BZOJ 1877-优快云博客

本文链接：https://blog.youkuaiyun.com/weixin_45946410/article/details/103408070

本文详细解析了SDOI2009年晨跑问题，使用Dinic算法解决网络流问题，通过具体代码展示了如何构建图、进行SPFA预处理并运用Dinic算法求解最大流最小费用路径。

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1877: [SDOI2009]晨跑

再此用来验证dinic板子

BZOJ 1877


/**************************************************************
    Problem: 1877
    User: Dream_Tonight
    Language: C++
    Result: Accepted
    Time:928 ms
    Memory:2544 kb
****************************************************************/
 
#include <algorithm>
#include <iostream>
#include <cstring>
#include <vector>
#include <string>
#include <cstdio>
#include <cmath>
#include <stack>
#include <queue>
#include <list>
#include <map>
#include <set>
#include <iostream>
#include <cstdio>
 
#define ll long long
#define pii pair<int, int>
#define lson l , m , rt << 1
#define rson m + 1 , r , rt << 1 | 1
#define inc(i, j, k) for(int i=j;i<=k;i++)
#define dec(i, j, k) for(int i=j;i>=k;i--)
using namespace std;
const int maxn = 20000 + 7;
const int inf = 2139062143;
struct node {
    int to, next, cap, cost;
} edge[60005];
int head[maxn], dis[maxn], vis[maxn], cur[maxn];
int n, m, cnt = 1, ans = 0, result = 0;
 
inline void add(int u, int v, int cap, int cost) {
    edge[++cnt].to = v;
    edge[cnt].cap = cap;
    edge[cnt].cost = cost;
    edge[cnt].next = head[u];
    head[u] = cnt;
}
 
inline void addEdge(int u, int v, int cap, int cost) { add(u, v, cap, cost), add(v, u, 0, -cost); }
 
int spfa(int s, int t) {
    queue<int> q;
    memset(vis, 0, sizeof(vis));
    memset(dis, 127, sizeof(dis));
    memcpy(cur, head, sizeof(head));
    q.push(t), vis[t] = 1, dis[t] = 0;
    while (!q.empty()) {
        int u = q.front();
        q.pop();
        vis[u] = 0;
        for (int i = head[u]; i; i = edge[i].next) {
            int to = edge[i].to;
            if (edge[i ^ 1].cap &&
                dis[to] > dis[u] + edge[i ^ 1].cost) {
                dis[to] = dis[u] + edge[i ^ 1].cost;
                if (!vis[to]) q.push(to), vis[to] = 1;
            }
        }
    }
    return dis[s] != inf;
}
 
int dfs(int x, int t, int limit) {
    if (x == t) return limit;
    int flow = 0;
    vis[x] = 1;
    for (int i = cur[x]; i; i = edge[i].next) {
        cur[x] = i;
        if (edge[i].cap && !vis[edge[i].to] && dis[x] + edge[i ^ 1].cost == dis[edge[i].to]) {
            if (int d = dfs(edge[i].to, t, min(edge[i].cap, limit))) {
                limit -= d, flow += d;
                edge[i].cap -= d, edge[i ^ 1].cap += d;
                ans += d * edge[i].cost;
                if (!limit) break;
            }
        }
    }
    return flow;
}
 
void dinic(int s, int t) {
    while (spfa(s, t)) {
        vis[t] = 1;
        while (vis[t]) {
            memset(vis, 0, sizeof(vis));
            int d = dfs(s, t, inf);
            result += d;
        }
    }
}
 
int main() {
//    freopen("weather.in", "r", stdin);
    scanf("%d%d", &n, &m);
    addEdge(1, n + 1, inf, 0), addEdge(n, n + n, inf, 0);
    for (int i = 2; i < n; i++) addEdge(i, i + n, 1, 0);
    int s = 1, t = n + n;
    int x, y, z;
    for (int i = 1; i <= m; i++) scanf("%d%d%d", &x, &y, &z), addEdge(x + n, y, 1, z);
    dinic(s, t);
    printf("%d %d\n", result, ans);
    return 0;
}