Search a 2D Matrix <leetcode>

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.

思路：首先遍历每一行的首元素，找到目标如果存在，应该在哪一行，然后在行里进行搜索，本来在这里想用二分查找，但是直接扫了一遍也ac了，代码如下（没有进行优化）：

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