ALDS1_6_D Minimum Cost Sort (最小成本排序)

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Minimum Cost Sort

Time Limit : 1 sec, Memory Limit : 131072 KB 
Japanese version is here

Minimum Cost Sort

You are given nn integers wi(i=0,1,...,n−1)wi(i=0,1,...,n−1) to be sorted in ascending order. You can swap two integers wiwi and wjwj. Each swap operation has a cost, which is the sum of the two integers wi+wjwi+wj. You can perform the operations any number of times.

Write a program which reports the minimal total cost to sort the given integers.

Input

In the first line, an integer nn is given. In the second line, nn integers wi(i=0,1,2,...n−1)wi(i=0,1,2,...n−1) separated by space characters are given.

Output

Print the minimal cost in a line.

Constraints

• 1≤n≤1,0001≤n≤1,000
• 0≤wi≤1040≤wi≤104
• wiwi are all different

Sample Input 1

5
1 5 3 4 2

Sample Output 1

7

Sample Input 2

4
4 3 2 1

Sample Output 2

10

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Source: https://onlinejudge.u-aizu.ac.jp/problems/ALDS1_6_D

---

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;
#define clr(a) memset(a,b,sizeof(a))
#define il     inline
#define reg    register
#define rep(i,a,n) for(reg int i=a;i<n;i++)
typedef long long ll;
const int maxn=10000+5;
const int minn=1000+5;
const int inf=2e9+2;
int n,a[minn],po[maxn];
void solve()
{

    sort(a+1,a+n+1);
    int f=0,tp=inf,t=0,tmin=a[1];
    ll w=0,ans=0;
    rep(i,1,n+1)
    {
        if(po[a[i]]==i){continue;}
        tp=inf;t=1;w=0;
        int f=po[a[i]];
        w+=a[i];
        tp=a[i];
        while(f!=i)
        {
            t++;tp=min(a[f],tp);
            w+=a[f];
            int tm=f;
            f=po[a[f]];
            po[a[tm]]=tm;
        }
        ans+=min(w+(t-2)*tp,w+tp+(t+1)*tmin);
    }
    printf("%lld\n",ans);
}
int main()
{
    scanf("%d",&n);
    rep(i,1,n+1)
    {
        scanf("%d",&a[i]);
        po[a[i]]=i;
    }
    solve();
    return 0;
}