ACM/ICPC 之 网络流入门-Ford Fulkerson与SAP算法(POJ1149-POJ1273)

　　　第一题：按顾客访问猪圈的顺序依次构图（顾客为结点），汇点->第一个顾客->第二个顾客->...->汇点

 

 

//第一道网络流
//Ford-Fulkerson
//Time:47Ms		Memory:276K
#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
using namespace std;

#define MAXN 105	//顾客
#define MAXM 1005	//猪圈
#define INF 0x3f3f3f3f

struct Arc {
	int c, f;
}e[MAXN][MAXN];

int n, m;
int s, t;
int pig[MAXM], last[MAXM];	//last[]:猪圈当前顾客(0为源点，n+1为汇点)
int pre[MAXN];		//1.从哪一个结点
int alpha[MAXN];	//2.可改进量

void ford()	//ford fulkerson
{
	alpha[s] = INF;	//源点可改进量无限
	while (1) {	//多次标号
		memset(pre, -1, sizeof(pre));	//初始标号
		queue<int> q;
		q.push(s);
		while (!q.empty() && pre[t] == -1) {
			int cur = q.front();	q.pop();
			for (int i = 1; i <= t; i++)
			{
				int tmp;
				//tmp 为非0可保证邻接且保证有剩余流量
				if (pre[i] == -1 && (tmp = e[cur][i].c - e[cur][i].f))
				{
					pre[i] = cur;
					q.push(i);
					alpha[i] = min(alpha[cur], tmp);
				}
			}
		}
		if (pre[t] == -1)	return;	//未找到增广路
		for (int i = pre[t], j = t; i != -1; j = i, i = pre[i])
		{
			e[i][j].f += alpha[t];
			e[j][i].f = -e[i][j].f;
		}
	}

}
 
int main()
{
	//freopen("in.txt", "r", stdin);

	memset(last, 0, sizeof(last));
	memset(e, 0, sizeof(e));
	scanf("%d%d", &m, &n);
	s = 0;	t = n + 1;
	for (int i = 1; i <= m; i++)
		scanf("%d", &pig[i]);
	for (int i = 1; i <= n; i++)
	{
		int num;	//钥匙数
		scanf("%d", &num);
		while (num--) {
			int pn;
			scanf("%d", &pn);
			if (last[pn] == 0)
				e[last[pn]][i].c += pig[pn];
			else e[last[pn]][i].c = INF;
			last[pn] = i;
		}
		scanf("%d", &e[i][t].c);
	}

	ford();

	int maxFlow = 0;
	for (int i = 1; i < t; i++)
		maxFlow += e[i][t].f;
	printf("%d\n", maxFlow);

	return 0;
}

 

　　第二道：最短增广路(SAP)算法，dinic算法前身，与dinic不同的是需要多次采用BFS进行构建层次网络，题目本身较直接。

 

//网络流
//一般最短增广路算法-Dinic算法的前身
//Time:16Ms		Memory:676K
#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
using namespace std;

#define MAX 205
#define INF 0x3f3f3f3f

struct Arc {
	int c, f;
}e[MAX][MAX];

int n, m;
int s, t;
int pre[MAX];
int res[MAX][MAX];	//残留网络->层次网络
bool v[MAX];

void bfs()
{
	while (1)	//多次BFS寻找增广路
	{
		memset(v, false, sizeof(v));
		memset(res, 0, sizeof(res));
		memset(pre, 0, sizeof(pre));
		queue<int> q;
		q.push(s);	v[s] = true;
		while (!q.empty() && pre[t] == 0)
		{	//BFS构造层次网络
			int cur = q.front();	q.pop();
			for (int i = 1; i <= n; i++)
			{
				if (!v[i]) {
					int tmp = e[cur][i].c - e[cur][i].f;
					if (tmp > 0) {	//正向有残留容量
						res[cur][i] = tmp;
						pre[i] = cur;
						q.push(i);	v[i] = true;
					}
					else if (e[i][cur].f > 0) {	//反向有流量
						res[cur][i] = e[i][cur].f;
						pre[i] = cur;
						q.push(i);	v[i] = true;
					}
				}
			}
		}
		if (pre[t] == 0)	return;
		int minroad = INF;	//最小可改进量
		for (int i = t; i != s; i = pre[i])
			minroad = min(minroad, res[pre[i]][i]);
		for (int i = t; i != s; i = pre[i])
		{
			if (e[pre[i]][i].c - e[pre[i]][i].f > 0)
				e[pre[i]][i].f += minroad;
			else if (e[i][pre[i]].f > 0)
				e[i][pre[i]].f -= minroad;
		}

	}
}

int main()
{
	//freopen("in.txt", "r", stdin);

	while (~scanf("%d%d", &m, &n))
	{
		memset(e, 0, sizeof(e));
		int u, v, c;
		for (int i = 0; i < m; i++)
		{
			scanf("%d%d%d", &u, &v, &c);
			e[u][v].c += c;
		}

		s = 1;	t = n;
		bfs();

		int maxFlow = 0;
		for (int i = 1; i < n; i++)
			maxFlow += e[i][t].f;
		printf("%d\n", maxFlow);
	}

	return 0;
}