hdu - 4888 - Redraw Beautiful Drawings（最大流）

题意：给一个N行M列的数字矩阵的行和以及列和，每个元素的大小不超过K，问这样的矩阵是否存在，是否唯一，唯一则求出各个元素N(1 ≤ N ≤ 400) , M(1 ≤ M ≤ 400), K(1 ≤ K ≤ 40)。

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4888

——>>建图：

1）超级源S = 0，超级汇T = N + M + 1；

2）S到每个行和各连一条边，容量为该行行和；

3）每个行和到每个列和各连一条边，容量为K；

4）每个列和到 T 各连一条边，容量为该列列和。

一个行到所有列连边，为的是让该行分流多少给各个列，正是该行某列元素的大小。。

所以，如果 S 到 T 的最大流 == 所有元素的和，则说明有解。。

残量网络中的行列结点之间如果有长度 > 2 的环（自环长度为2，但无法调整流量），则说明这个环中的流量可以调整，使得达到最大流时该环上的流量不唯一，即矩阵不唯一。。

#include <cstdio>#include <cstring>#include <queue>#include <algorithm>using std::min;using std::queue;const int MAXN = 400 * 2 + 10;const int MAXM = 400 * 400 + 2 * MAXN;const int INF = 0x3f3f3f3f;struct EDGE{    int to;    int cap;    int flow;    int nxt;} edge[MAXM << 1];int N, M, K;int sum;int S, T;int hed[MAXN], ecnt;int cur[MAXN], h[MAXN];bool impossible, bUnique;void Init(){    impossible = false;    bUnique = true;    ecnt = 0;    memset(hed, -1, sizeof(hed));}void AddEdge(int u, int v, int cap){    edge[ecnt].to = v;    edge[ecnt].cap = cap;    edge[ecnt].flow = 0;    edge[ecnt].nxt = hed[u];    hed[u] = ecnt++;    edge[ecnt].to = u;    edge[ecnt].cap = 0;    edge[ecnt].flow = 0;    edge[ecnt].nxt = hed[v];    hed[v] = ecnt++;}bool Bfs(){    memset(h, -1, sizeof(h));    queue<int> qu;    qu.push(S);    h[S] = 0;    while (!qu.empty())    {        int u = qu.front();        qu.pop();        for (int e = hed[u]; e != -1; e = edge[e].nxt)        {            int v = edge[e].to;            if (h[v] == -1 && edge[e].cap > edge[e].flow)            {                h[v] = h[u] + 1;                qu.push(v);            }        }    }    return h[T] != -1;}int Dfs(int u, int cap){    if (u == T || cap == 0) return cap;    int flow = 0, subFlow;    for (int e = cur[u]; e != -1; e = edge[e].nxt)    {        cur[u] = e;        int v = edge[e].to;        if (h[v] == h[u] + 1 && (subFlow = Dfs(v, min(cap, edge[e].cap - edge[e].flow))) > 0)        {            flow += subFlow;            edge[e].flow += subFlow;            edge[e ^ 1].flow -= subFlow;            cap -= subFlow;            if (cap == 0) break;        }    }    return flow;}int Dinic(){    int maxFlow = 0;    while (Bfs())    {        memcpy(cur, hed, sizeof(hed));        maxFlow += Dfs(S, INF);    }    return maxFlow;}void Read(){    int r, c;    int rsum = 0, csum = 0;    S = 0;    T = N + M + 1;    for (int i = 1; i <= N; ++i)    {        scanf("%d", &r);        rsum += r;        AddEdge(S, i, r);    }    for (int i = 1; i <= M; ++i)    {        scanf("%d", &c);        csum += c;        AddEdge(i + N, T, c);    }    if (rsum != csum)    {        impossible = true;        return;    }    sum = rsum;    for (int i = 1; i <= N; ++i)    {        for (int j = M; j >= 1; --j)        {            AddEdge(i, j + N, K);        }    }}void CheckPossible(){    if (impossible) return;    if (Dinic() != sum)    {        impossible = true;    }}bool vis[MAXN];bool CheckCircle(int x, int f){    vis[x] = true;    for (int e = hed[x]; e != -1; e = edge[e].nxt)    {        if (edge[e].cap > edge[e].flow)        {            int v = edge[e].to;            if (v == f) continue;            if (vis[v]) return true;            else            {                if (CheckCircle(v, x)) return true;            }        }    }    vis[x] = false;    return false;}void CheckUnique(){    if (impossible) return;    memset(vis, 0, sizeof(vis));    for (int i = 1; i <= N; ++i)    {        if (CheckCircle(i, -1))        {            bUnique = false;            return;        }    }}void Output(){    if (impossible)    {        puts("Impossible");    }    else if (!bUnique)    {        puts("Not Unique");    }    else    {        puts("Unique");        for (int i = 1; i <= N; ++i)        {            for (int e = hed[i], j = 1; e != -1 && j <= M; e = edge[e].nxt, ++j)            {                printf("%d", edge[e].flow);                if (j < M)                {                    printf(" ");                }            }            puts("");        }    }}int main(){    while (scanf("%d%d%d", &N, &M, &K) == 3)    {        Init();        Read();        CheckPossible();        CheckUnique();        Output();    }    return 0;}