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最新推荐文章于 2024-08-01 12:10:06 发布

G_congratulation

最新推荐文章于 2024-08-01 12:10:06 发布

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分类专栏：图论

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本文介绍了一个使用最小费用流算法解决特定网络流量问题的C++实现。通过定义边的数据结构和采用SPFA算法来更新节点状态，实现了从源点到汇点的最大流量传输，并计算了最小费用。该实现涉及了图论、最短路径算法和网络流等关键概念。

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#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<queue>
#define maxn 5550
#define maxm 25000
#define Inf 210000000
using namespace std;

struct Edge{
	int u, v, cap ,flow, cost;
	int next;
}e[maxm];

int fi[maxn], ecnt = 0;
int d[maxn], a[maxn], p[maxn];
bool inq[maxn];
int flow = 0, cost = 0;
int s, t, N;

void add_edge(int u, int v, int cap , int cost) {
	e[ecnt] = (Edge){u, v, cap, 0, cost, fi[u]};
	fi[u] = ecnt;
	ecnt++;
}

bool spfa(int s, int t) {
	memset(d, -1, sizeof(d));
	memset(inq, 0, sizeof(inq));
	d[s] = 0, inq[s] = 1, p[s] = 0, a[s] = Inf;
	int q[maxn*10], head = 0, tail = 1;
	q[head] = s;
	while(head < tail) {
		int u = q[head++];
		inq[u] = 0;
		for(int i = fi[u]; i != -1; i = e[i].next)
			if(e[i].cap > e[i].flow && d[e[i].v] < d[u] + e[i].cost) {
				d[e[i].v] = d[u] + e[i].cost;
				p[e[i].v] = i;
				a[e[i].v] = min(a[u], e[i].cap - e[i].flow);
				if(!inq[e[i].v]) {
					q[tail++] = e[i].v, inq[e[i].v] = 1;
				}
			}
	}
	if(d[t] == -1) return false;
	flow += a[t], cost += d[t]*a[t];
	int u = t;
	while(u != s) {
		e[p[u]].flow += a[t];
		e[p[u]^1].flow -= a[t];
		u = e[p[u]].u;
	}
	return true;
}

int main() {
	memset(fi, -1, sizeof(fi));
	int x, k = 2;
	int G[100][100];
	scanf("%d", &x);
	int n = x*x;
	int num = 0;
	int a, b, c; scanf("%d%d%d", &a, &b, &c);
	while(!(a == 0 && b == 0 && c == 0)) {
		G[a][b] = c;
		scanf("%d%d%d", &a, &b, &c);
	}
	for(int i = 1; i <= x; i++)
		for(int j = 1; j <= x; j++) {
			num++; 
			add_edge(num, num+n, 1, G[i][j]);
			add_edge(num+n, num, 0, -G[i][j]);
			add_edge(num, num+n, k, 0);
			add_edge(num+n, num, 0, 0);
			if(i != x)
				add_edge(num+n, num+x, Inf, 0), add_edge(num+x, num+n, 0, 0);
			if(j != x)
				add_edge(num+n, num+1, Inf, 0), add_edge(num+1, num+n, 0, 0);		
		}
	N = n*2+2;
	s = N-1, t = N;
	add_edge(s, 1, k, 0);     add_edge(1, s, 0, 0);
	add_edge(num+n, t, Inf, 0); add_edge(t, num+n, 0, 0);
	while(spfa(s, t));
	printf("%d", cost);
	return 0;
}