题目大意：

给你n个点，有m条边，让你求出这个图的最短路上的最小割，这个最小割。

解题思路：

直接求出最短路图然后dinic跑最小割就行。

我遇到的一些错误点：

1、用dinic算法求解最小割需要使用当前弧优化，否则会TLE

2、最短路图注意求最短路的时候，每个边都是长度为1，也就是说可以bfs求。千万不要把权值当成边长

3、构造最短路图注意不要重复构造

代码：

#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
#include <algorithm>
using namespace std;typedef struct node {int v, cap, nxt;node(int a = 0, int b = 0, int c = 0) {v = a; cap = b; nxt = c;}
}Edge;const int maxn = 1005;
const int maxm = 400005;
const int inf = 0x3f3f3f3f;Edge vec[maxm];
int cnt, vis[maxn], first[maxn];int s, t;
Edge edge[maxm];
int tot, cur[maxn], head[maxn], dis[maxn];void add(int u, int v, int cap) {edge[tot] = Edge(v, cap, head[u]);head[u] = tot++;edge[tot] = Edge(u, 0, head[v]);head[v] = tot++;
}
void addEdge(int u, int v, int w) {vec[cnt] = Edge(v, w, first[u]);first[u] = cnt++;vec[cnt] = Edge(u, w, first[v]);first[v] = cnt++;
}
void BFS(int n) {int x;queue<int> q;while (!q.empty()) q.pop();memset(vis, 0, sizeof(vis));q.push(1); vis[1] = 1;while (!q.empty()) {x = q.front(); q.pop();for (int i = first[x]; ~i; i = vec[i].nxt) {Edge &e = vec[i];if (!vis[e.v]) {vis[e.v] = vis[x] + 1;q.push(e.v);}}}
}
void BuildGraph(int n, int pre) {if (dis[n]) return;dis[n] = 1;for (int i = first[n]; ~i; i = vec[i].nxt) {Edge &e = vec[i];if (e.v != pre && vis[n] == vis[e.v] + 1) {add(e.v, n, e.cap);BuildGraph(e.v, n);}}
}
int bfs() {int x;queue<int> q;while (!q.empty()) q.pop();memset(dis, 0, sizeof(dis));dis[s] = 1; q.push(s);while (!q.empty()) {x = q.front(); q.pop();for (int i = head[x]; ~i; i = edge[i].nxt) {Edge &e = edge[i];if (e.cap && dis[e.v] == 0) {dis[e.v] = dis[x] + 1;q.push(e.v);}}}return dis[t];
}
int dfs(int x, int f) {int sum = 0;if (x == t) return f;for (int &i = cur[x]; ~i; i = edge[i].nxt) {Edge &e = edge[i];if (e.cap && dis[e.v] == dis[x] + 1) {int ret = dfs(e.v, min(e.cap, f));sum += ret; f -= ret;e.cap -= ret; edge[i ^ 1].cap += ret;}}return sum;
}
int dinic() {int ret = 0;while (bfs()) {for (int i = s; i <= t; ++i) cur[i] = head[i];ret += dfs(s, inf);}return ret;
}
int main() {int a, b, c, n, m, cas;scanf("%d", &cas);while (cas--) {scanf("%d%d", &n, &m);cnt = 0; tot = 0; s = 1; t = n;memset(dis, 0, sizeof(dis));memset(head, -1, sizeof(head));memset(first, -1, sizeof(first));for (int i = 0; i < m; ++i) {scanf("%d%d%d", &a, &b, &c);addEdge(a, b, c);}BFS(n);BuildGraph(n, n);int ans = dinic();printf("%d\n", ans);}return 0;
}