240. Search a 2D Matrix II

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 in ascending from left to right.
Integers in each column are sorted in ascending from top to bottom.
Example:

Consider the following matrix:

[
[1, 4, 7, 11, 15],
[2, 5, 8, 12, 19],
[3, 6, 9, 16, 22],
[10, 13, 14, 17, 24],
[18, 21, 23, 26, 30]
]
Given target = 5, return true.

Given target = 20, return false.

Approach #1 Using binary search in each column.

```CPP class Solution { public: bool searchMatrix(vector>& matrix, int target) { int len1 = matrix.size(); if (len1 == 0) return false; int len2 = matrix[0].size(); if (len2 == 0) return false; for (int i = 0; i < len1; ++i) { auto it = lower_bound(matrix[i].begin(), matrix[i].end(), target); if (it < matrix[i].end() && *it == target) return true; } return false; } };

</font>
Runtime: 88 ms, faster than 23.74% of C++ online submissions for Search a 2D Matrix II.


#### Approach #2  
```CPP
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();
        int i = 0, j = n - 1;
        for (; i < m && j >= 0; ) {
            if (matrix[i][j] == target) return true;
            else if (matrix[i][j] > target) j--;
            else i++;
        }
        return false;
    }
};

Runtime: 52 ms, faster than 55.98% of C++ online submissions for Search a 2D Matrix II.