2. Search a 2D Matrix

Description

You are given an m x n integer matrix matrix with the following two properties:

• Each row is sorted in non-decreasing order.
• The first integer of each row is greater than the last integer of the previous row.

Given an integer target, return true if target is in matrix or false otherwise.

You must write a solution in O(log(m * n)) time complexity.

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
• -10^4 <= matrix[i][j], target <= 10^4

Approach

• Think of this one big single array and perform binary search just one thing to access the element you need to calculate row and column
• Time:O(log(m*n) Space:O(1)

class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        int ROW = matrix.length, COL = matrix[0].length;
 
        int l = 0, r = ROW * COL - 1;
        while (l <= r) {
            int m = l + (r - l) / 2;
            int row = m / COL, col = m % COL;
            if (matrix[row][col] > target)
                r = m - 1;
            else if (matrix[row][col] < target)
                l = m + 1;
            else
                return true;        
        }
 
        return false;
    }
}