Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:

• Integers in each row are sorted in ascending from left to right.
• Integers in each column are sorted in ascending from top to bottom.

For example, Consider the following matrix:

[
  [1,   4,  7, 11, 15],
  [2,   5,  8, 12, 19],
  [3,   6,  9, 16, 22],
  [10, 13, 14, 17, 24],
  [18, 21, 23, 26, 30]
]

Given target = 5, return true.
Given target = 20, return false.

解题思路

O(m+n)。从矩阵右上角开始遍历元素，若小于目标，则说明第该行元素都不符合要求，行号加1；若大于目标，则说明该列元素都不符合要求，列号减1。

实现代码

// Runtime: 14 ms
public class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if (matrix.length == 0) {
            return false;
        }
        int i = 0;
        int j = matrix[0].length - 1;

        while (i < matrix.length && j >= 0) {
            if (matrix[i][j] > target) {
                j--;
            } else if (matrix[i][j] < target) {
                i++;
            } else {
                return true;
            }
        }

        return false;
    }
}