1067. Sort with Swap(0,*) (25)

Given any permutation of the numbers {0, 1, 2,..., N-1}, it is easy to sort them in increasing order. But what if Swap(0, *) is the ONLY operation that is allowed to use? For example, to sort {4, 0, 2, 1, 3} we may apply the swap operations in the following way:

Swap(0, 1) => {4, 1, 2, 0, 3}
Swap(0, 3) => {4, 1, 2, 3, 0}
Swap(0, 4) => {0, 1, 2, 3, 4}

Now you are asked to find the minimum number of swaps need to sort the given permutation of the first N nonnegative integers.

Input Specification:

Each input file contains one test case, which gives a positive N (<=10⁵) followed by a permutation sequence of {0, 1, ..., N-1}. All the numbers in a line are separated by a space.

Output Specification:

For each case, simply print in a line the minimum number of swaps need to sort the given permutation.

Sample Input:

10 3 5 7 2 6 4 9 0 8 1

Sample Output:

9

思路是在网上看的，主要就是a[num]=i;表示num这个数字在位置i上。然后交换的是位置

这样就避免了寻找0的位置和0归位后第一个不归位的数字

#include <cstdio>#include<cmath>#include<algorithm>#include<iostream>using namespace std;int main() {    int n;cin>>n;int a[100001];int cnt=0;for(int i=0;i<n;i++){int num;scanf("%d",&num);a[num]=i;if(a[num]==num) cnt++;} int sum=0;int index=0;while(cnt<n-1){if(a[0]==0){for(;index<n;index++){if(index!=a[index]){swap(a[0],a[index]);sum++;break;}}}while(a[0]!=0){swap(a[0],a[a[0]]);sum++;cnt++;}   // cout<<cnt<<endl;}cout<<sum;    return 0;}