74. 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.

1
2
3
4
Example 1:

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

1
2
3
4
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 <= 10^4

Solution

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        int cols = matrix.length;
        int rows = matrix[0].length;
        
        int lo = 0;
        int hi = cols * rows - 1;
        
        while (lo <= hi) {
            
            int mid = lo + (hi - lo) / 2;
            
            int value = matrix[mid / rows][mid % rows];
            
            if (value == target) {
                return true;
            }
            
            if (target < value) {
                hi = mid - 1;
            } else {
                lo = mid + 1;
            }
        }
        return false;
    }
}

Solution#

Solution