POJ 3270 Cow Sorting(置换群)

题目链接

很早之前就看过这题，思路题把，确实挺难想的，黑书248页有讲解。

#include <cstdio>
#include <cstring>
#include <iostream>
#include <cmath>
#include <algorithm>
using namespace std;
int p[10001];
struct node
{
    int id;
    int x;
    int pos;
}num[10001];
int flag[10001],minz;
int cmp1(node a,node b)
{
    return a.x < b.x;
}
int cmp2(node a,node b)
{
    return a.id < b.id;
}
int judge(int x)
{
    int res = 0,m,temp = 0;
    if(x == num[x].pos)
    {
        flag[x] = 1;
        return 0;
    }
    m = num[x].x;
    while(!flag[x])
    {
        flag[x] = 1;
        temp += num[x].x;
        x = num[x].pos;
        m = min(m,num[x].x);
        res ++;
    }
    return temp + min((res-2)*m,m+(res+1)*minz);
}
int main()
{
    int n,i,sum;
    scanf("%d",&n);
    minz = 100000000;
    sum = 0;
    for(i = 1;i <= n;i ++)
    {
        scanf("%d",&num[i].x);
        minz = min(num[i].x,minz);
        num[i].id = i;
    }
    sort(num+1,num+n+1,cmp1);
    for(i = 1;i <= n;i ++)
    {
        num[i].pos = i;
    }
    sort(num+1,num+n+1,cmp2);
    for(i = 1;i <= n;i ++)
    {
        if(!flag[i])
        {
            sum += judge(i);
        }
    }
    printf("%d
",sum);
    return 0;
}