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.

Example

Consider the following matrix:

[

    [1, 3, 5, 7],

    [10, 11, 16, 20],

    [23, 30, 34, 50]

]

Given target = 3, return true.

Challenge

O(log(n) + log(m)) time

class Solution {
public:
    /**
     * @param matrix, a list of lists of integers
     * @param target, an integer
     * @return a boolean, indicate whether matrix contains target
     */
    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 i = 0, j = m-1;
        while(i < j) {
            int k = (i + j + 1)/2;
            if (matrix[k][0] == target)  return true;
            if(matrix[k][0] > target) j = k - 1;
            else i = k; 
        }
        
        if (matrix[i][n-1] < target) return false;
        
        int row = i;
        i = 0, j = n-1;
        while(i <= j) {
            int m = (i+j)/2;
            if (matrix[row][m] == target) return true;
            if (matrix[row][m] > target) j = m-1;
            else i = m+1;
        }
        return false;
    }
};