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.

class Solution {
public:
    bool searchMatrix(vector<vector<int> > &matrix, int target) {
        if(target<matrix[0][0])
            return false;
        int row    = matrix.size();
        int column = matrix[0].size();
        if(target>matrix[row-1][column-1])
            return false;
         int i,j;
         
        if(row==1)
     {       for(j=0;j<column;j++)
            {
                if(target==matrix[0][j])
                    return true;
            }
            return false;
    }
       
        for(i=0;i<row;i++)
        {
            if(target<matrix[i][0])
                {
                    for(j=0;j<column;j++)
                    {
                        if(target==matrix[i-1][j])
                            return true;
                    }
                    return false;
                }
        }
         for(j=0;j<column;j++)
             {
                if(target==matrix[row-1][j])
                    return true;
             }
                    return false;
    }
};