hdu - 4975 - A simple Gaussian elimination problem.（最大流量）

意甲冠军：要在N好M行和列以及列的数字矩阵和，每个元件的尺寸不超过9，询问是否有这样的矩阵，是独一无二的N(1 ≤ N ≤ 500) , M(1 ≤ M ≤ 500)。

主题链接：http://acm.hdu.edu.cn/showproblem.php?

pid=4975

——>>方法如：http://blog.csdn.net/scnu_jiechao/article/details/40658221

先做hdu - 4888，再来做此题的时候，感觉这题好 SB 呀。将代码提交后自己就 SB 了。咋 TLE 了？？

此题卡时间比較严。。能够在判环的地方优化一下4888的代码。由于原选建好的图中的行到列的边，在判环的时候，每条边会被判 (N - 1) * (M - 1) + 1 次，假设先对残量网络又一次建图，那么就仅仅会在建图的时候被判一次。差距甚远。

注：输入开挂会RE。猜想输入数据中有负数。。

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>

using std::min;
using std::queue;

const int MAXN = 500 * 2 + 10;
const int MAXM = 500 * 500 + 2 * MAXN;
const int INF = 0x3f3f3f3f;

struct EDGE
{
    int from;
    int to;
    int cap;
    int flow;
    int nxt;
} edge[MAXM << 1];

int N, M, kase;
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].from = u;
    edge[ecnt].to = v;
    edge[ecnt].cap = cap;
    edge[ecnt].flow = 0;
    edge[ecnt].nxt = hed[u];
    hed[u] = ecnt++;
    edge[ecnt].from = v;
    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;
}

int ReadInt()
{
    int ret = 0;
    char ch;

    while ((ch = getchar()) && ch >= '0' && ch <= '9')
    {
        ret = ret * 10 + ch - '0';
    }

    return ret;
}

void Read()
{
    int r, c;
    int rsum = 0, csum = 0;

    scanf("%d%d", &N, &M);
    S = 0;
    T = N + M + 1;
    getchar();
    for (int i = 1; i <= N; ++i)
    {
//        r = ReadInt();
        scanf("%d", &r);
        rsum += r;
        AddEdge(S, i, r);
    }
    for (int i = 1; i <= M; ++i)
    {
//        c = ReadInt();
        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, 9);
        }
    }
}

void CheckPossible()
{
    if (impossible) return;
    if (Dinic() != sum)
    {
        impossible = true;
    }
}

void AddEdge(int u, int v)
{
    edge[ecnt].to = v;
    edge[ecnt].nxt = hed[u];
    hed[u] = ecnt++;
}

void ReBuild()
{
    memset(hed, -1, sizeof(hed));
    int total = ecnt;
    ecnt = 0;
    for (int e = 0; e < total; ++e)
    {
        if (edge[e].cap > edge[e].flow)
        {
            AddEdge(edge[e].from, edge[e].to);
        }
    }
}

bool vis[MAXN];
bool CheckCircle(int x, int f)
{
    vis[x] = true;
    for (int e = hed[x]; e != -1; e = edge[e].nxt)
    {
        int v = edge[e].to;
        if (v != f)
        {
            if (vis[v]) return true;
            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()
{
    printf("Case #%d: ", ++kase);
    if (impossible)
    {
        puts("So naive!");
    }
    else if (bUnique)
    {
        puts("So simple!");
    }
    else
    {
        puts("So young!");
    }
}

int main()
{
    int T;

    scanf("%d", &T);
    while (T--)
    {
        Init();
        Read();
        CheckPossible();
        ReBuild();
        CheckUnique();
        Output();
    }

    return 0;
}