c\u4e24\u4e2a\u6574\u6570 nn<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u548c kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>，\u6ee1\u8db3 n\u22641015n \\\\le 10^{15}<\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>15<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，1\u2264k\u226410151 \\\\le k \\\\le 10^{15}<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>15<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5e76\u4e14\u4fdd\u8bc1 n\/k<500n \/ k < 500<\/span><\/span>n<\/span>\/<\/span>k<\/span><\/span><<\/span><\/span><\/span><\/span>500<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u8f93\u51fa\u683c\u5f0f<\/h3>\n

\u5bf9\u4e8e\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b，\u8f93\u51fa\u4e00\u884c，\u683c\u5f0f\u4e3a Case X: Y，\u5176\u4e2d XX<\/span><\/span>X<\/span><\/span><\/span><\/span><\/span> \u662f\u6d4b\u8bd5\u7528\u4f8b\u7f16\u53f7（\u4ece 11<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5f00\u59cb），YY<\/span><\/span>Y<\/span><\/span><\/span><\/span><\/span> \u662f\u7b54\u6848\u5bf9 10000000071000000007<\/span><\/span>1000000007<\/span><\/span><\/span><\/span><\/span> \u53d6\u6a21\u540e\u7684\u503c\u3002<\/p>\n

\u6837\u4f8b<\/h3>\n

\u8f93\u5165<\/p>\n

5
\n10 2
\n10 3
\n10 4
\n10 5
\n10 8<\/p>\n

\u8f93\u51fa<\/p>\n

Case 1: 24
\nCase 2: 0
\nCase 3: 4
\nCase 4: 0
\nCase 5: 1<\/p>\n

\u9898\u76ee\u5206\u6790<\/h3>\n

\u672c\u9898\u662f\u7ecf\u5178\u95ee\u9898\u201c\u9636\u4e58\u672b\u5c3e\u96f6\u201d\u7684\u9006\u5411\u7248\u672c\u3002\u5df2\u77e5 n!n!<\/span><\/span>n<\/span>!<\/span><\/span><\/span><\/span><\/span> \u5728\u5341\u8fdb\u5236\u4e0b\u7684\u672b\u5c3e\u96f6\u4e2a\u6570\u7531\u56e0\u5b50 10=2\u00d7510 = 2 \\\\times 5<\/span><\/span>10<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>5<\/span><\/span><\/span><\/span><\/span> \u51b3\u5b9a，\u66f4\u4e00\u822c\u5730，\u5728\u8fdb\u5236 bb<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span> \u4e2d，\u82e5 b=\u220fpieib = \\\\prod p_i^{e_i}<\/span><\/span>b<\/span><\/span>=<\/span><\/span><\/span><\/span>\u220f<\/span><\/span>p<\/span><\/span>i<\/span><\/span><\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5219 n!n!<\/span><\/span>n<\/span>!<\/span><\/span><\/span><\/span><\/span> \u5728 bb<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span> \u8fdb\u5236\u4e0b\u672b\u5c3e\u96f6\u7684\u4e2a\u6570\u4e3a<\/p>\n

min\u2061i\u230avpi(n!)ei\u230b,
\n\\\\min_i \\\\left\\\\lfloor \\\\frac{v_{p_i}(n!)}{e_i} \\\\right\\\\rfloor,
\n<\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>min<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u230a<\/span><\/span><\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>p<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>n<\/span>!)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u230b<\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d vp(n!)v_p(n!)<\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>n<\/span>!)<\/span><\/span><\/span><\/span><\/span> \u8868\u793a n!n!<\/span><\/span>n<\/span>!<\/span><\/span><\/span><\/span><\/span> \u4e2d\u8d28\u56e0\u5b50 pp<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span> \u7684\u6307\u6570\u3002\u9898\u76ee\u8981\u6c42\u8fd9\u4e2a\u6700\u5c0f\u503c\u6070\u597d\u7b49\u4e8e kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u76f4\u63a5\u679a\u4e3e bb<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span> \u7684\u8303\u56f4\u663e\u7136\u4e0d\u53ef\u884c（bb<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span> \u53ef\u4ee5\u5927\u5230 n!n!<\/span><\/span>n<\/span>!<\/span><\/span><\/span><\/span><\/span> \u672c\u8eab）\u3002\u9700\u8981\u5229\u7528 n\/k<500n\/k < 500<\/span><\/span>n<\/span>\/<\/span>k<\/span><\/span><<\/span><\/span><\/span><\/span>500<\/span><\/span><\/span><\/span><\/span> \u8fd9\u4e00\u5173\u952e\u6761\u4ef6\u3002\u56e0\u4e3a\u82e5\u67d0\u4e2a\u8d28\u6570 p>n\/k+1p > n\/k + 1<\/span><\/span>p<\/span><\/span>><\/span><\/span><\/span><\/span>n<\/span>\/<\/span>k<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u5219 vp(n!)\u2264n\/(p\u22121)<kv_p(n!) \\\\le n\/(p-1) < k<\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>n<\/span>!)<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span>\/<\/span>(<\/span>p<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span><<\/span><\/span><\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>，\u8fd9\u6837\u7684\u8d28\u6570\u4e0d\u53ef\u80fd\u5728 bb<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span> \u4e2d\u51fa\u73b0（\u5426\u5219\u6307\u6570 ei\u22651e_i \\\\ge 1<\/span><\/span>e<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2265<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u4f1a\u5bfc\u81f4\u6700\u5c0f\u503c\u5c0f\u4e8e kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>）\u3002\u56e0\u6b64，\u53ea\u9700\u8003\u8651\u6240\u6709\u4e0d\u8d85\u8fc7 500500<\/span><\/span>500<\/span><\/span><\/span><\/span><\/span> \u7684\u8d28\u6570，\u95ee\u9898\u89c4\u6a21\u5927\u5e45\u7f29\u5c0f\u3002<\/p>\n

\u89e3\u9898\u601d\u8def<\/h3>\n

\u5b9a\u4e49\u4e0e\u7b26\u53f7<\/h4>\n

\u8bbe vp=vp(n!)v_p = v_p(n!)<\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>n<\/span>!)<\/span><\/span><\/span><\/span><\/span>\u3002\u5bf9\u4e8e\u4efb\u610f\u6b63\u6574\u6570 KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span>，\u5b9a\u4e49 f(K)f(K)<\/span><\/span>f<\/span>(<\/span>K<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6ee1\u8db3\u201c\u672b\u5c3e\u96f6\u4e2a\u6570\u81f3\u5c11\u4e3a KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span>\u201d\u7684\u8fdb\u5236\u6570（\u5305\u62ec b=1b=1<\/span><\/span>b<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u8fd9\u4e2a\u5e73\u51e1\u60c5\u51b5）\u7684\u4e2a\u6570\u3002\u6839\u636e\u4e0a\u8ff0\u6700\u5c0f\u503c\u7684\u6761\u4ef6，bb<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span> \u7684\u8d28\u56e0\u6570\u5206\u89e3\u4e2d，\u6bcf\u4e2a\u8d28\u56e0\u5b50 pp<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span> \u7684\u6307\u6570 epe_p<\/span><\/span>e<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5fc5\u987b\u6ee1\u8db3<\/p>\n

\u230avpep\u230b\u2265K\u27faep\u2264\u230avpK\u230b.
\n\\\\left\\\\lfloor \\\\frac{v_p}{e_p} \\\\right\\\\rfloor \\\\ge K \\\\quad \\\\Longleftrightarrow \\\\quad e_p \\\\le \\\\left\\\\lfloor \\\\frac{v_p}{K} \\\\right\\\\rfloor.
\n<\/span><\/span>\u230a<\/span><\/span><\/span><\/span>e<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u230b<\/span><\/span><\/span><\/span>\u2265<\/span><\/span><\/span><\/span>K<\/span><\/span><\/span>\u27fa<\/span><\/span><\/span><\/span><\/span>e<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2264<\/span><\/span><\/span><\/span>\u230a<\/span><\/span><\/span><\/span>K<\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u230b<\/span><\/span><\/span><\/span>.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u56e0\u6b64，\u6bcf\u4e2a pp<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span> \u53ef\u9009\u7684\u6307\u6570\u8303\u56f4\u4e3a 0,1,\u2026,\u230avp\/K\u230b0, 1, \\\\dots, \\\\left\\\\lfloor v_p \/ K \\\\right\\\\rfloor<\/span><\/span>0<\/span>,<\/span><\/span>1<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>\u230a<\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>K<\/span>\u230b<\/span><\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d 00<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u8be5\u8d28\u56e0\u5b50\u4e0d\u51fa\u73b0\u3002\u72ec\u7acb\u9009\u62e9\u5404\u8d28\u56e0\u5b50\u7684\u6307\u6570\u5373\u53ef\u786e\u5b9a\u4e00\u4e2a bb<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>（\u6ce8\u610f b=1b=1<\/span><\/span>b<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5bf9\u5e94\u6240\u6709\u6307\u6570\u5747\u4e3a 00<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>），\u6240\u4ee5<\/p>\n

f(K)=\u220fp:\u2009vp\u2265K(\u230avpK\u230b+1).
\nf(K) = \\\\prod_{p:\\\\, v_p \\\\ge K} \\\\left( \\\\left\\\\lfloor \\\\frac{v_p}{K} \\\\right\\\\rfloor + 1 \\\\right).
\n<\/span><\/span>f<\/span>(<\/span>K<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>p<\/span>:<\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2265<\/span>K<\/span><\/span><\/span><\/span><\/span>\u220f<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>\u230a<\/span><\/span><\/span><\/span>K<\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u230b<\/span><\/span><\/span><\/span>+<\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span>.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8fd9\u91cc\u4e58\u79ef\u4e2d\u4ec5\u5305\u542b\u6ee1\u8db3 vp\u2265Kv_p \\\\ge K<\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2265<\/span><\/span><\/span><\/span>K<\/span><\/span><\/span><\/span><\/span> \u7684\u8d28\u6570，\u56e0\u4e3a\u82e5 vp<Kv_p < K<\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span><\/span><\/span>K<\/span><\/span><\/span><\/span><\/span>，\u5219 \u230avp\/K\u230b=0\\\\lfloor v_p \/ K \\\\rfloor = 0<\/span><\/span>\u230a<\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>K<\/span>\u230b<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>，\u53ea\u6709\u6307\u6570 00<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u53ef\u9009，\u56e0\u5b50\u4e3a 11<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u4e0d\u8d21\u732e\u3002<\/p>\n

\u5bb9\u65a5\u6c42\u6070\u597d kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u4e2a\u96f6<\/h4>\n

\u4ee4 g(K)g(K)<\/span><\/span>g<\/span>(<\/span>K<\/span>)<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u6ee1\u8db3\u201c\u672b\u5c3e\u96f6\u4e2a\u6570\u6070\u597d\u4e3a KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span>\u201d\u7684\u8fdb\u5236\u6570（b\u22652b \\\\ge 2<\/span><\/span>b<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>）\u3002\u663e\u7136，\u6070\u597d\u4e3a kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u7684\u4e2a\u6570\u7b49\u4e8e\u81f3\u5c11\u4e3a kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u7684\u4e2a\u6570\u51cf\u53bb\u81f3\u5c11\u4e3a k+1k+1<\/span><\/span>k<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u7684\u4e2a\u6570：<\/p>\n

g(k)=(f(k)\u22121)\u2212(f(k+1)\u22121)=f(k)\u2212f(k+1).
\ng(k) = \\\\left( f(k) – 1 \\\\right) – \\\\left( f(k+1) – 1 \\\\right) = f(k) – f(k+1).
\n<\/span><\/span>g<\/span>(<\/span>k<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>f<\/span>(<\/span>k<\/span>)<\/span><\/span>\u2212<\/span><\/span>1<\/span>)<\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>(<\/span>f<\/span>(<\/span>k<\/span><\/span>+<\/span><\/span>1<\/span>)<\/span><\/span>\u2212<\/span><\/span>1<\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>f<\/span>(<\/span>k<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>f<\/span>(<\/span>k<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>)<\/span>.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u56e0\u4e3a f(K)f(K)<\/span><\/span>f<\/span>(<\/span>K<\/span>)<\/span><\/span><\/span><\/span><\/span> \u5305\u542b\u4e86 b=1b=1<\/span><\/span>b<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u800c\u9898\u76ee\u8981\u6c42 b\u22652b \\\\ge 2<\/span><\/span>b<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>，\u51cf\u53bb 11<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u540e\u76f8\u51cf\u62b5\u6d88，\u6545\u7b54\u6848\u5373 f(k)\u2212f(k+1)f(k) – f(k+1)<\/span><\/span>f<\/span>(<\/span>k<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>f<\/span>(<\/span>k<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u8ba1\u7b97 vp(n!)v_p(n!)<\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>n<\/span>!)<\/span><\/span><\/span><\/span><\/span><\/h4>\n

\u5229\u7528\u52d2\u8ba9\u5fb7\u516c\u5f0f：<\/p>\n

vp(n!)=\u2211j\u22651\u230anpj\u230b.
\nv_p(n!) = \\\\sum_{j \\\\ge 1} \\\\left\\\\lfloor \\\\frac{n}{p^j} \\\\right\\\\rfloor.
\n<\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>n<\/span>!)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>j<\/span>\u2265<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u230a<\/span><\/span><\/span><\/span>p<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u230b<\/span><\/span><\/span><\/span>.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u7531\u4e8e p\u2264500p \\\\le 500<\/span><\/span>p<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>500<\/span><\/span><\/span><\/span><\/span> \u4e14 n\u22641015n \\\\le 10^{15}<\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>15<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u76f4\u63a5\u7528\u5faa\u73af\u7d2f\u9664\u8ba1\u7b97\u5373\u53ef，\u590d\u6742\u5ea6\u6781\u5c0f\u3002<\/p>\n

\u7b97\u6cd5\u6b65\u9aa4<\/h4>\n
  • \u9884\u5904\u7406\u51fa\u6240\u6709\u4e0d\u8d85\u8fc7 500500<\/span><\/span>500<\/span><\/span><\/span><\/span><\/span> \u7684\u8d28\u6570\u3002<\/li>\n
  • \u5bf9\u4e8e\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b (n,k)(n, k)<\/span><\/span>(<\/span>n<\/span>,<\/span><\/span>k<\/span>)<\/span><\/span><\/span><\/span><\/span>：\n
      \n
    • \u521d\u59cb\u5316\u4e24\u4e2a\u4e58\u79ef prod1=1\\\\textit{prod1} = 1<\/span><\/span>prod1<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>（\u5bf9\u5e94 K=kK = k<\/span><\/span>K<\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>）\u548c prod2=1\\\\textit{prod2} = 1<\/span><\/span>prod2<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>（\u5bf9\u5e94 K=k+1K = k+1<\/span><\/span>K<\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>）\u3002<\/li>\n
    • \u904d\u5386\u6bcf\u4e2a\u8d28\u6570 pp<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>（\u82e5 p>np > n<\/span><\/span>p<\/span><\/span>><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u5219\u8df3\u8fc7，\u56e0\u4e3a vp=0v_p = 0<\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>）：\n
        \n
      • \u8ba1\u7b97 v=vp(n!)v = v_p(n!)<\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>n<\/span>!)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n
      • \u5982\u679c v\u2265kv \\\\ge k<\/span><\/span>v<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>，\u5219 prod1\u2190prod1\u00d7(\u230av\/k\u230b+1)\u200amod\u200aMOD\\\\textit{prod1} \\\\gets \\\\textit{prod1} \\\\times (\\\\lfloor v\/k \\\\rfloor + 1) \\\\bmod \\\\textit{MOD}<\/span><\/span>prod1<\/span><\/span><\/span>\u2190<\/span><\/span><\/span><\/span>prod1<\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(\u230a<\/span>v<\/span>\/<\/span>k<\/span>\u230b<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span><\/span>mod<\/span><\/span><\/span><\/span><\/span><\/span><\/span>MOD<\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n
      • \u5982\u679c v\u2265k+1v \\\\ge k+1<\/span><\/span>v<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>k<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u5219 prod2\u2190prod2\u00d7(\u230av\/(k+1)\u230b+1)\u200amod\u200aMOD\\\\textit{prod2} \\\\gets \\\\textit{prod2} \\\\times (\\\\lfloor v\/(k+1) \\\\rfloor + 1) \\\\bmod \\\\textit{MOD}<\/span><\/span>prod2<\/span><\/span><\/span>\u2190<\/span><\/span><\/span><\/span>prod2<\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(\u230a<\/span>v<\/span>\/<\/span>(<\/span>k<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>)\u230b<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span><\/span>mod<\/span><\/span><\/span><\/span><\/span><\/span><\/span>MOD<\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n<\/li>\n
      • \u7b54\u6848 =(prod1\u2212prod2+MOD)\u200amod\u200aMOD= (\\\\textit{prod1} – \\\\textit{prod2} + \\\\textit{MOD}) \\\\bmod \\\\textit{MOD}<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>prod1<\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>prod2<\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>MOD<\/span><\/span>)<\/span><\/span><\/span>mod<\/span><\/span><\/span><\/span><\/span><\/span><\/span>MOD<\/span><\/span><\/span><\/span><\/span><\/span>，\u8f93\u51fa\u3002<\/li>\n<\/ul>\n<\/li>\n

        \u6b63\u786e\u6027\u8bc1\u660e<\/h4>\n

        \u7531\u4e0a\u8ff0\u5206\u6790，f(K)f(K)<\/span><\/span>f<\/span>(<\/span>K<\/span>)<\/span><\/span><\/span><\/span><\/span> \u7684\u8ba1\u7b97\u6b63\u786e\u53cd\u6620\u4e86\u6240\u6709\u6ee1\u8db3\u81f3\u5c11 KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span> \u4e2a\u96f6\u7684\u8fdb\u5236\u6570（\u5305\u62ec b=1b=1<\/span><\/span>b<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>）\u3002\u7531\u4e8e b=1b=1<\/span><\/span>b<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5728\u6240\u6709 KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span> \u4e0b\u90fd\u88ab\u8ba1\u5165，\u5bb9\u65a5\u540e\u6070\u597d\u5f97\u5230 b\u22652b \\\\ge 2<\/span><\/span>b<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u7684\u4e2a\u6570\u3002\u540c\u65f6，\u7531\u4e8e n\/k<500n\/k < 500<\/span><\/span>n<\/span>\/<\/span>k<\/span><\/span><<\/span><\/span><\/span><\/span>500<\/span><\/span><\/span><\/span><\/span>，\u6240\u6709\u53ef\u80fd\u5f71\u54cd\u7ed3\u679c\u7684\u8d28\u6570\u90fd\u88ab\u8986\u76d6，\u9057\u6f0f\u7684\u8d28\u6570\u4e0d\u4f1a\u6539\u53d8\u4e58\u79ef（\u5176\u5bf9\u5e94\u56e0\u5b50\u4e3a 11<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>）\u3002<\/p>\n

        \u590d\u6742\u5ea6\u5206\u6790<\/h4>\n
          \n
        • \u9884\u5904\u7406\u8d28\u6570：O(500log\u2061log\u2061500)O(500 \\\\log \\\\log 500)<\/span><\/span>O<\/span>(<\/span>500<\/span><\/span>log<\/span><\/span><\/span>log<\/span><\/span><\/span>500<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n
        • \u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b：\u904d\u5386\u4e0d\u8d85\u8fc7 500500<\/span><\/span>500<\/span><\/span><\/span><\/span><\/span> \u7684\u8d28\u6570\u4e2a\u6570（\u7ea6 9595<\/span><\/span>95<\/span><\/span><\/span><\/span><\/span> \u4e2a），\u6bcf\u6b21\u8ba1\u7b97 vp(n!)v_p(n!)<\/span><\/span>v<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>n<\/span>!)<\/span><\/span><\/span><\/span><\/span> \u7684\u5faa\u73af\u6b21\u6570\u4e3a log\u2061pn\u2264log\u206121015\u224850\\\\log_p n \\\\le \\\\log_2 10^{15} \\\\approx 50<\/span><\/span>log<\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>15<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>50<\/span><\/span><\/span><\/span><\/span>\u3002\u603b\u64cd\u4f5c\u91cf\u7ea6\u4e3a T\u00d795\u00d750T \\\\times 95 \\\\times 50<\/span><\/span>T<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>95<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>50<\/span><\/span><\/span><\/span><\/span>，\u5f53 T=10000T = 10000<\/span><\/span>T<\/span><\/span>=<\/span><\/span><\/span><\/span>10000<\/span><\/span><\/span><\/span><\/span> \u65f6\u7ea6\u4e3a 4.75\u00d71074.75 \\\\times 10^7<\/span><\/span>4.75<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5b8c\u5168\u53ef\u4ee5\u63a5\u53d7\u3002<\/li>\n
        • \u65f6\u95f4\u590d\u6742\u5ea6：O(T\u22c5\u03c0(500)\u22c5log\u2061n)O(T \\\\cdot \\\\pi(500) \\\\cdot \\\\log n)<\/span><\/span>O<\/span>(<\/span>T<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u03c0<\/span>(<\/span>500<\/span>)<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u7a7a\u95f4\u590d\u6742\u5ea6 O(1)O(1)<\/span><\/span>O<\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n

          \u4ee3\u7801\u5b9e\u73b0<\/h3>\n

          \/\/ All Your Bases Belong to Us<\/span>
          \n\/\/ UVa ID: 11802<\/span>
          \n\/\/ Verdict: Accepted<\/span>
          \n\/\/ Submission Date: 2026-06-20<\/span>
          \n\/\/ UVa Run Time: 0.050s<\/span>
          \n\/\/<\/span>
          \n\/\/ \u7248\u6743\u6240\u6709（C）2026，\u90b1\u79cb\u3002metaphysis # yeah dot net<\/span><\/p>\n

          #<\/span>include<\/span> <bits\/stdc++.h><\/span><\/span>
          \nusing<\/span> namespace<\/span> std;<\/span><\/p>\n

          typedef<\/span> long<\/span> long<\/span> int64;<\/span>
          \nconst<\/span> int<\/span> MOD =<\/span> 1000000007<\/span>;<\/span>
          \nconst<\/span> int<\/span> MAXP =<\/span> 500<\/span>;<\/span><\/p>\n

          vector<<\/span>int<\/span>><\/span> getPrimes<\/span>(<\/span>int<\/span> limit)<\/span> {<\/span>
          \n vector<<\/span>bool<\/span>><\/span> isComp<\/span>(<\/span>limit +<\/span> 1<\/span>,<\/span> false<\/span>)<\/span>;<\/span>
          \n vector<<\/span>int<\/span>><\/span> primes;<\/span>
          \n for<\/span> (<\/span>int<\/span> i =<\/span> 2<\/span>;<\/span> i <=<\/span> limit;<\/span> ++<\/span>i)<\/span> {<\/span>
          \n if<\/span> (<\/span>!<\/span>isComp[<\/span>i]<\/span>)<\/span> {<\/span>
          \n primes.<\/span>push_back<\/span>(<\/span>i)<\/span>;<\/span>
          \n if<\/span> (<\/span>(<\/span>int64)<\/span>i *<\/span> i <=<\/span> limit)<\/span>
          \n for<\/span> (<\/span>int<\/span> j =<\/span> i *<\/span> i;<\/span> j <=<\/span> limit;<\/span> j +=<\/span> i)<\/span> isComp[<\/span>j]<\/span> =<\/span> true<\/span>;<\/span>
          \n }<\/span>
          \n }<\/span>
          \n return<\/span> primes;<\/span>
          \n}<\/span><\/p>\n

          int<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
          \n vector<<\/span>int<\/span>><\/span> primes =<\/span> getPrimes<\/span>(<\/span>MAXP)<\/span>;<\/span>
          \n int<\/span> T;<\/span>
          \n scanf<\/span>(<\/span>"%d"<\/span>,<\/span> &<\/span>T)<\/span>;<\/span>
          \n for<\/span> (<\/span>int<\/span> caseNo =<\/span> 1<\/span>;<\/span> caseNo <=<\/span> T;<\/span> ++<\/span>caseNo)<\/span> {<\/span>
          \n int64 n,<\/span> k;<\/span>
          \n scanf<\/span>(<\/span>"%lld %lld"<\/span>,<\/span> &<\/span>n,<\/span> &<\/span>k)<\/span>;<\/span>
          \n int64 prod1 =<\/span> 1<\/span>;<\/span> \/\/ \u5bf9\u5e94 K = k<\/span>
          \n int64 prod2 =<\/span> 1<\/span>;<\/span> \/\/ \u5bf9\u5e94 K = k+1<\/span>
          \n for<\/span> (<\/span>int<\/span> p :<\/span> primes)<\/span> {<\/span>
          \n if<\/span> (<\/span>p ><\/span> n)<\/span> break<\/span>;<\/span>
          \n int64 m =<\/span> 0<\/span>;<\/span>
          \n int64 tmp =<\/span> n;<\/span>
          \n while<\/span> (<\/span>tmp)<\/span> {<\/span>
          \n tmp \/=<\/span> p;<\/span>
          \n m +=<\/span> tmp;<\/span>
          \n }<\/span>
          \n if<\/span> (<\/span>m >=<\/span> k)<\/span> {<\/span>
          \n int64 cnt =<\/span> m \/<\/span> k +<\/span> 1<\/span>;<\/span>
          \n prod1 =<\/span> prod1 *<\/span> (<\/span>cnt %<\/span> MOD)<\/span> %<\/span> MOD;<\/span>
          \n }<\/span>
          \n if<\/span> (<\/span>m >=<\/span> k +<\/span> 1<\/span>)<\/span> {<\/span>
          \n int64 cnt =<\/span> m \/<\/span> (<\/span>k +<\/span> 1<\/span>)<\/span> +<\/span> 1<\/span>;<\/span>
          \n prod2 =<\/span> prod2 *<\/span> (<\/span>cnt %<\/span> MOD)<\/span> %<\/span> MOD;<\/span>
          \n }<\/span>
          \n }<\/span>
          \n int64 ans =<\/span> (<\/span>prod1 –<\/span> prod2 +<\/span> MOD)<\/span> %<\/span> MOD;<\/span>
          \n printf<\/span>(<\/span>"Case %d: %lld\\\\n"<\/span>,<\/span> caseNo,<\/span> ans)<\/span>;<\/span>
          \n }<\/span>
          \n return<\/span> 0<\/span>;<\/span>
          \n}<\/span><\/p>\n

          \u603b\u7ed3<\/h3>\n

          \u672c\u9898\u7684\u5173\u952e\u5728\u4e8e\u5229\u7528 n\/k<500n\/k < 500<\/span><\/span>n<\/span>\/<\/span>k<\/span><\/span><<\/span><\/span><\/span><\/span>500<\/span><\/span><\/span><\/span><\/span> \u7684\u6761\u4ef6\u5c06\u9700\u8981\u8003\u8651\u7684\u8d28\u6570\u8303\u56f4\u7f29\u5c0f\u5230 500500<\/span><\/span>500<\/span><\/span><\/span><\/span><\/span> \u4ee5\u5185，\u4ece\u800c\u907f\u514d\u4e86\u679a\u4e3e\u6240\u6709\u53ef\u80fd\u7684\u8fdb\u5236 bb<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u3002\u901a\u8fc7\u5bb9\u65a5\u539f\u7406，\u5c06\u201c\u6070\u597d\u4e3a kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u201d\u8f6c\u5316\u4e3a\u4e24\u4e2a\u201c\u81f3\u5c11\u4e3a KK<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span>\u201d\u7684\u8ba1\u6570\u76f8\u51cf，\u800c\u540e\u8005\u53ef\u4ee5\u901a\u8fc7\u8d28\u56e0\u6570\u5206\u89e3\u548c\u4e58\u6cd5\u539f\u7406\u8f7b\u677e\u6c42\u51fa\u3002<\/p>\n

          \u8be5\u89e3\u6cd5\u4f53\u73b0\u4e86\u4ee5\u4e0b\u6280\u5de7：<\/p>\n

            \n
          • \u7f29\u5c0f\u89c4\u6a21：\u5229\u7528\u6570\u636e\u8303\u56f4\u9650\u5236\u8fc7\u6ee4\u65e0\u5173\u8d28\u6570\u3002<\/li>\n
          • \u5bb9\u65a5\u8f6c\u6362：\u5c06\u7cbe\u786e\u6761\u4ef6\u8f6c\u5316\u4e3a\u4e24\u4e2a\u4e0b\u754c\u6761\u4ef6\u7684\u5dee\u3002<\/li>\n
          • \u6a21\u8fd0\u7b97：\u6ce8\u610f\u53d6\u6a21，\u907f\u514d\u6ea2\u51fa\u3002<\/li>\n<\/ul>\n

            \u6b64\u65b9\u6cd5\u5bf9\u540c\u7c7b\u95ee\u9898（\u5982\u6c42\u9636\u4e58\u5728\u7ed9\u5b9a\u8fdb\u5236\u4e0b\u672b\u5c3e\u96f6\u4e2a\u6570\u7684\u9006\u5411\u95ee\u9898）\u5177\u6709\u901a\u7528\u6027，\u503c\u5f97\u501f\u9274\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

            \u9898\u76ee\u63cf\u8ff0
            \n\u7ed9\u5b9a\u4e24\u4e2a\u975e\u8d1f\u6574\u6570 nnn \u548c kkk，\u6c42\u6709\u591a\u5c11\u4e2a\u4e0d\u540c\u7684\u8fdb\u5236 bbb（b\u22652b \\\\ge 2b\u22652），\u4f7f\u5f97 n!n!n! \u5728 bbb \u8fdb\u5236\u4e0b\u672b\u5c3e\u6070\u597d\u6709 kkk \u4e2a\u96f6\u3002
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            \n\u8f93\u5165\u7b2c\u4e00\u884c\u5305\u542b\u4e00\u4e2a\u6b63\u6574\u6570 TTT（T\u226410000T \\\\le 10000T\u226410000），\u8868\u793a\u6d4b\u8bd5\u7528\u4f8b\u6570\u3002
            \n\u63a5\u4e0b\u6765 TTT \u884c，\u6bcf\u884c\u4e24\u4e2a\u6574\u6570 nnn \u548c kkk，\u6ee1\u8db3 n\u2264<\/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":[55,427,4405],"topic":[],"class_list":["post-98207","post","type-post","status-publish","format-standard","hentry","category-server","tag-c","tag-427","tag-4405"],"yoast_head":"\nUVa 11802 All Your Bases Belong to Us - \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\/98207.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"UVa 11802 All Your Bases Belong to Us - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u9898\u76ee\u63cf\u8ff0 \u7ed9\u5b9a\u4e24\u4e2a\u975e\u8d1f\u6574\u6570 nnn \u548c kkk，\u6c42\u6709\u591a\u5c11\u4e2a\u4e0d\u540c\u7684\u8fdb\u5236 bbb（b\u22652b \\ge 2b\u22652），\u4f7f\u5f97 n!n!n! 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