洛谷P2740 草地排水

最大流

一道完全符合最大流定义的板子题。。重新学了一次网络流，希望有更深的理解把。。

#include <bits/stdc++.h>

#define INF 0x3f3f3f3f

#define full(a, b) memset(a, b, sizeof a)

using namespace std;

typedef long long ll;

inline int lowbit(int x){ return x & (-x); }

inline int read(){

    int X = 0, w = 0; char ch = 0;

    while(!isdigit(ch)) { w |= ch == '-'; ch = getchar(); }

    while(isdigit(ch)) X = (X << 3) + (X << 1) + (ch ^ 48), ch = getchar();

    return w ? -X : X;

}

inline int gcd(int a, int b){ return a % b ? gcd(b, a % b) : b; }

inline int lcm(int a, int b){ return a / gcd(a, b) * b; }

template<typename T>

inline T max(T x, T y, T z){ return max(max(x, y), z); }

template<typename T>

inline T min(T x, T y, T z){ return min(min(x, y), z); }

template<typename A, typename B, typename C>

inline A fpow(A x, B p, C lyd){

    A ans = 1;

    for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;

    return ans;

}

const int N = 205;

int n, m, cnt, head[N], depth[N];

struct Edge{ int v, next, w; } edge[N<<2];

void addEdge(int a, int b, int w){

    edge[cnt].v = b, edge[cnt].w = w, edge[cnt].next = head[a], head[a] = cnt ++;

    edge[cnt].v = a, edge[cnt].w = 0, edge[cnt].next = head[b], head[b] = cnt ++;

}

bool bfs(){

    full(depth, 0);

    queue<int> q;

    q.push(1);

    depth[1] = 1;

    while(!q.empty()){

        int s = q.front(); q.pop();

        for(int i = head[s]; i != -1; i = edge[i].next){

            int u = edge[i].v;

            if(!depth[u] && edge[i].w > 0){

                depth[u] = depth[s] + 1;

                q.push(u);

            }

        }

    }

    return depth[m] != 0;

}

int dfs(int s, int a){

    if(s == m) return a;

    int flow = 0;

    for(int i = head[s]; i != -1; i = edge[i].next){

        int u = edge[i].v;

        if(depth[u] == depth[s] + 1 && edge[i].w > 0){

            int k = dfs(u, min(a, edge[i].w));

            flow += k, a -= k, edge[i].w -= k, edge[i^1].w += k;

        }

        if(!a) break;

    }

    if(a) depth[s] = -1;

    return flow;

}

int dinic(){

    int ans = 0;

    while(bfs()){

        ans += dfs(1, INF);

    }

    return ans;

}

int main(){

    full(head, -1);

    n = read(), m = read();

    for(int i = 0; i < n; i ++){

        int u = read(), v = read(), w = read();

        addEdge(u, v, w);

    }

    printf("%d\n", dinic());

    return 0;

}