【LeetCode】74. Search a 2D Matrix

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.

 

思路：纵向二分查找确定target所在行，再进行普通的二分查找。

 

class Solution {
public:
    bool searchMatrix(vector<vector<int> > &matrix, int target) {
        if(matrix.empty() || matrix[0].empty())
            return false;
        int m = matrix.size();
        int n = matrix[0].size();
        
        int low = 0;
        int high = m-1;
        while(low <= high)
        {
            int mid = low+(high-low)/2;
            if(matrix[mid][0] == target)
                return true;
            else if(matrix[mid][0] > target)
                high = mid-1;
            else
                low = mid+1;
        }
        low --;
        if(low < 0)
            return false;
        int left = 0;
        int right = n-1;
        while(left <= right)
        {
            int mid = left+(right-left)/2;
            if(matrix[low][mid] == target)
                return true;
            else if(matrix[low][mid] > target)
                right = mid-1;
            else
                left = mid+1;
        }
        
        return false;
    }
};