# Search a 2D Matrix

### 描述​

Write an efficient algorithm that searches for a value in an m × 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.

### 代码​

// Search a 2D Matrix// 时间复杂度O(logn)，空间复杂度O(1)public class Solution {    public boolean searchMatrix(int[][] matrix, int target) {        if (matrix.length == 0) return false;        final int  m = matrix.length;        final int n = matrix[0].length;        int first = 0;        int last = m * n;        while (first < last) {            int mid = first + (last - first) / 2;            int value = matrix[mid / n][mid % n];            if (value == target)                return true;            else if (value < target)                first = mid + 1;            else                last = mid;        }        return false;    }}