Search a 2D Matrix

Problem

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.

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

Code - Java

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) {
        int rowIndex = binarySearchRow(matrix, target);
        if (rowIndex == -1) {
            return false;
        }
        return binarySearchElement(matrix[rowIndex], target);
    }

    private int binarySearchRow(int[][] matrix, int target) {
        int start = 0, end = matrix.length - 1;
        while (start <= end) {
            int mid = (start + end) / 2;
            int[] row = matrix[mid];
            if (target < row[0]) {
                end = mid - 1;
            } else if (target > row[row.length - 1]) {
                start = mid + 1;
            } else {
                return mid;
            }
        }
        return -1;
    }

    private boolean binarySearchElement(int[] row, int target) {
        int start = 0, end = row.length - 1;
        while (start <= end) {
            int mid = (start + end) / 2;
            if (target < row[mid]) {
                end = mid - 1;
            } else if (target > row[mid]) {
                start = mid + 1;
            } else {
                return true;
            }
        }
        return false;
    }
}