/*
 *  378. Find the kth smallest number in at row and column sorted matrix.
 */
public class KthSmallest {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        int[][] matrix = {
                          {1 ,5 ,7},
                          {3 ,7 ,8},
                          {4 ,8 ,9},
                    };
        KthSmallest ks = new KthSmallest();
        
        int k = 4;
        int res = ks.kthSmallest(matrix, k);
        System.out.println("res: " + res);
    }
    
    /*
     *  解題報(bào)告：
             Java 1ms nlog(max -min) solution
        Main loop is binary search of max - min.
        Swap from left-bottom to right-top can get count <= mid in O(n) time instead of O(nlogn), 

        total complexity will be O(nlogm) while m = max - min.
        ref: https://leetcode.com/problems/kth-smallest-element-in-a-sorted-matrix/#/solutions
     */
    public int kthSmallest(int[][] matrix, int k) {
        int n = matrix.length;
        int lo = matrix[0][0], hi = matrix[n-1][n-1];
        while (lo <= hi) {
            int mid = lo + (hi - lo) / 2;
            int cout = getLessEqual(matrix, mid);
            
            if (cout < k) lo = mid + 1;
            else 
                hi = mid - 1;
        }
        return lo;
            
    }
    
    public int getLessEqual(int[][] matrix, int val) {
        int res = 0;
        int n = matrix.length;
        int i = n - 1, j = 0;
        while (i >= 0 && j < n) {
            if (matrix[i][j] > val) i--;
            else {
                res += i + 1;
                j++;
            }
        }
        return res;
    }
}