POJ 3270

省赛被虐了，最近就搞搞数论和组合数学的题目。

这题主要运用了组合数学中的置换群概念，其他也没什么好说的了。

#include<iostream>
#include<cstdio>
#include<queue>
#include<vector>
#include<algorithm>
#define MAXN 10005
using namespace std;
int data[MAXN],note[MAXN];
bool vis[MAXN];

int search(int n, int x)
{
  int l(1),r(n);
  int mid = (l + r)/2;
  while (l <= r) {
    if (note[mid] == x)return mid;
    if (note[mid] < x)l = mid + 1;
    if (note[mid] > x)r = mid - 1;
    mid = (l + r)/2;  
  }  
  return 0;
}

void ini(int n)
{
  memset(vis,false,sizeof(vis));
  for (int i(1); i<=n; ++i) {
    scanf("%d",&data[i]);
    note[i] = data[i];  
  }
  sort(note+1,note+n+1);
  for (int i(1); i<=n; ++i) {
    data[i] = search(n+1,data[i]);    
  }     
}

int main()
{
  int n;
  scanf("%d",&n);
  ini(n);
  priority_queue<int, vector<int>, greater<int> > Q;
  int sum1(0), sum2(0), ans = 0;
  for (int i(1); i<=n; ++i) {
    if (!vis[i]) {
      sum1 = sum2 = 0;
      vis[i] = true;
      Q.push(i);
      int temp = i;
      sum1 += 2*note[i] + 2*note[1];
      while (!vis[data[temp]]) {
        temp = data[temp];
        vis[temp] = true;
        sum1 += note[temp] + note[1];
        Q.push(temp);  
      }
      if (Q.size() == 1) {
        Q.pop();
        continue;
      }
      int x = Q.top();//cout<<x<<" ";
      Q.pop();
      while (!Q.empty()) {
        //cout<<Q.top()<<" ";
        sum2 += note[x] + note[Q.top()];
        Q.pop();  
      }
      //cout<<sum1<<" "<<sum2<<endl;
      ans += min(sum1,sum2);  
    }    
  }
  cout<<ans<<endl;
  system("pause");
  return 0;  
}