[LeetCode] Problem 378 - Kth Smallest Element in a Sorted Matrix

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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

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

k = 8,

return 13.

Note

You may assume k is always valid, 1 ≤ k ≤ n^2.

Code

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// 第k小的数一定在left和right之间：即 left<= answer <= right
// 循环结束的条件必定是：left >= right
// 所以：left == answer == right
public int kthSmallest(int[][] matrix, int k) {
   int m = matrix.length;
   int n = matrix[0].length;
   int left = matrix[0][0];
   int right = matrix[m - 1][n - 1];

   while (left < right) {
      int mid = (left + right) >> 1;
      int count = count(matrix, mid, m, n);

      if (count < k)
            left = mid + 1;
      else
            right = mid;
   }

   return right;
}

private int count(int[][] matrix, int mid, int m, int n) {
   int i = m - 1;
   int j = 0;
   int count = 0;

   while (i >= 0 && j < n) {
      if (matrix[i][j] <= mid) {
            j++;
            count += i + 1;
      }
      else
            i--;
   }

   return count;
}