Search a 2D Matrix

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 from left to right.
• The first integer of each row is greater than the last integer of the previous row.

Have you met this question in a real interview? 

Yes

Example

Consider the following matrix:

[
    [1, 3, 5, 7],
    [10, 11, 16, 20],
    [23, 30, 34, 50]
]

Given target = 3, return true.

Challenge

O(log(n) + log(m)) time

public class Solution {
    /**
     * @param matrix, a list of lists of integers
     * @param target, an integer
     * @return a boolean, indicate whether matrix contains target
     */
    public boolean searchMatrix(int[][] matrix, int target) {
        // write your code here
        if(matrix == null || matrix.length == 0 || matrix[0].length == 0) return false;
        int m = matrix.length, n = matrix[0].length;
        int i = 0, j = m * n - 1;
        while(i <= j){
            int mid = (i+j) / 2;
            if(matrix[mid/n][mid%n] < target) i = mid + 1;
            else if(matrix[mid/n][mid%n] > target) j = mid - 1;
            else {
                return true;
            }  
        }
        return false;
    }
}