Search a 2D Matrix II

Problem statement

Write an efficient algorithm that searches for a value target in an m x n integer matrix 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.

Example 1:

Input: 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]], target = 5Output: true

Example 2:

Input: 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]], target = 20Output: false

Constraints:

• m == matrix.length
• n == matrix[i].length
• 1 <= n, m <= 300
• -109 <= matrix[i][j] <= 109
• All the integers in each row are sorted in ascending order.
• All the integers in each column are sorted in ascending order.
• -109 <= target <= 109

My solution

/**
 * @param {number[][]} matrix
 * @param {number} target
 * @return {boolean}
 */
var searchMatrix = function(matrix, target) {
    if (matrix.length === 0) {
        return false;
    }
    
    for (let i = 0; i < matrix.length; i++) {
        const row = matrix[i];
        
        if (row.length > 0 && row[0] <= target && row[row.length - 1] >= target) {
            if (search(row, target)) {
                return true;
            }
        }
    }
    
    return false;
};

function search(arr, target) {
    let left = 0;
    let right = arr.length;
    
    while (left < right) {
        const mid = Math.floor((right + left) / 2);
        
        const curr = arr[mid]
        
        if (curr === target) {
            return true
        } else {
             if (arr[mid] < target) {
                left = mid + 1
            } else {
                right = mid
            }
        }
    }
    
    return false;
}