Problem: Example

Input

3 2 3 1 3
1 2 2 1
2 3 1 2


Output

6.0000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxn = 210;
const int maxm = 4010;
const int INF = 0x3f3f3f3f;
struct Edge{
    int to,next,cap,flow,cost;
}edge[maxm];
int head[maxn],tol;
int pre[maxn],dis[maxn];
bool vis[maxm];
int n,m,p;
void init(){
    tol=0;
    for(int i=1;i<=n;++i) head[i]=-1;
}
void addedge(int u,int v,int cap,int cost){
    edge[tol].to=v;
    edge[tol].cap=cap;
    edge[tol].cost=cost;
    edge[tol].flow=0;
    edge[tol].next=head[u];
    head[u]=tol++;
    edge[tol].to=u;
    edge[tol].cap=0;
    edge[tol].cost=-cost;
    edge[tol].flow=0;
    edge[tol].next=head[v];
    head[v]=tol++;
}
bool spfa(int s,int t){
    queue<int> q;
    for(int i=1;i<=n;++i){
        dis[i]=INF; vis[i]=false; pre[i]=-1;
    }
    dis[s]=0; vis[s]=true;
    q.push(s);
    while (!q.empty()){
        int u = q.front(); q.pop();
        vis[u]=false;
        for(int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;
            if(edge[i].cap>edge[i].flow&&dis[v]>dis[u]+edge[i].cost){
                dis[v]=dis[u]+edge[i].cost;
                pre[v]=i;
                if(!vis[v]){
                    vis[v]=true;
                    q.push(v);
                }
            }
        }
    }
    if(pre[t]==-1) return false;
    else return true;
}
double minCostMaxflow(int s,int t){
    int flow=0,cost=0; double ans=INF;
    while (spfa(s,t)){
        int Min = INF;
        for(int i=pre[t];i!=-1;i=pre[edge[i^1].to]){
            if(Min>edge[i].cap-edge[i].flow)
                Min=edge[i].cap-edge[i].flow;
        }
        for(int i=pre[t];i!=-1;i=pre[edge[i^1].to]){
            edge[i].flow+=Min;
            edge[i^1].flow-=Min;
            cost+=edge[i].cost*Min;
        }
        flow+=Min;
        ans=min(ans,(1.0*cost+p)/flow);
    }
    return ans;
}

int s,t,u,v,d,c;
int main(){
    scanf("%d %d %d %d %d",&n,&m,&p,&s,&t); init();
    while(m--){
        scanf("%d %d %d %d",&u,&v,&d,&c);
        addedge(u,v,c,d);
    }
    printf("%lf\n",minCostMaxflow(s,t));
}