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Minimum Swaps to Sort

Tags : graph, sorting, array, dfs, geeksforgeeks, cpp, medium

Problem Statement - link #

Given an array of n distinct elements. Find the minimum number of swaps required to sort the array in strictly increasing order.

Your Task: You do not need to read input or print anything. Your task is to complete the function minSwaps() which takes the nums as input parameter and returns an integer denoting the minimum number of swaps required to sort the array. If the array is already sorted, return 0.

Expected Time Complexity: O(nlogn)
Expected Auxiliary Space: O(n)

Examples #

Example 1:

Input:
nums = {2, 8, 5, 4}
Output:
1
Explaination:
swap 8 with 4.

Example 2:

Input:
nums = {10, 19, 6, 3, 5}
Output:
2
Explaination:
swap 10 with 3 and swap 19 with 5.

Constraints #

Solutions #

class Solution
{
    public:
    void dfs(vector<int>&nums,bool vis[],int &cur,int i,vector<pair<int,int>>&v){
        vis[i]=1;
        cur++;
        if(vis[v[i].second]) return;
        dfs(nums,vis,cur,v[i].second,v);
    }
    //Function to find the minimum number of swaps required to sort the array. 
	int minSwaps(vector<int>&nums)
	{
	    // Code here
	    vector<pair<int,int>> v;
	    for(int i=0;i<nums.size();i++)
	        v.push_back({nums[i],i});
	    sort(v.begin(),v.end());
	    bool vis[v.size()]={0};
	    int res=0;
	    for(int i=0;i<v.size();i++)
	        if(!vis[i]){
	            int cur=-1;
	            dfs(nums,vis,cur,i,v);
	            res += cur;
	        }
	    return res;
	}
};