{"id":409,"date":"2022-10-06T20:55:27","date_gmt":"2022-10-06T12:55:27","guid":{"rendered":"https:\/\/blog.cirno.fun\/?p=409"},"modified":"2024-09-12T09:31:08","modified_gmt":"2024-09-12T01:31:08","slug":"%e7%bb%8f%e5%85%b8%e4%b8%8e%e5%a4%9a%e4%ba%ba%e8%83%8c%e5%8c%85%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/blog.sssn.tech\/?p=409","title":{"rendered":"\u7ecf\u5178\u4e0e\u591a\u4eba\u80cc\u5305\u95ee\u9898"},"content":{"rendered":"

\u7ecf\u5178\u80cc\u5305\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u6240\u5173\u5fc3\u7684\u95ee\u9898\u5728\u4e8e\u201c\u62ff\u4e0e\u4e0d\u62ff\u201d\uff0c\u62ff\u4e86\u5c31\u4ed8\u51fa\u4ee3\u4ef7\uff0c\u83b7\u5f97\u6536\u76ca\uff0c\u6211\u4eec\u7528f[ i ][ j ]\u8868\u793a\u7b2ci\u4e2a\u7269\u4f53\uff0c\u5728j\u9650\u5ea6\u5185\u6240\u80fd\u83b7\u5f97\u7684\u6700\u5927\u6536\u76ca\uff0c\u52a8\u89c4\u65b9\u7a0b\uff1a<\/p>\n

f[i][j]=max(f[i-1][j],f[i-1][j-cst[i]]+val[i]),j>=cst[i]<\/code><\/p>\n

\u5176\u63cf\u8ff0\u5185\u5bb9\u662f\u5bf9\u4e8e\u7b2ci\u4e2a\u7269\u54c1\u7684\u6700\u5927\u6536\u76ca\uff0c\u53d6\u51b3\u4e8e\u62ff\u4e0d\u62ff\u4ed6\uff0c\u5982\u679c\u4e0d\u62ff\uff0c\u6536\u76ca\u4e0e\u4e0a\u4e00\u4e2a\u7269\u54c1\u7684\u72b6\u6001\u76f8\u540c\uff0c\u53cd\u4e4b\u5982\u679c\u62ff\u4e86\uff0c\u6b64\u65f6\u6536\u76ca\u5c31\u662f\u4ed8\u51fa\u4ee3\u4ef7\u540e\u7d2f\u52a0\u4e00\u4e2ai\u7269\u54c1\u7684\u6536\u76ca\u503c<\/p>\n

\u6211\u4eec\u53d1\u73b0\uff0c\u4e0a\u8ff0\u52a8\u89c4\u65b9\u7a0b\u7684\u4f9d\u8d56\u5173\u7cfb\u662f\u4e00\u4e2a\u70b9\u4f9d\u8d56\u5176\u4e0a\u65b9\u548c\u5de6\u4e0a\u65b9\u7684\u70b9\uff0c\u8fd9\u6837\u6211\u4eec\u53ef\u4ee5\u5c06\u6570\u7ec4\u538b\u7f29\u6210\u4e24\u884c\uff0c\u7528\u53d6\u6a21\u64cd\u4f5c\u63a7\u5236\u5f53\u524d\u884c\u548c\u4e0a\u4e00\u884c<\/p>\n

f[i\\%2][j]=max\\{f[(i+1)\\%2][j],f[(i+1)\\%2][j-cst[i]]+val[i]\\},j>=cst[i]<\/code><\/p>\n

\u6211\u4eec\u8fd8\u53ef\u4ee5\u7ee7\u7eed\u8003\u8651\uff0c\u5982\u679c\u4e00\u4e2a\u70b9\u53ea\u662f\u4f9d\u8d56\u4e0a\u65b9\u7684\u70b9\uff08\u539f\u59cb\u72b6\u6001\uff09\u548c\u5de6\u4e0a\u65b9\u7684\u70b9\uff08\u5de6\u8fb9\u70b9\u7684\u539f\u59cb\u72b6\u6001\uff09\uff0c\u6211\u4eec\u4e0d\u59a8\u53ea\u7528\u4e00\u4e2a\u4e00\u7ef4\u6570\u7ec4\u6765\u50a8\u5b58\u4fe1\u606f\uff0c\u8fd9\u6837\u5728\u8fdb\u884c\u6bcf\u4e00\u8f6e\u64cd\u4f5c\u65f6\uff0c\u6bcf\u4e2a\u70b9\u90fd\u662f$f[i-1][j]$\u7684\u72b6\u6001\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u4f9d\u8d56\u5173\u7cfb\u6210\u7acb\uff0c\u6211\u4eec\u4ece\u8fd9\u4e2a\u6570\u7ec4\u7684\u53f3\u8fb9\u5411\u5de6\u64cd\u4f5c<\/p>\n

\u8fd9\u662f\u7ec8\u6781\u7248\uff1a f[j]=max(f[j],f[j-cst[i]]),j>=cst[i]<\/code><\/p>\n

\u4ee3\u7801\u662f\u8fd9\u4e2a\u6837\u5b50\u7684\uff1a<\/p>\n

int f[maxV],cst[maxn],val[maxn],V,n;\nint main(){\n    sf("%d%d",&V,&n);\n        for(int i=1;i<=n;i++)\n        sf("%d%d",&cst[i],&val[i]);\n\n    memset(f,0,sizeof(f));\n    for(int i=1;i<=n;i++)\n        for(int j=V;j>=cst[i];j--)\n            f[j]=max(f[j],f[j-cst[i]]+val[i]);\n\n    pf("%d",f[V]);\n    return 0;\n}<\/code><\/pre>\n
\u8fd9\u4fbf\u662f\u7ecf\u5178\u80cc\u5305\u95ee\u9898\u4e86\uff0c\u800c\u597d\u6d88\u606f\u662f\u8fd9\u79cd\u95ee\u9898\u57fa\u672c\u4e0a\u4e0d\u80af\u8003\u5230\uff0c\u51fa\u9898\u7684\u7272\u53e3\u4eec\u81f3\u5c11\u4e5f\u4f1a\u51fa\u5f62\u5982P1858\u8fd9\u7c7b\u5347\u7ea7\u7248\u95ee\u9898<\/p>\n
\u9898\u76ee\u5927\u610f\uff1a\u5728\u7ecf\u5178\u80cc\u5305\u95ee\u9898\u4e2d\uff0c\u89c4\u5b9a\u80cc\u5305\u5fc5\u987b\u88c5\u6ee1\uff0c\u6c42\u524dk\u4f18\u89e3\u4e4b\u548c<\/p>\n
\u6211\u4eec\u4e0d\u53ef\u80fd\u518d\u7528\u4e00\u7ef4\u6570\u7ec4\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u4e86\uff0c\u4e0d\u8fc7\u501f\u7528\u5176\u601d\u8def\uff1a\u539f\u6765f[ j ]\u8868\u793a\u7a7a\u95f4\u4e3aj\u65f6\u7684\u6700\u5927\u6536\u76ca\uff0c\u6211\u4eec\u589e\u52a0\u4e00\u7ef4\uff0c\u7528f[ j ][ k ]\u6765\u8868\u793a\u7a7a\u95f4\u4e3aj\u65f6\u7684\u7b2ck\u5927\u6536\u76ca\uff0c\u90a3\u4e48f[ j ][ k ]\u6240\u4f9d\u8d56\u7684\u5b50\u95ee\u9898\u5c06\u4f1a\u662f\u96c6\u5408{f[ j ][]}\u4e0e\u96c6\u5408{f[ j-cst[ i ] ][]}\u4e86\uff0c\u56e0\u4e3a\u8be5\u4f4d\u7f6e\u6bcf\u4e00\u4e2a\u89e3\u90fd\u6709\u53ef\u80fd\u66f4\u65b0\u4f60\u7684\u6bcf\u4e00\u4e2a\u89e3\uff0c\u4e0a\u4ee3\u7801\uff1a<\/p>\n
int f[maxV][maxk],cst[maxn],val[maxn],k,V,n;\nint main(){\n    sf("%d%d%d",&k,&V,&n);\n    for(int i=1;i<=n;i++)\n        sf("%d%d",&cst[i],&val[i]);\n    \/\/f[i][j]\u8868\u793ai\u4f53\u79ef\u4e0b\u7b2cj\u4f18\u89e3\uff08\u6536\u76ca\n\n    memset(f,0x83,sizeof(f));\n    f[0][1]=0;\/\/\u5fc5\u987b\u88c5\u6ee1\u7684\u521d\u59cb\u5316\n\n    int a[maxn];\/\/\u4e34\u65f6\u5b58\u653e\u6570\u636e\u7528\u7684\n    for(int i=1;i<=n;i++)\n        for(int j=V;j>=cst[i];j--){\/\/\u524d\u9762\u5b8c\u5168\u4e00\u81f4\n            int p=1,q=1;\/\/p\u4e0d\u4e70\uff0cq\u4e70\n            for(int l=1;l<=k;l++)\/\/\u7528l\u53bb\u5217\u4e3e\u6bcf\u4e00\u4e2a\u89e3\n                if(f[j][p]>f[j-cst[i]][q]+val[i])\n                    a[l]=f[j][p++];\n                else\n                    a[l]=f[j-cst[i]][q++]+val[i];\n            for(int l=1;l<=k;l++)\n                f[j][l]=a[l];\/\/\u8fd9\u91cc\u662f\u7b54\u6848\n        }\n\n    int ans=0;\n    for(int i=1;i<=k;i++)\n        ans+=f[V][i];\n    pf("%d",ans);\n\n    return 0;\n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
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