Search a 2D Matrix II

问题描述

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.

 

解决思路

从最左下角的元素开始判断，最坏情况为遍历完矩阵的对角线上的元素，时间复杂度为O(n).

 

程序

public class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
            return false;
        }
        
        int rows = matrix.length, cols = matrix[0].length;
        // left bottom number
        int i = rows - 1, j = 0;
        
        while (i >= 0 && j <= cols - 1) {
            int num = matrix[i][j];
            if (num == target) {
                return true;
            }
            if (num > target) {
                --i;
                continue;
            }
            if (num < target) {
                ++j;
            }
        }
        
        return false;
    }
}