1. 首页
2. 二分匹配
3. 本页

UVALive 6129 Sofa, So Good (KM)

题意：~

思路：最小权匹配，跑两遍KM，第二次建边要处理每个工人第一次做工的时间差。

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int, int> PI;
typedef pair< PI, int> PII;
#define pb push_back
#define Key_value ch[ch[root][1]][0]
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define MS(x,y) memset(x,y,sizeof(x))
const double eps = 1e-8;
const double pi = acos (-1.0);
const int mod = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const int M = 1000100;
const int MAXN = 10010;
const int MAXM = 100010;

const int N = 310;
int nx, ny;
int g[N][N];
int linker[N], lx[N], ly[N];
int slack[N];
bool visx[N], visy[N];

bool DFS(int x)
{
    visx[x] = true;
    for(int y = 1; y <= ny; y++)
    {
        if(visy[y])continue;
        int tmp = lx[x] + ly[y] - g[x][y];
        if(tmp == 0)
        {
            visy[y] = true;
            if(linker[y] == -1 || DFS(linker[y]))
            {
                linker[y] = x;
                return true;
            }
        }
        else if(slack[y] > tmp)
            slack[y] = tmp;
    }
    return false;
}

int KM()
{
    memset(linker, -1, sizeof(linker));
    memset(ly, 0, sizeof(ly));
    for(int i = 1; i <= nx; i++)
    {
        lx[i] = -INF;
        for(int j = 1; j <= ny; j++)
            if(g[i][j] > lx[i])
                lx[i] = g[i][j];
    }
    for(int x = 1; x <= nx; x++)
    {
        for(int i = 1; i <= ny; i++)
            slack[i] = INF;
        while(true)
        {
            memset(visx, false, sizeof(visx));
            memset(visy, false, sizeof(visy));
            if(DFS(x))break;
            int d = INF;
            for(int i = 1; i <= ny; i++)
                if(!visy[i] && d > slack[i])
                    d = slack[i];
            for(int i = 1; i <= nx; i++)
                if(visx[i])
                    lx[i] -= d;
            for(int i = 1; i <= ny; i++)
            {
                if(visy[i])ly[i] += d;
                else slack[i] -= d;
            }
        }
    }
    int res = 0;
    for(int i = 1; i <= ny; i++)
    {
        if(linker[i] != -1)
            res += g[linker[i]][i];
    }
    return res;
}

struct mmp
{
    int a, b, c;
} wk[55];

int kk[50];
int mp[50][50];

int main()
{
    int n;
    int casee = 1;
    while(~scanf("%d", &n), n)
    {
        int tmp;
        for(int i = 1; i <= n; ++i)
        {
            for(int j = 1; j <= n; ++j)
            {
                scanf("%d", &tmp);
                g[i][j] = -tmp;
            }
        }
        nx = ny = n;
        KM();
        for(int i = 1; i <= n; ++i)
        {
            wk[linker[i]].a = i;
            wk[linker[i]].c = -g[linker[i]][i];
        }
        for(int i = 1; i <= n; ++i)
        {
            kk[i] = -g[linker[i]][i];
        }
        for(int i = 1; i <= n; ++i)
        {
            for(int j = 1; j <= n; ++j)
            {
                scanf("%d", &tmp);
                mp[i][j] = tmp;
                if(kk[j] - wk[i].c > 0)
                    tmp += kk[j] - wk[i].c;
                g[i][j] = -tmp;
            }
        }
        KM();
        for(int i = 1; i <= n; ++i)
        {
            wk[linker[i]].b = i;
            wk[linker[i]].c += -g[linker[i]][i];
        }
        int time = 0;
        for(int i = 1; i <= n; ++i)
        {
            time += abs(mp[i][wk[i].b] + g[i][wk[i].b]);
        }
        printf("Case %d:\n", casee++);
        for(int i = 1; i <= n; ++i)
        {
            printf("Worker %d: %d %d %d\n", i, wk[i].a, wk[i].b, wk[i].c);
        }
        printf("Total idle time: %d\n", time);
    }
    return 0;
}

/*
4
8 6 12 19
13 2 18 10
9 15 16 17
5 18 4 10
2 6 3 3
8 5 9 2
5 8 4 3
4 4 5 2
0

*/