Kth smallest element

Last updated: 17th Jan, 2021

Problem Statment

Given a N x N matrix, where every row and column is sorted in non-decreasing order. Find the kth smallest element in the matrix.

Example 1:

N = 4
mat[][] = {
{10, 20, 30, 40}
{15, 25, 35, 45}
{24, 29, 37, 48}
{32, 33, 39, 50}
}
K = 7

>>Output: 30

Explanation: 30 is the 7th smallest element.

Approach:

Min Heap stores the elements with minimum element at the top. Firstly add all elements and indexes of first column in heap/priority queue. Then add neighbour of topmost element and pop top of heap.Keep a count of popped elements. When count reaches k, then heap top will be kth smallest

Time and Space Complexity :
Time - O(N+log(k))
Space - O(N), where N is number of rows

C++ Code

#define M 4 
#define N 4
int kSmallest(int mat[M][N], int k){
	//declare min heap with (int , (i,j)) structure
	priority_queue<< pair >, vector > >, greater > > > min_heap;
	
	//insert first column
	for (int i = 0; i < M; ++i)
	{
		min_heap.push(make_pair(mat[i][0], make_pair(i,0)));

	}
	int count=7, ans;

	// keep inserting next column element of current top and pop
	while(count--){
		int tempi=min_heap.top().second.first;
		int tempj=min_heap.top().second.second;
		ans=min_heap.top().first;
		min_heap.pop();
		min_heap.push(make_pair(mat[tempi][tempj+1], make_pair(tempi, tempj+1)));
	}
	return ans;
}


int main()
{
   int mat[M][N] = { {10, 20, 30, 40}, 
                    {15, 25, 35, 45}, 
                    {24, 29, 37, 48}, 
                    {32, 33, 39, 50}, 
                };  
  	int k=7;
    cout<<kSmallest(mat, k);  
    return 0;
}