{"id":120,"date":"2010-08-19T08:32:25","date_gmt":"2010-08-19T00:32:25","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=120"},"modified":"2012-03-03T19:35:46","modified_gmt":"2012-03-03T11:35:46","slug":"zoj-1994-budget","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/zoj-1994-budget\/","title":{"rendered":"ZOJ 1994. Budget"},"content":{"rendered":"<h3>Brief description :<\/h3>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u77e9\u9635\u7684\u5404\u79cd\u9650\u5236\uff0c\u95ee\u662f\u5426\u5b58\u5728\u53ef\u884c\u89e3\u3002<br \/>\n<!--more--><\/p>\n<h3>Analyse :<\/h3>\n<p>&#8230; \u8fde\u8fb9\u6784\u56fe\uff0c\u8f6c\u5316\u6210\u6709\u4e0a\u4e0b\u754c\u7684\u6d41\u7f51\u7edc\u662f\u5426\u5b58\u5728\u53ef\u884c\u6d41\u7684\u95ee\u9898\u3002<\/p>\n<pre lang=\"cpp\" file=\"ZOJ_1994.cpp\">\r\n\/*\r\n    Author: xiaodao\r\n    Prob: ZOJ 1994. \/ POJ 2396. Budget\r\n    Status: Accepted\r\n    Tags: Network-Flow, Dinitz\r\n    Last modify: GMT +8 Aug.19th 08:13\r\n*\/\r\n\r\n#include <iostream>\r\n#include <cstdio>\r\n#include <cstring>\r\n#include <vector>\r\nusing namespace std;\r\nconst int INF = 0x7fffffff;\r\nconst int ROW = 201, COL = 21;\r\nconst int N = ROW*COL+ROW+COL+4, M = 4000000;\r\n\r\n\r\nstruct edge{\r\n    int v, c;\r\n    void insert(int, int);\r\n};\r\n\r\nstruct node{\r\n    vector<int> adj;\r\n    int D;\r\n};\r\n\r\nstruct network_flow{\r\n    node V[N+1]; edge E[M+1];\r\n    int edge_count, max_flow, necessary_flow;\r\n    int n, m, s, t;\r\n    void init();\r\n    void add_edge(int, int, int);\r\n    void add_edge(int, int, int, int);\r\n    void bfs();\r\n    void Dinitz();\r\n};\r\n\r\nint _r(int x){\r\n    return x ^ 1;\r\n}\r\n\r\n\r\nvoid edge::insert(int a, int b){\r\n    v = a; c = b;\r\n};\r\n\r\nvoid network_flow::add_edge(int x, int y, int c){\r\n    V[x].adj.push_back(edge_count); E[edge_count++].insert(y, c);\r\n    V[y].adj.push_back(edge_count); E[edge_count++].insert(x, 0);\r\n}\r\n\r\nvoid network_flow::add_edge(int x, int y, int l, int r){\r\n    add_edge(x, y, r-l); add_edge(s, y, l); add_edge(x, t, l);\r\n    necessary_flow += l;\r\n}\r\n\r\nvoid network_flow::bfs(){\r\n    int Q[N], head, tail;\r\n    for (int i=1;i<=n;i++) V[i].D = -1; \/\/memset(V.D, -1, sizeof(V.D));\r\n    head = 0; tail = 1; Q[0] = s; V[s].D = 0;\r\n\r\n    int u;\r\n    while (head<tail){\r\n        u = Q[head];\r\n        for (size_t i=0;i<V[u].adj.size();i++){\r\n            edge &#038;arc = E[V[u].adj[i]];\r\n            if (V[arc.v].D==-1 &#038;&#038; arc.c!=0){\r\n                Q[tail] = arc.v; V[arc.v].D = V[u].D + 1;\r\n                if (arc.v == t) return;\r\n                tail++;\r\n            }\r\n        }\r\n        head++;\r\n    }\r\n}\r\n\r\nvoid network_flow::Dinitz(){\r\n    max_flow = 0;\r\n    E[M].v = s;\r\n\r\n    bfs();\r\n    while (V[t].D!=-1){\r\n        int stack[n+1], cur[n+1], top = 0;\r\n        memset(cur, 0, sizeof(cur));\r\n        stack[0] = M;\r\n\r\n        int u; size_t i;\r\n        while (top!=-1){\r\n            u = E[stack[top]].v;\r\n            if (u == t){\r\n                int delta = INF, handle;\r\n                for (int i=1;i<=top;i++){\r\n                    edge &#038;arc = E[stack[i]];\r\n                    if (arc.c < delta){\r\n                        delta = arc.c;\r\n                        handle = i;\r\n                    }\r\n                }\r\n                max_flow += delta;\r\n                for (int i=1;i<=top;i++){\r\n                    E[stack[i]].c -= delta;\r\n                    E[_r(stack[i])].c += delta;\r\n                }\r\n                top = handle-1;\r\n                continue;\r\n            }\r\n\r\n            for (i=cur[u];i<V[u].adj.size();i++){\r\n                edge &#038;arc = E[V[u].adj[i]];\r\n                if (V[arc.v].D == V[u].D + 1 &#038;&#038; arc.c!=0) break;\r\n            }\r\n\r\n            if (i == V[u].adj.size()){\r\n                V[u].D = -1, top--;\r\n            }\r\n            else {\r\n                cur[u] = i + 1;\r\n                stack[++top] = V[u].adj[i];\r\n            }\r\n        }\r\n        bfs();\r\n    }\r\n}\r\n\r\n\r\n\r\nvoid network_flow::init(){\r\n    necessary_flow = 0; edge_count = 0;\r\n    for (int i=0;i<=N;i++) V[i].adj.clear();\r\n}\r\n\r\n\r\n\r\n\r\n\r\n\r\nint L[ROW][COL], R[ROW][COL];\r\nint *h1[ROW][COL], *h2[ROW][COL];\r\nint necessary_flow, sum_row, sum_column;\r\nint r, c;\r\n\r\nnetwork_flow G;\r\n\r\n\r\nint row(int x){\r\n    return r*c+c+x;\r\n}\r\n\r\nint column(int y){\r\n    return r*c+y;\r\n}\r\n\r\nint A(int x, int y){\r\n   return *h1[x][y] + *h2[x][y];\r\n}\r\n\r\n\r\nbool error(){\r\n    if (sum_column != sum_row) return true;\r\n    for (int i=1;i<=r;i++)\r\n        for (int j=1;j<=c;j++)\r\n            if (L[i][j]>R[i][j]) return true;\r\n    return false;\r\n}\r\n\r\n\r\n\r\n\r\nvoid load(network_flow &G){\r\n    G.init(); sum_row = sum_column = 0;\r\n\r\n    int s, t;\r\n    scanf(\"%d%d\", &r, &c);\r\n    s = r * c + r + c + 1; t = s + 1;\r\n    G.s = 0; G.n = G.t = t + 1;\r\n\r\n\r\n\r\n    int cc;\r\n    for (int i=1;i<=r;i++){\r\n        scanf(\"%d\", &#038;cc);\r\n        G.add_edge(s, row(i), cc, cc);\r\n        sum_row += cc;\r\n    }\r\n\r\n    for (int i=1;i<=c;i++){\r\n        scanf(\"%d\", &#038;cc); G.add_edge(column(i), t, cc, cc);\r\n        sum_column += cc;\r\n    }\r\n\r\n    for (int i=1;i<=r;i++)\r\n        for (int j=1;j<=c;j++)\r\n            L[i][j] = 0, R[i][j] = INF;\r\n\r\n    int a, b; char ccc; int d;\r\n    int a0, b0, ar, bc;\r\n\r\n    scanf(\"%d\", &#038;cc);\r\n    for (int i=0;i<cc;i++){\r\n        scanf(\" %d %d %c %d\", &#038;a, &#038;b, &#038;ccc, &#038;d);\r\n        if (a == 0) a0 = 1, ar = r; else a0 = ar = a;\r\n        if (b == 0) b0 = 1, bc = c; else b0 = bc = b;\r\n        for (a=a0;a<=ar;a++)\r\n            for (b=b0;b<=bc;b++){\r\n                if (ccc=='>') L[a][b] = max(L[a][b], d+1);\r\n                else if (ccc=='<') R[a][b] = min(R[a][b], d-1);\r\n                else L[a][b] = max(L[a][b], d), R[a][b] = min(R[a][b], d);\r\n            }\r\n    }\r\n\r\n    for (int i=1;i<=r;i++)\r\n        for (int j=1;j<=c;j++){\r\n            G.add_edge(row(i), (i-1)*c+j, L[i][j], R[i][j]);\r\n            h1[i][j] = &#038;G.E[G.edge_count-3].c;\r\n            h2[i][j] = &#038;G.E[G.edge_count-5].c;\r\n        }\r\n\r\n\r\n    for (int i=0;i<r;i++)\r\n        for (int j=1;j<=c;j++)\r\n            G.add_edge(i*c+j, (i+1)*c+j, INF);\r\n\r\n    G.add_edge(t, s, INF);\r\n}\r\n\r\nbool judge(){\r\n    for (int i=1;i<=r;i++)\r\n        for (int j=1;j<=c;j++)\r\n            if (A(i, j)<L[i][j] || A(i, j)>R[i][j]) return false;\r\n    return true;\r\n}\r\n\r\n\r\n\r\nint main(){\r\n    \/\/freopen(\"budget.in\", \"r\", stdin);\r\n    \/\/freopen(\"budget.out\", \"w\", stdout);\r\n    int T; cin >> T;\r\n    for (int i=0;i<T;i++){\r\n        load(G); if (error()) printf(\"IMPOSSIBLE\\n\");\r\n        else {\r\n            G.Dinitz();\r\n            if (G.max_flow != G.necessary_flow) printf(\"IMPOSSIBLE\\n\");\r\n            else {\r\n                for (int i=1;i<=r;i++){\r\n                    for (int j=1;j<c;j++)\r\n                        printf(\"%d \", A(i, j));\r\n                    printf(\"%d\\n\", A(i, c));\r\n                }\r\n            }\r\n            \/\/cout << (judge()?\"Accepted\":\"Wrong answer!\") << endl;\r\n        }         \r\n        if (i!=T-1) printf(\"\\n\");\r\n        \/\/printf(\"\\n\");        \r\n    }\r\n}\r\n<\/pre>\n<h3>Further discussion :<\/h3>\n<p>\u6211\u662f\u7167\u7740\u4e00\u4efd\u9898\u5355\u5f80\u4e0b\u505a\u7684\uff0c\u56e0\u6b64\u8fd8\u6ca1\u8bfb\u9898\u5c31\u5f00\u59cb\u7f51\u7edc\u6d41\u4e86\uff0c\uff08\u4f46\u662f\u8fd9\u9898\u5c45\u7136\u628a\u81ea\u5df1\u5305\u88f9\u6210\u4e00\u4e2a\u77e9\u9635\u3002\u3002\u5176\u5b9e\u8981\u662f\u6570\u636e\u89c4\u6a21\u7a0d\u5fae\u518d\u7ed9\u6211\u4e00\u70b9\u7684\u8bdd\uff0c\u6211\u5c31\u8981\u60f3\u7740\u641c\u7d22\u526a\u679d\u4e86\u3002\u3002\uff09\u4e00\u6b21\u6027\u7f16\u5199\u90a3\u4e48\u957f\u7684\u4ee3\u7801\uff0c\u8fd8\u662f\u86ee\u4ee4\u6211\u5934\u75db\u7684\uff0c\u597d\u5728\u786c\u7740\u5934\u76ae\u5199\u4e0b\u6765\u4e86...<\/p>\n<p>\u5728\u6211\u5199\u8fd9\u9898\u4e4b\u524d\uff0c\u5305\u62ec\u73b0\u5728\uff0c\u6211\u4e00\u76f4\u8ba4\u4e3a\u53ef\u4ee5\u7ed9\u8fd9\u9898\u5f00\u53d1\u4e00\u4e2a\u7279\u5236\u7b97\u6cd5\uff0c\u56e0\u4e3a\u6bcf\u884c\u548c\u4e0d\u662f\u56fa\u5b9a\u7684\u4e48\u3002\uff08\u800c\u4e14\u6ce8\u610f\u5230\u5440\uff0c\u884c\u5217\u4e0d\u4e00\u6837\u591a\u5462\u3002#\uff09\u3002\u3002\u53ef\u4ee5\u50cf Relabel_to_Front \u91cc\u90a3\u6837\u7ef4\u62a4\u4e00\u4e2a\u524d\u7f6e\u6d41\uff08preflow\uff09\uff0c\u7136\u540e ....\uff08\u5e76\u4e14\u8fd9\u4e2a\u7f51\u7edc\u7684\u6df1\u5ea6\u5f88\u6d45\uff0c\u5e94\u8be5\u8fd9\u4e9b\u90fd\u662f\u53ef\u4ee5\u518d\u60f3\u60f3\u7684\u5730\u65b9\uff0c\u4e0d\u8fc7\u6211\u8fd8\u662f\u5148\u5199\u4e00\u4e2a\u6bd4\u8f83\u683c\u5f0f\u5316\u7684\u5148A\u4e86\u4ed6\u518d\u8bf4\uff0c\u81f3\u4e8e\u63a5\u4e0b\u6765\u6211\u60f3\u8fd8\u6709\u4e00\u4e9b\u5de5\u4f5c...\uff09<\/p>\n<p>1. \u6b64\u9898\u662f\u4e00\u4e2a\u7a00\u758f\u56fe\uff0c\u56e0\u6b64\u4e0d\u53ef\u4ee5\u7528\u90bb\u63a5\u77e9\u9635\uff0c\u4f46\u8fd9\u6837\u5c31\u4f1a\u5e26\u6765\u5f88\u591a\u95ee\u9898\uff0c\u6bd4\u5982\u8bf4\u4e0d\u80fd\u50cf\u4e4b\u524d\u90a3\u6837\u7b80\u5355\u7684\u5904\u7406\u53cd\u5411\u8fb9\u3002\uff08\u4e0d\u8fc7\u8fd9\u51e0\u5929\u51c6\u5907\u7f51\u7edc\u6d41\uff0c\u6211\u4e5f\u79ef\u7d2f\u4e86\u4e00\u4e9b\u4e0d\u540c\u7684\u7ecf\u9a8c\uff0c\u5404\u65b9\u9762\u7684\u90fd\u6709\u4e00\u4e9b\uff0c\u518d\u505a\u51e0\u9053\u7ec3\u4e60\u4e4b\u540e\u6211\u4f1a\u5199\u4e2a\u5c0f\u7ed3\u3002\uff09<\/p>\n<p>2. \u5bf9\u4e8e\u6761\u4ef6\u7684\u5904\u7406\uff0c\u6211\u5f00\u4e86 L, R \u4e24\u4e2a\u6570\u7ec4\uff0c\u611f\u89c9\u4ee3\u7801\u8fd8\u662f\u5f88\u6574\u9f50\u7684\u3002\uff08\u554a\uff0cthis-> \u6307\u9488\u53ef\u4ee5\u7701\u7565\u5440\u3002\u3002\uff09\u5199\u6210\u8fd9\u6837\u4ee5\u540e\uff0c\u5927\u6982\u6574\u4e2a\u6548\u7387\u4f1a\u6162 4 \u4e2a\u5e38\u6570\u500d\uff0c\u4e0d\u8fc7\u8003\u8651\u5230\u73b0\u5728\u5e76\u4e0d\u662f\u7279\u522b\u8ffd\u6c42\u901f\u5ea6\uff0c\u6240\u4ee5\u5c31\u5f53\u770b\u4e0d\u89c1\u4e86\uff0c\u8fb9\u76ee\u5f55\u5148\u662f\u5355\u72ec\u653e\u5728\u4e00\u4e2a\u72ec\u7acb\u7684\u6570\u7ec4\u91cc\u7684\uff0c\u7136\u540e\u90bb\u63a5\u8868\u91cc\u5728\u5355\u72ec\u5b58\u7d22\u5f15\u3002\uff08\u8fd9\u6837\u7684\u4e00\u4e2a\u597d\u5904\u662f\uff0c\u53ef\u4ee5\u7528\u4e00\u6b65\u6807\u51c6\u7684\u5f02\u6216\u8fd0\u7b97\u83b7\u5f97\u53cd\u5411\u8fb9\u3002\uff09\uff08\u5173\u4e8e\u8fd9\u70b9\uff0c\u8bf7\u53c2\u8003\u4ee3\u7801\u7684\u7b2c 216 \u81f3 217 \u884c\u3002\u3002\u30020(\u2229_\u2229)o \uff09<\/p>\n<p>3. \u6211\u5728\u5f00\u59cb\u7f51\u7edc\u6d41\u4e4b\u524d\u505a\u4e86\u4e00\u4e9b\u5fc5\u8981\u6027\u5224\u65ad\uff0c\u6bd4\u5982\u8bf4\u5982\u679c\u4e0d\u8fd9\u4e48\u505a\u7684\u8bdd\uff0c\u6709\u53ef\u80fd\u6c42\u51fa\u8d1f\u6570\u5440\u3002\u8fd8\u6709\u4e00\u4e9b\u95ee\u9898\u6709\u4eba\u8d28\u7591\u8fd9\u9898\u7684 Special_judge \uff0c\u4e8e\u662f\u6211\u81ea\u5df1\u5199\u4e86\u4e2a\u68c0\u6d4b\u7684\u5b50\u7a0b\u5e8f\u3002\uff08\u4e0d\u8fc7\u8fd9\u9898WA\u7684\u539f\u56e0\u4e5f\u8bb8\u662f\u4f60\u884c\u5c3e\u7559\u6709\u591a\u4f59\u7684\u4e00\u4e2a\u7a7a\u683c\u6216\u8005\u6700\u540e\u591a\u6253\u5370\u4e00\u4e2a\u7a7a\u683c\u3002\u7c7b\u4f3c\u7684\u60c5\u51b5\u5728\u4e24\u4e2a OJ \u91cc\u90fd\u4e0d\u4f1a\u62a5 PE \u4e86\uff0c\u8981\u7279\u522b\u5c0f\u5fc3\u624d\u662f\uff0c\u4f8b\u5982\u8fd9\u4e00\u9898\uff0c\u5982\u679c\u6211\u628a\u6700\u540e\u8f93\u51fa\u7a7a\u884c\u7684\u90a3\u4e2a\u8bed\u53e5\u6362\u6210\u4e0d\u52a0\u6700\u540e\u4e00\u4e2a\u5224\u65ad\u7684\uff0c\u90a3\u4e48\u5728 POJ \u4e0a\u4ecd\u7136\u53ef\u4ee5 AC\uff0c\u4f46 ZOJ \u5c31 WA \u4e86\uff0c\u8fd9\u6837\u7684\u539f\u56e0\u975e\u5e38\u6d6a\u8d39\u65f6\u95f4\uff0c\uff08\u7279\u522b\u662f\u6211\u4eec\u603b\u8981\u770b\u5230 AC \u4ee5\u540e\u611f\u89c9\u4e00\u5757\u77f3\u5934\u843d\u4e86\u5730\uff09\u56e0\u6b64\u5728\u6700\u540e\u4e00\u6761\u7279\u522b\u6307\u51fa\u3002\uff09<\/p>\n<h3>External link :<\/h3>\n<p>http:\/\/acm.pku.edu.cn\/JudgeOnline\/problem?id=2396<br \/>\nhttp:\/\/acm.zju.edu.cn\/onlinejudge\/showProblem.do?problemId=994<br \/>\nhttp:\/\/hi.baidu.com\/forsona\/blog\/item\/662c07d5401fd209a18bb709.html<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Brief description : \u7ed9\u5b9a\u4e00\u4e2a\u77e9\u9635\u7684\u5404\u79cd\u9650\u5236\uff0c\u95ee\u662f\u5426\u5b58\u5728\u53ef\u884c\u89e3\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[1],"tags":[],"class_list":["post-120","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-1W","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/120","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=120"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/120\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=120"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=120"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}