最小费用最大流(洛谷-P3381)
题目描述
如题,给出一个网络图,以及其源点和汇点,每条边已知其最大流量和单位流量费用,求出其网络最大流和在最大流情况下的最小费用。
输入输出格式
输入格式:
第一行包含四个正整数N、M、S、T,分别表示点的个数、有向边的个数、源点序号、汇点序号。
接下来M行每行包含四个正整数ui、vi、wi、fi,表示第i条有向边从ui出发,到达vi,边权为wi(即该边最大流量为wi),单位流量的费用为fi。
输出格式:
一行,包含两个整数,依次为最大流量和在最大流量情况下的最小费用。
输入输出样例
输入样例#1:
4 5 4 3
4 2 30 2
4 3 20 3
2 3 20 1
2 1 30 9
1 3 40 5输出样例#1:
50 280
思路:最小费用最大流模版题,利用 zkw 费用流解决
源代码
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<string>
#include<cstring>
#include<cmath>
#include<ctime>
#include<algorithm>
#include<utility>
#include<stack>
#include<queue>
#include<vector>
#include<set>
#include<map>
#include<bitset>
#define PI acos(-1.0)
#define INF 0x3f3f3f3f
#define LL long long
#define Pair pair<LL,LL>
LL quickPow(LL a,LL b){ LL res=1; while(b){if(b&1)res*=a; a*=a; b>>=1;} return res; }
LL multMod(LL a,LL b,LL mod){ a%=mod; b%=mod; LL res=0; while(b){if(b&1)res=(res+a)%mod; a=(a<<=1)%mod; b>>=1; } return res%mod;}
LL quickPowMod(LL a, LL b,LL mod){ LL res=1,k=a; while(b){if((b&1))res=multMod(res,k,mod)%mod; k=multMod(k,k,mod)%mod; b>>=1;} return res%mod;}
LL getInv(LL a,LL mod){ return quickPowMod(a,mod-2,mod); }
LL GCD(LL x,LL y){ return !y?x:GCD(y,x%y); }
LL LCM(LL x,LL y){ return x/GCD(x,y)*y; }
const double EPS = 1E-10;
const int MOD = 998244353;
const int N = 500000+5;
const int dx[] = {-1,1,0,0,1,-1,1,1};
const int dy[] = {0,0,-1,1,-1,1,-1,1};
using namespace std;
struct Edge {
int to;
int next;
int cap, cost;
} edge[N];
int head[N], tot;
bool vis[N];
int dis[N], level[N];
void addEdge(int x, int y, int cap, int cost) {
edge[++tot].to = y;
edge[tot].next = head[x];
edge[tot].cap = cap;
edge[tot].cost = cost;
head[x] = tot;
edge[++tot].to = x;
edge[tot].next = head[y];
edge[tot].cap = 0;
edge[tot].cost = -cost;
head[y] = tot;
}
bool SPFA(int S, int T, int n) {
memset(dis, INF, sizeof(dis));
memset(vis, false, sizeof(vis));
memset(level, 0, sizeof(level));
dis[S] = 0;
level[S] = 1;
vis[S] = true;
deque<int> Q;
Q.push_back(S);
while (!Q.empty()) {
int x = Q.front();
Q.pop_front();
vis[x] = false;
for (int i = head[x]; i != -1; i = edge[i].next) {
int to = edge[i].to;
if (dis[to] > dis[x] + edge[i].cost && edge[i].cap > 0) {
dis[to] = dis[x] + edge[i].cost;
level[to] = level[x] + 1;
if (!vis[to]) {
vis[to] = true;
if (!Q.empty() && dis[to] < dis[Q.front()])
Q.push_front(to);
else
Q.push_back(to);
}
}
}
}
return dis[T] != dis[n + 1];
}
bool flag = false;
int dfs(int x, int T, int t, int &flow, int &cost) {
if (x == T) {
flow += t;
flag = true;
return t;
}
int num = 0, newFlow = 0;
for (int i = head[x]; i != -1; i = edge[i].next) {
int to = edge[i].to;
if (t == num)
break;
if (dis[x] + edge[i].cost == dis[to] && level[x] + 1 == level[to] && edge[i].cap > 0) {
newFlow = dfs(to, T, min(t - num, edge[i].cap), flow, cost);
num += newFlow;
cost += newFlow * edge[i].cost;
edge[i].cap -= newFlow;
edge[i ^ 1].cap += newFlow;
}
}
return num;
}
void zkw(int S, int T, int n) {
int flow = 0, cost = 0;
while (SPFA(S, T, n)) {
flag = true;
while (flag) {
flag = false;
dfs(S, T, INF, flow, cost);
}
}
printf("%d %d\n", flow, cost);
}
int main() {
int n, m;
while (scanf("%d%d", &n, &m) != EOF) {
memset(head, -1, sizeof(head));
tot = 1;
int S, T;
scanf("%d%d", &S, &T);
for (int i = 1; i <= m; i++) {
int x, y, cap, cost;
scanf("%d%d%d%d", &x, &y, &cap, &cost);
addEdge(x, y, cap, cost);
}
zkw(S, T, n);
}
return 0;
}