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 1:

Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 3
Output: true

Example 2:

Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13
Output: false

 

Constraints:

• m == matrix.length
• n == matrix[i].length
• 1 <= m, n <= 100
• -104 <= matrix[i][j], target <= 104

Solution

/**
 * @param {number[][]} matrix
 * @param {number} target
 * @return {boolean}
 */
var searchMatrix = function(matrix, target) {
    const m = matrix.length;
    const n = matrix[0].length;
    let lo = 0;
    let hi = m * n - 1;

    while (lo <= hi) {
        const mid = Math.floor((lo + hi) / 2);
        const r = Math.floor(mid / n);
        const c = mid % n;
        if (matrix[r][c] < target) {
            lo = mid + 1;
        } else if (matrix[r][c] > target) {
            hi = mid - 1;
        } else {
            return true;
        }
    }
    return false;
};

Treat matrix as a 1D sorted list and apply standard binary search. To do so, we need to convert from 1D index to 2D index whenever we need to find the value at mid.