POJ 1273 最大流 Dinic

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题目链接

思路

求最大流，运用Dinic算法，先求分层图，然后用多次DFS求出增广路，把每次增广路的中的最小值相加即为最大流。

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#include <iostream>
#include <algorithm>
#include <string>
#include <cstring>
#include <queue>
using namespace std;
const int maxn = 10005;
const int inf = 0x3f3f3f3f;
typedef long long ll;
int head[maxn];
struct edge
{
    int v,w,next;
} edge[10005];
bool vis[10005];
int tot;
int deep[maxn];
int bfs(int s, int t)
{
    queue<int>Q;
    memset(deep, 0, sizeof(deep));
    deep[s] = 1;
    Q.push(s);
    while(!Q.empty())
    {
        int u = Q.front();
        Q.pop();
        for(int k = head[u]; k != -1; k = edge[k].next)
        {

            int v = edge[k].v;
            int w = edge[k].w;
            if(deep[v] == 0 && w > 0)
            {
                deep[v] = deep[u] + 1;
                Q.push(v);
            }
        }
    }
    if(deep[t] == 0)
        return 0;
    return 1;
}
void add(int u,int v, int w)
{
    edge[tot].v = v;
    edge[tot].w = w;
    edge[tot].next = head[u];
    head[u] = tot;
    tot++;
}
int t;
int dfs(int s, int dis)
{
    if(s == t)
        return dis;
    for(int k = head[s]; k != -1; k = edge[k].next)
    {
        int v = edge[k].v;
        int w = edge[k].w;
        if(deep[v] == deep[s] + 1 && w > 0)
        {
            int d = dfs(v,min(w, dis));
            if(d > 0)
            {
                edge[k].w -= d;
                edge[k^1].w += d;
                return d;
            }
        }
    }
    return 0;
}
int main()
{
    int n, m,u,v,w;
    while(cin >> m >> n)
    {
        tot = 0;
        t = n;
        memset(head, -1, sizeof(head));
        for(int i = 1; i <= m; ++i)
        {
            scanf("%d %d %d",&u,&v,&w);
            add(u,v,w);
            add(v,u,0);
        }
        ll sum = 0;
        while(bfs(1,n))
        {
            while(int d = dfs(1, inf))
                sum += d;
        }
        cout << sum << '\n';
    }
}