240.md

240. Search a 2D Matrix II

Description

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.

Thinking Process

1. Search from the right corner of the matrix[i][j]
2. If matrix[i][j] > target, decrease j, otherwise increase i

Code

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)
                return true;
            else if(matrix[i][j] > target){
                j--;
            }else{
                i++;
            }
        }
        return false;
    }
}

Complexity

1. Time complexity is O(n + m)
2. Space complexity is O(1)