\u72b6\u538bdp\uff0c\u987e\u540d\u601d\u4e49\uff0c\u5c31\u662f\u628a\u67d0\u4e2a\u4e1c\u897f\u7684\u67d0\u4e2a\u72b6\u6001\uff0c\u8fdb\u884c\u538b\u7f29\u8868\u793a\u3002\u6bd4\u5982\u4e00\u884c\u6570\uff0c\u6709n\u4e2a\uff0c\u8fdb\u884c\u9009\u6570\uff0c\u6bcf\u4e2a\u6570\u6709\u9009(1)\u548c\u4e0d\u9009(0)\u8fd9\u4e24\u79cd\u60c5\u51b5\uff0c\u603b\u5171\u6709 \u5728\u72b6\u538bdp\u4e2d\u5e38\u6570\u4f18\u5316\u548c\u526a\u679d\u662f\u975e\u5e38\u91cd\u8981\u7684\uff01\uff01<\/p>\n \u9898\u610f\uff1a\u6709\u4e00M x N\u7684\u7389\u7c73\u7530\uff0c\u6bcf\u5757\u7389\u7c73\u7530\u6709\u53ef\u9009\u548c\u4e0d\u53ef\u9009\u4e24\u79cd\u72b6\u6001\uff0c\u73b0\u4ece\u4e2d\u9009\u53d6\u4e00\u4e9b\u7389\u7c73\u7530\uff0c\u8981\u6c42\u6ca1\u6709\u4efb\u610f\u4e24\u5757\u7389\u7c73\u7530\u6709\u516c\u5171\u8fb9\uff0c\u6c42\u5171\u6709\u591a\u5c11\u79cd\u9009\u7684\u65b9\u5f0f\uff0c\u7ed3\u679c\u5bf91e8\u53d6\u6a21\u3002 dp[i][j]\u8868\u793a\u7b2ci\u884c\u571f\u5730\u7684\u9009\u53d6\u72b6\u6001\u4e3aj\u65f6\uff0c\u6709\u591a\u5c11\u79cd\u9009\u53d6\u65b9\u6cd5\u3002 \u65f6\u95f4\u590d\u6742\u5ea6 \u9898\u610f\uff1a\u6709n\u5757\u5976\u916a\uff0c\u8f93\u5165n\u548c\u6bcf\u5757\u5976\u916a\u7684\u5750\u6807\uff0c\u4ece(0,0)\u51fa\u53d1\uff0c\u95ee\u5982\u4f55\u8d70\uff0c\u624d\u80fd\u904d\u5386\u6240\u6709\u5976\u916a\u4ec5\u4e00\u6b21\uff0c\u4e14\u4f7f\u8def\u7a0b\u6700\u77ed\u3002 dp\u6570\u7ec4\u5f00\u59cb\u8981\u8d4b\u503c\u65e0\u7a77\u5927\u3002<\/p>\n \u9898\u610f\uff1a\u8f93\u5165n\uff0ck\u3002\u5728 \u5206\u6790\uff1a\u72b6\u538bdp\u3002\u6bcf\u4e00\u884c\u7684\u56fd\u738b\u5206\u5e03\u72b6\u6001\u7528\u4e00\u4e2a\u4e8c\u8fdb\u5236\u6570j\u6765\u8868\u793a\u3002dp[i][j][k]\u8868\u793a\u7b2ci\u884c\u7684\u56fd\u738b\u5206\u5e03\u72b6\u6001\u4e3aj\u65f6\uff0c\u524di\u884c\u5171\u653e\u5165\u6ee1\u8db3\u6761\u4ef6\u7684k\u4e2a\u56fd\u738b\u6709\u591a\u5c11\u79cd\u65b9\u5f0f\u3002<\/p>\n dp[i][j][k] = sum(dp[i-1][x][k-con[j]]),x\u4e3a\u7b2ci-1\u884c\u7684\u72b6\u6001\u3002con[j]\u8868\u793a\u72b6\u6001j\u6709\u591a\u5c11\u4e2a\u56fd\u738b\u3002<\/p>\n \u6bcf\u4e00\u884c\u7684\u51b2\u7a81\u68c0\u6d4b\u5c31\u662f\u8be5\u884c\u7684\u67d0\u4e2a\u4f4d\u7f6e\u548c\u5b83\u524d\u4e00\u4f4d\u4e0e\u8fd0\u7b97\u5373\u53ef\uff0c\u6bcf\u4e24\u884c\u4e4b\u95f4\u7684\u51b2\u7a81\u68c0\u6d4b\u4e3a ((j&k) || (j&(k<<1)) || (j&(k>>1)))<\/strong>\uff0c\u5373\u5224\u65adj\u80fd\u5426\u653b\u51fb\u5230k\u4e2d\u5f53\u524d\u4f4d\u7f6e\u7684\u524d\u4e00\u4f4d\u548c\u540e\u4e00\u4f4d\u3002<\/p>\n \u65f6\u95f4\u590d\u6742\u5ea6 \u72b6\u538bdp\uff0c\u4e00\u4e9b\u9700\u8981\u7684\u5c0f\u4f18\u5316(\u5176\u5b9e\u5f88\u6709\u5fc5\u8981)\u662f\uff1a\u6700\u597d\u628a\u6bcf\u79cd\u72b6\u6001\u4e0b\u7684\u6743\u503c\u5927\u5c0f\u63d0\u524d\u8ba1\u7b97\u51fa\u6765\uff0c\u8fd9\u6837\u7684\u8bdd\u53ea\u8981\u8ba1\u7b97\u4e00\u6b21\u5c31\u884c\u4e86\uff0c\u5728dp\u524d\uff0c\u628a\u6240\u9700\u7684\u6240\u6709\u72b6\u6001\u90fd\u63d0\u524d\u8ba1\u7b97\u597d\uff01\u8fd9\u6837\u53ef\u80fd\u4f1a\u66f4\u5feb\u54e6\u3002 \u72b6\u6001\u538b\u7f29dp \u72b6\u538bdp\uff0c\u987e\u540d\u601d\u4e49\uff0c\u5c31\u662f\u628a\u67d0\u4e2a\u4e1c\u897f\u7684\u67d0\u4e2a\u72b6\u6001\uff0c\u8fdb\u884c\u538b\u7f29\u8868\u793a\u3002\u6bd4\u5982\u4e00\u884c\u6570\uff0c\u6709n\u4e2a\uff0c\u8fdb\u884c\u9009 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[38],"tags":[],"_links":{"self":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/394"}],"collection":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/comments?post=394"}],"version-history":[{"count":18,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/394\/revisions"}],"predecessor-version":[{"id":480,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/394\/revisions\/480"}],"wp:attachment":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/media?parent=394"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/categories?post=394"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/tags?post=394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}2^n<\/code>\u79cd\u60c5\u51b5\uff0c\u9010\u4e2a\u8fdb\u884c\u679a\u4e3e\u53ef\u80fd\u6709\u70b9\u6162\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u4e2a\u4e8c\u8fdb\u5236\u6570\u6765\u8868\u793a\uff0c\u4e8c\u8fdb\u5236\u4e0a\u7684\u6bcf\u4e00\u4f4d\u5bf9\u5e94\u7684\u6570\u5b57\u5c31\u8868\u793a\u8fd9\u4e2a\u6570\u9009\u8fd8\u662f\u4e0d\u9009\u3002\u8fd9\u6837\u7684\u8bdd\u5c31\u53ef\u4ee5\u75280~2^{n}-1<\/code>\u8fd9\u4e9b\u6574\u6570\u6765\u5206\u522b\u8868\u793a\u8fd9\u4e9b\u72b6\u6001\u4e86\u3002\u8fd9\u5c31\u662f\u72b6\u6001\u538b\u7f29\u7684\u57fa\u672c\u601d\u60f3\u3002<\/p>\n\u6d1b\u8c37 P1897 \u7389\u7c73\u7530<\/a><\/h4>\n
\n\u5206\u6790\uff1a\u72b6\u538bdp\u3002\u76f8\u90bb\u53ef\u4ee5\u6709\u540c\u4e00\u884c\u76f8\u90bb\u548c\u540c\u4e00\u5217\u76f8\u90bb\u8fd9\u4e24\u79cd\u60c5\u51b5\u3002\u6bcf\u884c\u7684\u72b6\u6001\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u4e2a\u4e8c\u8fdb\u5236\u6570\u6765\u8868\u793a\uff0c\u5176\u4e2d\u6bcf\u884c\u7684\u72b6\u6001\u662f\u53d6\u51b3\u4e8e\u8fd9\u884c\u571f\u5730\u7684\u53ef\u9009\u60c5\u51b5\u548c\u4e0a\u4e00\u884c\u571f\u5730\u7684\u9009\u53d6\u60c5\u51b5\u7684\u3002
\n\u679a\u4e3e\u6bcf\u4e00\u884c\u7684\u5404\u79cd\u72b6\u6001\uff0c1.\u5148\u5224\u65ad\u8fd9\u79cd\u72b6\u6001\u662f\u5426\u5408\u6cd5(\u6240\u9009\u7684\u571f\u5730\u662f\u5426\u90fd\u662f\u53ef\u9009\u7684\uff0c\u6240\u9009\u7684\u571f\u5730\u662f\u5426\u6709\u76f8\u90bb\u7684\u60c5\u51b5) 2.\u518d\u679a\u4e3e\u4e0a\u4e00\u884c\u7684\u6240\u6709\u72b6\u6001\uff0c\u770b\u8fd9\u4e24\u884c\u7684\u8fd9\u4e24\u79cd\u72b6\u6001\u662f\u5426\u51b2\u7a81\uff0c\u82e5\u4e0d\u51b2\u7a81\uff0c\u52a0\u4e0a\u5c31\u884c\u4e86\u3002<\/p>\n
\ndp[i][j] = sum{dp[i-1][k], 0<=k<=2^n-1}<\/p>\nO(M*2^N*2^N)<\/code><\/strong><\/p>\n#include <bits\/stdc++.h>\nusing namespace std;\nconst int maxn = 13,mod = 1e8;\nint M,N;\nint a[maxn][maxn];\nint dp[13][1 << maxn];\nbool isok(int con,int i){\n for (int j=1;j<=N;j++)\n if (!a[i][j] && ((con>>(N-j)) & 1)) return false;\n for (int j=2;j<=N;j++)\n if (((con>>(N-j)) & 1) && ((con>>(N-j+1)) & 1)) return false;\n return true;\n}\nint main(){\n int ans = 0;\n cin >> M >> N;\n for (int i=1;i<=M;i++) for (int j=1;j<=N;j++)\n cin >> a[i][j];\n for (int j=0;j<(1<<N);j++){\n if (isok(j,1)) dp[1][j] = 1;\n }\n for (int i=2;i<=M;i++){\n for (int j=0;j<(1<<N);j++){\n if (i==1 && j==0) continue;\n if (!isok(j,i)) continue;\n for (int k=0;k<(1<<N);k++) if ((j&k)==0)\n dp[i][j] = (dp[i][j]+dp[i-1][k])%mod;\n }\n }\n for (int j=0;j<(1<<N);j++) ans = (ans+dp[M][j])%mod;\n cout << ans;\n return 0;\n}<\/code><\/pre>\n\u6d1b\u8c37 P1433 \u5403\u5976\u916a<\/a><\/h4>\n
\n\u5206\u6790\uff1a\u4ee4\u72b6\u6001j\u8868\u793a\u53ea\u8003\u8651\u5176\u4e2d\u7684\u82e5\u5e72\u5757\u5976\u916a\u3002
\ndp[i][j]\u8868\u793a\u5728j\u72b6\u6001\u5305\u542b\u7684\u5976\u916a\u4e2d\uff0c\u4ece\u7b2ci\u5757\u51fa\u53d1\u6240\u5f97\u7684\u6700\u4f18\u89e3\u3002
\n\u90a3\u4e48\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\uff1a
\ndp[i][j] = min(dp[i][j],dis(i,k)+dp[k][j-i]) k\u5c5e\u4e8ej
\n\u5c31\u662f\u5728j\u5305\u542b\u7684\u6240\u6709\u5976\u916a\u4e2d\uff0c\u9664\u53bbi\u8fd9\u5757\u5976\u916a\u4e4b\u540e\uff0c\u5269\u4e0b\u7684\u5976\u916a\u6240\u7ec4\u6210\u7684\u72b6\u6001j'\u4e0b\uff0c\u627e\u51fa\u6700\u4f18\u89e3k\u6ee1\u8db3\uff08i\u5230k\u7684\u8ddd\u79bb\u52a0\u4e0a\u4ecek\u51fa\u53d1\u5728j'\u72b6\u6001\u4e0b\u7684\u6700\u4f18\u89e3\uff09\u7684\u548c\u7684\u6700\u4f18\u89e3\u3002
\n\u53ef\u4ee5\u53d1\u73b0\u8fd9\u662f\u4e00\u4e2a\u9012\u5f52\u7684\u8fc7\u7a0b\uff0c\u8fb9\u754c\u6761\u4ef6\u662fdp[i][j] = 0,j\u53ea\u5305\u542bi\u3002<\/p>\n#include <bits\/stdc++.h>\nusing namespace std;\n\nint n;\ndouble point[20][2];\ndouble dp[16][1<<15];\ninline double dis(int a,int b){\n return sqrt((double)pow(point[a][0]-point[b][0],2.0)+pow(point[a][1]-point[b][1],2.0));\n}\nint main(){\n double ans = 999999999;\n cin >> n;\n for (int i=1;i<=n;i++)\n cin >> point[i][0] >> point[i][1];\n for (int j=1;j<(1<<n);j++){\n for (int i=1;i<=n;i++){\n dp[i][j] = 999999999;\n }\n }\n for (int j=1;j<(1<<n);j++){\n for (int i=1;i<=n;i++){\n if (!(j&(1<<(n-i)))) continue;\n if (j-(1<<(n-i))==0){\n dp[i][j] = 0;\n continue;\n }\n double tmp = 999999;\n for (int k=1;k<=n;k++){\n if (!(j&(1<<(n-k))) || k==i) continue;\n dp[i][j] = min(dp[i][j],dis(i,k)+dp[k][j-(1<<(n-i))]);\n }\n }\n }\n for (int i=1;i<=n;i++){\n ans = min(ans,dp[i][(1<<n)-1]+dis(0,i));\n }\n printf ("%.2lf",ans);\n return 0;\n}<\/code><\/pre>\n\u6d1b\u8c37 P1896 \u4e92\u4e0d\u4fb5\u72af<\/a><\/h4>\n
n*n<\/code>\u7684\u68cb\u76d8\u4e0a\uff0c\u653e\u5165k\u4e2a\u56fd\u738b\uff0c\u6c42\u6709\u591a\u5c11\u79cd\u65b9\u6cd5\u3002\u6bcf\u4e2a\u56fd\u738b\u7684\u653b\u51fb\u8303\u56f4\u662f\u5b83\u4e00\u5468\u76848\u4e2a\u4f4d\u7f6e\uff0c\u8981\u6c42\u4efb\u610f\u4e24\u4e2a\u56fd\u738b\u4e4b\u95f4\u4e0d\u80fd\u4e92\u76f8\u653b\u51fb\u3002<\/p>\nO(n^3*2^{2n})<\/code><\/strong>
\n\u56e0\u4e3a\u4e2d\u95f4\u6709\u597d\u591a\u526a\u679d\u548c\u4f18\u5316\uff0c\u6240\u4ee5\u8fd9\u4e2a\u590d\u6742\u5ea6\u662f\u53ef\u4ee5\u8fc7\u7684\u3002
\n\u4e00\u4e2a\u4f18\u5316\u662fcon\u6570\u7ec4\uff0ccon[j]\u8868\u793a\u72b6\u6001j\u662f\u5426\u5408\u6cd5(\u4e92\u4e0d\u4fb5\u72af)\uff0c\u5982\u679c\u503c\u4e3a-1\u5219\u8868\u793a\u4e0d\u5408\u6cd5\uff0c\u5426\u5219con[j]\u7684\u503c\u4e3aj\u72b6\u6001\u4e0b\u8be5\u884c\u7684\u56fd\u738b\u6570\u76ee\u3002
\n\u56e0\u4e3a\u6b64\u9898\u6bcf\u4e00\u884c\u90fd\u6ca1\u6709\u8bbe\u7f6e\u969c\u788d\uff0c\u6240\u4ee5\u6240\u6709\u884c\u7684\u72b6\u6001\u60c5\u51b5\u53ef\u4ee5\u76f4\u63a5\u7528\u4e00\u4e2a\u6570\u7ec4\u8868\u793a\uff0c\u5f53\u6bcf\u4e00\u884c\u6709\u81ea\u5df1\u7279\u5b9a\u7684\u969c\u788d\u65f6\uff0c\u53ef\u4ee5\u7528\u4e8c\u7ef4\u6570\u7ec4\u6765\u8868\u793a\u3002\u6b64\u6570\u7ec4\u53ef\u4ee5\u5927\u5927\u8282\u7ea6\u65f6\u95f4\u3002<\/p>\n#include <bits\/stdc++.h>\nusing namespace std;\ntypedef long long ll;\nll n,k1;\nll dp[10][1<<9][85];\nll con[1<<9];\nint check(int j){\n int ans = (j>>(n-1))&1;\n for (int i=2;i<=n;i++) if ((j>>(n-i))&1){\n if ((j>>(n-i+1))&1) return -1;\n ans++;\n }\n return ans;\n}\nint main(){\n ll ans = 0;\n cin >> n >> k1;\n for (int j=0;j<(1<<n);j++)\n con[j] = check(j);\n for (int j=0;j<(1<<n);j++) if (con[j]!=-1)\n dp[1][j][con[j]] = 1;\n for (int i=2;i<=n;i++){\n for (int j=0;j<(1<<n);j++){\n if (con[j]==-1) continue;\n for (int k=0;k<(1<<n);k++) if (con[k]!=-1){\n if ((j&k) || (j&(k<<1)) || (j&(k>>1))) continue;\n for (int x=con[j];x<=k1;x++)\n dp[i][j][x] += dp[i-1][k][x-con[j]];\n }\n }\n }\n for (int j=0;j<(1<<n);j++)\n ans += dp[n][j][k1];\n cout << ans;\n return 0;\n}<\/code><\/pre>\nPOJ1185 \u70ae\u5175\u9635\u5730<\/a><\/h4>\n
\ndp[i][j][k]\u8868\u793a\u7b2ci\u884c\u4e3aj\u72b6\u6001\uff0c\u7b2ci-1\u884c\u4e3ak\u72b6\u6001\u65f6\u7684\u6700\u4f18\u89e3\u3002
\ncon[i][j]\u8868\u793a\u7b2ci\u884c\u4e3aj\u72b6\u6001\u65f6\u662f\u5426\u5408\u6cd5\uff0c\u82e5\u4e0d\u5408\u6cd5\uff0c\u503c\u4e3a-1\uff0c\u82e5\u5408\u6cd5\uff0c\u503c\u4e3a\u8be5\u72b6\u6001\u4e0b\u7684\u70ae\u5175\u9635\u5730\u4e2a\u6570\u3002<\/p>\n#include <iostream>\n#include <algorithm>\n#include <cstring>\n\/\/#pragma GCC optimize(2)\nusing namespace std;\nint n,m;\nchar s[105][15];\nint con[105][1<<10],con2[1<<10];\nint dp[105][1<<10][1<<10];\ninline int check(int i,int j){\n for (int k=1;k<=m;k++) if (s[i][k]=='H' && ((j>>(m-k))&1))\n return -1;\n return con2[j];\n}\nint check2(int j){\n int ans = 0;\n for (int k=m;k>=1;k--){\n if (j&1){\n if (((j>>1)&1) || ((j>>2)&1)) return -1;\n ans++;\n }\n j >>= 1;\n }\n return ans;\n}\nint main(){\n \/\/std::ios::sync_with_stdio(false);\n int ans = 0;\n cin >> n >> m;\n if (!n || !m){\n cout << "0";\n return 0;\n }\n for (int i=1;i<=n;i++) cin >> s[i]+1;\n for (int j=0;j<(1<<m);j++) con2[j] = check2(j);\n for (int i=1;i<=n;i++){\n for (int j=0;j<(1<<m);j++)\n con[i][j] = check(i,j);\n }\n for (int j=0;j<(1<<m);j++) ans = max(ans,con[1][j]);\n for (int j=0;j<(1<<m);j++) if (con[2][j]!=-1){\n for (int k=0;k<(1<<m);k++) if (con[1][k]!=-1 && (k&j)==0){\n dp[2][j][k] = max(dp[2][j][k],con[2][j]+con[1][k]);\n }\n }\n for (int i=3;i<=n;i++){\n for (int j=0;j<(1<<m);j++) if (con[i][j]!=-1) {\n for (int k=0;k<(1<<m);k++) if (con[i-1][k]!=-1 && ((k&j)==0)){\n for (int x=0;x<(1<<m);x++) if (con[i-2][x]!=-1 && ((x&j)==0) && ((x&k)==0)){\n dp[i][j][k] = max(dp[i][j][k],dp[i-1][k][x]+con[i][j]);\n ans = max(ans,dp[i][j][k]);\n }\n }\n }\n }\n cout << ans;\n return 0;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"