POJ 3686 The Windy's

The Windy's

Time Limit: 5000MS Memory Limit: 65536KTotal Submissions: 3299 Accepted: 1413

Description

The Windy's is a world famous toy factory that owns M top-class workshop to make toys. This year the manager receivesN orders for toys. The manager knows that every order will take different amount of hours in different workshops. More precisely, thei-th order will take Z_ij hours if the toys are making in thej-th workshop. Moreover, each order's work must be wholly completed in the same workshop. And a workshop can not switch to another order until it has finished the previous one. The switch does not cost any time.

The manager wants to minimize the average of the finishing time of the N orders. Can you help him?

Input

The first line of input is the number of test case. The first line of each test case contains two integers,N and M (1 ≤ N,M ≤ 50).
The next N lines each contain M integers, describing the matrixZ_ij (1 ≤ Z_ij ≤ 100,000) There is a blank line before each test case.

Output

For each test case output the answer on a single line. The result should be rounded to six decimal places.

Sample Input

33 4100 100 100 199 99 99 198 98 98 13 41 100 100 10099 1 99 9998 98 1 983 41 100 100 1001 99 99 9998 1 98 98

Sample Output

2.0000001.0000001.333333

Source

POJ Founder Monthly Contest – 2008.08.31, windy7926778

/***************************************************************> File Name:    POJ3686.cpp> Author:       SDUT_GYX> Mail:         [e-mail]> Created Time: 2013/6/4 0:16:38 **************************************************************/#include <iostream>#include <cstring>#include <algorithm>#include <cstdio>#include <queue>#include <cstdlib>#include <iomanip>#include <string>#include <vector>#include <map>#include <cmath>#include <stack>#define LL long long#define N 3600#define inf 0x7ffffffusing namespace std;int lx[N],ly[N],slack[N],linky[N],w[N][N],n,m;bool visitx[N],visity[N];int main(){//freopen("data1.in","r",stdin);int KM();int t;scanf("%d",&t);while(t--){scanf("%d %d",&n,&m);int x;for(int i=1;i<=n;i++){for(int j=1;j<=m;j++){scanf("%d",&x);for(int k=1;k<=n;k++){w[i][(j-1)*n + k] = -x*k;}}}m=n*m;int res=KM();printf("%.6lf\n",(double)res/n);}return 0;}bool find(int k){visitx[k] = true;for(int i=1;i<=m;i++){if(visity[i]){continue;}int t=lx[k] + ly[i] - w[k][i];if(t==0){visity[i] = true;if(!linky[i]||find(linky[i])){linky[i] = k;return true;}}else {slack[i]=min(slack[i],t);}}return false;}int KM(){memset(ly,0,sizeof(ly));memset(linky,0,sizeof(linky));for(int i=1;i<=n;i++){lx[i] = -inf;}for(int i=1;i<=n;i++){for(int j=1;j<=m;j++){lx[i] = max(lx[i],w[i][j]);}}for(int i=1;i<=n;i++){for(int j=1;j<=m;j++){slack[j] = inf;}while(1){memset(visitx,false,sizeof(visitx));memset(visity,false,sizeof(visity));if(find(i)){break;}int d=inf;for(int i=1;i<=m;i++){if(!visity[i]){d = min(d,slack[i]);}}for(int i=1;i<=n;i++){if(visitx[i]){lx[i] -=d;}}for(int i=1;i<=m;i++){if(visity[i]){ly[i] +=d;}else{slack[i] -=d;}}}}int s=0;for(int i=1;i<=m;i++){if(linky[i]){int j=linky[i];            s+=w[j][i];}}return -s;}