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Task Assignment.cpp
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Task Assignment.cpp
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#include<bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define FASTIO ios_base::sync_with_stdio(false);cin.tie(NULL); cout.tie(NULL);
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef long long T1;//for cost
typedef long long T2;//for flow
const int maxn = 5005;
const T1 INF = 1e12;
const T2 inf = 1e12;
const T1 eps = 0;
struct Edge {
int from, to;
T2 cap, flow;
T1 cost;
};
struct MCMF {//0-indexed
int n, m, s, t;
vector<Edge> edges;
vector<int> G[maxn];
int p[maxn],inq[maxn];
T1 d[maxn];
T2 a[maxn];
void init(int n) {
this->n = n;
for(int i = 0; i < n; i++) G[i].clear();
edges.clear();
}
void AddEdge(int from,int to,T2 cap,T1 cost) {
edges.push_back((Edge){from, to, cap, 0, cost});
edges.push_back((Edge){to, from, 0, 0, -cost});
m = edges.size();
G[from].push_back(m-2);
G[to].push_back(m-1);
}
pair<T1,T2> Mincost(int s,int t) {//SPFA
T1 tot_cost = 0;
T2 tot_flow = 0;
while(true) {
for(int i = 0; i < n; i++) d[i] = INF;
memset(inq, 0, sizeof(inq));
d[s] = 0;
inq[s] = 1;
p[s] = 0;
a[s] = inf;
queue<int> Q;
srand(time(NULL));
Q.push(s);
while(!Q.empty()) {
int u = Q.front();
Q.pop();
inq[u] = 0;
for(int i = 0; i < G[u].size(); i++) {
Edge& e = edges[G[u][i]];
if(e.cap > e.flow && d[e.to] > d[u] + e.cost+eps) {
d[e.to] = d[u] + e.cost;
p[e.to] = G[u][i];
a[e.to] = min(a[u], e.cap - e.flow);
if(!inq[e.to]) {
Q.push(e.to);
inq[e.to] = 1;
}
}
}
}
if(abs(d[t]-INF)<=eps)break;
tot_cost += (T1)d[t] * a[t];
tot_flow += a[t];
int u = t;
while(u != s) {
edges[p[u]].flow += a[t];
edges[p[u]^1].flow -= a[t];
u = edges[p[u]].from;
}
}
return {tot_cost,tot_flow};
}
};
void solve(){
int n;
cin>>n;
MCMF mcmf;
mcmf.init(2*n+2);
int s=0,t=2*n+1;
int cost[n+1][n+1];
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++){
cin>>cost[i][j];
mcmf.AddEdge(i,j+n,1,cost[i][j]);
}
for(int i=1;i<=n;i++){
mcmf.AddEdge(0,i,1,0);
mcmf.AddEdge(i+n,2*n+1,1,0);
}
auto [c,f] = mcmf.Mincost(s,t);
cout<<c<<endl;
for(auto edge:mcmf.edges){
if( edge.flow == 1 and edge.from>=1 and edge.from<=n ) cout<<edge.from<<" "<<edge.to-n<<endl;
}
}
int main(){
FASTIO;
solve();
}
// https://cses.fi/problemset/task/2121/