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.

 

A: 非常简单，二分查找。

    bool searchMatrix(vector<vector<int> > &matrix, int target) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        if(matrix.empty()||matrix[0].empty())
            return false;
            
        int rows = matrix.size();
        int cols = matrix[0].size();
        
        int begin = 0,end = rows*cols-1;
        int mid;
        
        while(begin<=end)
        {
            mid = begin+(end-begin)/2;
            if(matrix[mid/cols][mid%cols]==target)
                return true;
            else if(matrix[mid/cols][mid%cols]>target)
                end = mid-1;
            else begin = mid+1;
            
        }
        return false;
        
    }