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.

 

For example,

Consider the following matrix:

[
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]

Given target = 3, return true.

---

consider the matrix as a one-dimensional sorted array

do a binary search

T: O(lg(M*N)) = O(lgM+lgN)

---

public class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        int rows = matrix.length;
        int cols = matrix[0].length;
        int low = 0;
        int high = rows * cols - 1;
        while (low <= high) {
            int mid = (low + high) / 2;
            if (matrix[mid/cols][mid%cols] == target)
                return true;
            else if (matrix[mid/cols][mid%cols] < target)
                low = mid + 1;
            else if (matrix[mid/cols][mid%cols] > target)
                high = mid - 1;
        }
        return false;
        
    }
}