378. Kth Smallest Element in a Sorted Matrix

Given a n x n matrix where each of the rows and columns are sorted in ascending order, find the kth smallest element in the matrix.

Note that it is the kth smallest element in the sorted order, not the kth distinct element.

Example:

matrix = [
   [ 1,  5,  9],
   [10, 11, 13],
   [12, 13, 15]
],
k = 8,

return 13.

Note: 

You may assume k is always valid, 1 ≤ k ≤ n2.

堆/优先队列，从最小开始，每次把相邻的加入优先队列，直到K个为止

public class Solution {
    public int kthSmallest(int[][] matrix, int k)
	{
		int m=matrix.length;
		if(m==0)
			return 0;
		
		int n=matrix[0].length;
		int cnt=0;
		boolean[][] used=new boolean[m][n];
		PriorityQueue<kthsNode> heap=new PriorityQueue<>();
		heap.add(new kthsNode(0, 0, matrix[0][0]));
		used[0][0]=true;
		kthsNode node=null;
		int[] xoff={0,1};
		int[] yoff={1,0};
		while(cnt<k)
		{
			node=heap.poll();
			int x=node.x;
			int y=node.y;
			for(int i=0;i<2;i++)
			{
				int xx=x+xoff[i];
				int yy=y+yoff[i];
				if(xx>=0&&xx<m&&yy>=0&&yy<n&&!used[xx][yy])
				{
					used[xx][yy]=true;
					heap.add(new kthsNode(xx, yy, matrix[xx][yy]));
				}
			}
			cnt++;
		}
		
		return node.val;
	}
}


class kthsNode implements Comparable<kthsNode>
{
	int x,y;
	int val;
	public kthsNode(int x,int y,int val)
	{
		this.x=x;
		this.y=y;
		this.val=val;
		// TODO Auto-generated constructor stub
	}
	@Override
	public int compareTo(kthsNode o)
	{
		// TODO Auto-generated method stub
		return val-o.val;
	}
}