Leetcode: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.

分析：将二维数组看为一个一维sorted数组，然后用bianry search。时间复杂度为O(log(m*n)),代码如下：

class Solution {
public:
    bool searchMatrix(vector<vector<int> > &matrix, int target) {
        int m = matrix.size();
        if(m == 0) return false;
        int n = matrix[0].size();
        if(n == 0) return false;
        
        int l = 0, r = m * n - 1;
        while(l <= r){
            int mid = (l + r)/2;
            int row = mid/n, col = mid%n;
            if(matrix[row][col] == target) return true;
            if(matrix[row][col] < target) l = mid + 1;
            else r = mid - 1;
        }
        
        return false;
    }
};