{"id":1173,"date":"2023-12-25T20:48:33","date_gmt":"2023-12-25T12:48:33","guid":{"rendered":"http:\/\/www.forillusion.com\/?p=1173"},"modified":"2025-02-14T11:39:10","modified_gmt":"2025-02-14T03:39:10","slug":"basic-algorithms-training50-5-prefixsum-and-difference","status":"publish","type":"post","link":"https:\/\/www.forillusion.com\/index.php\/basic-algorithms-training50-5-prefixsum-and-difference\/","title":{"rendered":"\u7b97\u6cd5\u57fa\u7840\u8bad\u7ec3 50 \u9898\uff08\u4e94\uff09\u524d\u7f00\u548c\u4e0e\u5dee\u5206"},"content":{"rendered":"\n

<\/div><\/p>\n\n\n\n

#JC0501. Subsequences Summing to Sevens S<\/h2>\n\n\n\n

\u9898\u76ee\u63cf\u8ff0<\/a><\/p>\n\n\n\n

\u5148\u5bf9\u8f93\u5165\u6570\u636e\u6c42\u524d\u7f00\u548c\uff0c\u540c\u65f6\u5c06\u524d\u7f00\u548c\u6a217\u3002\u4ece\u5934\u5f00\u59cb\u904d\u5386\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u6570\uff0c\u518d\u4ece\u672b\u5c3e\u5f80\u524d\u5bfb\u627e\uff0c\u627e\u5230\u548c\u6a217\u4e3a0\u7684\u6570\uff0c\u5e76\u8bb0\u5f55\u533a\u95f4\u957f\u5ea6\u3002\u76f4\u63a5\u8fd9\u6837\u4f1a\u5bfc\u81f4\u8d85\u65f6\u3002\u5b9e\u9645\u4e0a\u7531\u4e8e\u8bb0\u5f55\u524d\u7f00\u548c\u65f6\u8fdb\u884c\u4e86\u6a217\uff0c\u6240\u4ee5\u524d\u7f00\u548c\u53ea\u4f1a\u662f0-6\u4e2d\u7684\u6570\uff0c\u533a\u95f4\u5f00\u59cb\u4f4d\u7f6e\u7684\u6570\u76f8\u540c\u65f6\u533a\u95f4\u7684\u7ed3\u5c3e\u4e5f\u76f8\u540c\uff0c\u4f46\u662f\u540e\u904d\u5386\u7684\u5f00\u59cb\u4f4d\u7f6e\u533a\u95f4\u957f\u5ea6\u5fc5\u5b9a\u6bd4\u7b2c\u4e00\u6b21\u904d\u5386\u65f6\u7684\u77ed\uff0c\u6240\u4ee5\u53ef\u4ee5\u8bb0\u5f55\u4e0b\u5df2\u7ecf\u904d\u5386\u8fc7\u54ea\u4e9b\u533a\u95f4\u5f00\u59cb\u65f6\u7684\u6570\uff0c\u518d\u6b21\u9047\u5230\u76f8\u540c\u7684\u6570\u65f6\u8df3\u8fc7\u3002<\/p>\n\n\n\n

#include<bits\/stdc++.h>\nint n,x,ans,z;\nint a[500005],b[7];\nint main()\n{\n    ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);\n    CI n;\n    F(i,1,n)\n    {\n        CI x;\n        a[i]=(a[i-1]+x)%7;\n    }\n\n    F(i,1,n)\n        if (!b[a[i-1]])\n        {\n            b[a[i-1]]=1;\n            z++;\n            for (int j=n;j>=i+1&&(j-i+1)>ans;j--)\n            {\n                if ((a[j]-a[i-1]+7)%7==0)\n                {\n                    ans=j-i+1;\n                    break;\n                }\n            }\n            if (z==7) break;\n        }\n\n    CO ans L;\n    return 0;\n}<\/code><\/pre>\n\n\n\n
#JC0502. \u5730\u6bef<\/h2>\n\n\n\n
\u9898\u76ee\u63cf\u8ff0<\/a><\/p>\n\n\n\n
\u6b64\u9898\u5957\u7528\u4e8c\u7ef4\u5dee\u5206\u7684\u6a21\u7248\u5373\u53ef<\/p>\n\n\n\n
#include<bits\/stdc++.h>\nint n,m,a[10001][10001],d[10001][1001];\nint main()\n{\n    int x1,y1,x2,y2;\n    cin>>n>>m;\n    for (int i=1;i<=m;i++)\n    {\n        cin>>x1>>y1>>x2>>y2;\n        d[x1][y1]+=1;\n        d[x2+1][y1]-=1;\n        d[x1][y2+1]-=1;\n        d[x2+1][y2+1]+=1;\n    }\n\t\n    for (int i=1;i<=n;i++)\n    {\n        for (int j=1;j<=n;j++)\n        {\n            a[i][j] = a[i-1][j] + a[i][j-1] - a[i-1][j-1] + d[i][j];\n            cout<<a[i][j]<<\" \";\n        }\n    cout<<endl;\n    } \n    return 0;\n}\n<\/code><\/pre>\n\n\n\n
#JC0503. \u6fc0\u5149\u70b8\u5f39<\/h2>\n\n\n\n
\u9898\u76ee\u63cf\u8ff0<\/a><\/p>\n\n\n\n
\u5229\u7528\u4e8c\u7ef4\u524d\u7f00\u548c\u5373\u53ef\uff0c\u662f\u8f93\u5165\u7684\u5750\u6807\u8303\u56f4\u4ece0\u5f00\u59cb\uff0c\u4e3a\u4e86\u65b9\u4fbf\u8ba1\u7b97\uff0c\u7edf\u4e00\u5c06\u6240\u6709\u5750\u6807+1\uff0c\u8fd9\u6837\u5750\u6807\u5c31\u4ece1\u5f00\u59cb\u4e86\u3002\u540c\u65f6\u4f1a\u5b58\u5728\u591a\u4e2a\u76ee\u6807\u5904\u4e8e\u540c\u4e00\u4e2a\u5750\u6807\u7684\u60c5\u51b5\uff0c\u6240\u4ee5\u4e0d\u80fd\u76f4\u63a5\u5c06\u76ee\u6807\u4ef7\u503c\u8986\u76d6\u5230\u5730\u56fe\u4e0a\u800c\u8981\u7d2f\u52a0\u3002\u7136\u540e\u751f\u6210\u4e8c\u7ef4\u524d\u7f00\u548c\u6570\u7ec4\uff0c\u6700\u540e\u6839\u636e\u5de6\u4e0a\u89d2\u5750\u6807\u548cm\u503c\u904d\u5386\u6bcf\u4e00\u4e2a\u53ef\u80fd\uff0c\u8bb0\u5f55\u6700\u5927\u503c\u3002<\/p>\n\n\n\n
#include<bits\/stdc++.h>\nint n,m,a,b,c;\nint p[5003][5003],v;\nint main()\n{\n    \/\/ ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);\n    CI n>>m;\n    F(i,1,n)\n    {\n        CI a>>b>>c;\n        p[a+1][b+1]+=c;\n    }\n    F(i,1,5001)\n    {\n        F(j,1,5001)\n            p[i][j]=p[i][j]+p[i-1][j]+p[i][j-1]-p[i-1][j-1];\n    }\n    \n    F(i,0,5001-m)\n    {\n        F(j,0,5001-m)\n            v=max(v,p[i+m][j+m]-p[i][j+m]-p[i+m][j]+p[i][j]);\n    }\n    CO v L;\n    return 0;\n}<\/code><\/pre>\n\n\n\n
#JC0504. IncDec Sequence<\/h2>\n\n\n\n
\u9898\u76ee\u63cf\u8ff0<\/a><\/p>\n\n\n\n
\u8ba9\u6bcf\u4e2a\u6570\u90fd\u4e00\u6837\uff0c\u5373\u5bf9\u5e94\u7684\u5dee\u5206\u6570\u7ec4\u9664\u4e86\u7b2c\u4e00\u4e2a\uff0c\u5176\u4ed6\u90fd\u662f0\u3002\u6839\u636e\u5dee\u5206\u6570\u7ec4\u7684\u64cd\u4f5c\u65b9\u5f0f\uff0c\u4fee\u6539\u533a\u95f4[l,r]\u65f6d[l]+=c,d[r+1]-=c\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u533a\u95f4\u5f00\u59cb\u548c\u533a\u95f4\u7ed3\u5c3e\u7684\u8fd0\u7b97\u7b26\u76f8\u53cd\u3002\u6240\u4ee5\u4e3a\u4e86\u6c42\u51fa\u6700\u5c0f\u64cd\u4f5c\u6570\uff0c\u8981\u8ba9\u533a\u95f4\u5f00\u59cb\u548c\u7ed3\u5c3e\u7684\u5dee\u5206\u6570\u7b26\u53f7\u76f8\u53cd\uff0c\u8fd9\u6837\u4e00\u6b21\u64cd\u4f5c\u53ef\u4ee5\u6539\u53d8\u4e24\u4e2a\u5dee\u5206\u503c\uff0c\u76f4\u5230\u5176\u4e2d\u4e00\u4e2a\u7b26\u53f7\u5b8c\u5168\u88ab\u6d88\u6389\uff0c\u4e5f\u5c31\u662f\u53ea\u5269\u4e0b\u4e00\u79cd\u7b26\u53f7\u7684\u5dee\u5206\u503c\u4e86\uff0c\u8fd9\u65f6\u6bcf\u6b21\u64cd\u4f5c\u53ea\u80fd\u6539\u53d8\u4e00\u4e2a\u5dee\u5206\u503c\u3002\u5047\u8bbe\u4ece\u4e0b\u68072\u5f00\u59cb\u7684\u5dee\u5206\u6570\u7ec4\u4e2d\u6b63\u6570\u548c\u4e3asum1\uff0c\u8d1f\u6570\u548c\u7684\u7edd\u5bf9\u503c\u4e3asum2\uff0c\u5219\u533a\u95f4\u5f00\u59cb\u548c\u7ed3\u5c3e\u7684\u5dee\u5206\u6570\u7b26\u53f7\u76f8\u53cd\u7684\u64cd\u4f5c\u5171\u6709min(sum1,sum2)\u6b21\uff0c\u64cd\u4f5c\u5b8c\u540e\u53ea\u5269\u4e0b\u4e00\u79cd\u7b26\u53f7\u7684\u5dee\u5206\u503c\uff0c\u53e6\u4e00\u79cd\u7b26\u53f7\u7684\u5dee\u5206\u503c\u88ab\u5b8c\u5168\u6d88\u6389\uff0c\u4e8e\u662f\u8fd8\u9700\u8981\u8fdb\u884cmax(sum1,sum2)-min(sum1,sum2)=abs(sum1-sum2)\u6b21\u64cd\u4f5c\u3002\u6240\u4ee5\u603b\u5171\u662fmax(sum1,sum2)\u6b21\u64cd\u4f5c\u3002\u5bf9\u4e8e\u7b2c\u4e8c\u95ee\uff0c\u5047\u8bbesum1>sum2\uff0c\u5219\u8fdb\u884cmin(sum1,sum2)\u6b21\u64cd\u4f5c\u540e\u8d1f\u6570\u7684\u5dee\u5206\u503c\u88ab\u5168\u90e8\u6d88\u6389\uff0c\u53ea\u5269\u4e0b\u6b63\u5dee\u5206\u503c\u3002\u63a5\u4e0b\u6765\u7684sum1-sum2\u6b21\u64cd\u4f5c\u5c31\u662f\u5c06\u9664\u4e0b\u68071\u5916\u7684\u6b63\u5dee\u5206\u503c\u5168\u90e8\u6539\u4e3a0\u3002\u7531\u4e8e\u53ea\u5269\u4e0b\u6b63\u5dee\u5206\u503c\uff0c\u6240\u4ee5\u6574\u4e2a\u6570\u7ec4\u662f\u5355\u8c03\u9012\u589e\u7684\uff0c\u800c\u5c06\u5dee\u5206\u503c\u53d8\u4e3a0,\u7684\u8fc7\u7a0b\u5c31\u662f\u4e0d\u65ad\u8ba9\u540e\u9762\u5143\u7d20\u5411\u7b2c\u4e00\u4e2a\u5143\u7d20\u9760\u62e2\u3002\u8fd9\u65f6\u6709\u4e24\u79cd\u9760\u62e2\u65b9\u5f0f\uff0c\u7b2c\u4e00\u79cd\u662f\u5c06\u5927\u4e8e\u7b2c\u4e00\u4e2a\u6570\u7684\u5143\u7d20-1\uff0c\u7b2c\u4e8c\u79cd\u5c31\u662f\u5c06\u7b2c\u4e00\u4e2a\u6570\u4ee5\u53ca\u548c\u4ed6\u76f8\u7b49\u7684\u6570\u90fd+1\u3002\u4e8e\u662f\u5c31\u80fd\u5f97\u5230\u4e0d\u540c\u7684\u7ed3\u679c\u3002\u7531\u4e8e\u6bcf\u4e00\u6b21\u64cd\u4f5c\u90fd\u67092\u4e2d\u65b9\u6cd5\uff0c\u6240\u4ee5\u603b\u5171\u80fd\u5f97\u5230abs(sum1,sum2)+1\u79cd\u7ed3\u679c\u3002<\/p>\n\n\n\n
#include<bits\/stdc++.h>\nLL n,a[100005],d[100005],sum1,sum2;\r\nint main()\r\n{\r\n    \/\/ ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);\r\n    CI n;\r\n    F(i,1,n)\r\n    {\r\n        CI a[i];\r\n        d[i]=a[i]-a[i-1];\r\n    }\r\n    F(i,2,n)\r\n    {\r\n        if (d[i]>0) sum1+=d[i];\r\n        else sum2+=-d[i];\r\n    }\r\n    cout<<max(sum1,sum2)<<endl<<abs(sum1-sum2)+1<<endl;\r\n    return 0;\r\n}<\/code><\/pre>\n\n\n\n
#JC0505. \u6c34\u58f6<\/h2>\n\n\n\n
\u9898\u76ee\u63cf\u8ff0<\/a><\/p>\n\n\n\n
\u6b64\u9898\u5c31\u662f\u6c42\u957f\u5ea6\u4e3ak+1\u7684\u533a\u95f4\u548c\u7684\u6700\u5927\u503c\u4e3a\u591a\u5c11\u3002<\/p>\n\n\n\n
#include<bits\/stdc++.h>\r\nint n,k;\r\nLL x,p[1000006],ans;\r\nint main()\r\n{\r\n    \/\/ ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);\r\n    CI n>>k;\r\n    F(i,1,n)\r\n    {\r\n        CI x;\r\n        p[i]=p[i-1]+x;\r\n    }\r\n    F(i,1,n-k)\r\n        ans=max(p[i+k]-p[i-1],ans);\r\n    CO ans L;\r\n    return 0;\r\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
#JC0501. Subsequences Summing to Sevens S \u9898\u76ee\u63cf\u8ff0 \u5148\u5bf9\u8f93\u5165\u6570\u636e\u6c42\u524d\u7f00\u548c\uff0c\u540c\u65f6\u5c06\u524d\u7f00\u548c\u6a21 …<\/p>","protected":false},"author":1,"featured_media":1267,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,35],"tags":[12,34,22,39],"class_list":["post-1173","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-3","category-35","tag-12","tag-34","tag-22","tag-39"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1173","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=1173"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1173\/revisions"}],"predecessor-version":[{"id":1744,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1173\/revisions\/1744"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1267"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}