题目

Write an efficient algorithm that searches for a value target in an m x n integer matrix 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 1:

Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 3
Output: true

Example 2:

Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13
Output: false

思路

两次二分查找，第一次查找目标值在数组的哪一列，第二次查找目标值在数组的哪一行。

代码

python版本：

class Solution:
    def searchMatrix(self, matrix: List[List[int]], target: int) -> bool:
        l, r = 0, len(matrix)
        while l < r:
            mid = (l+r)//2
            if matrix[mid][0] > target:
                r = mid
            elif matrix[mid][-1] >= target:
                l = mid
                break
            else:
                l = mid+1
        x = l
        if x < 0 or x >= len(matrix):
            return False
        l, r = 0, len(matrix[x])
        while l < r:
            mid = (l+r)//2
            if matrix[x][mid] > target:
                r = mid
            elif matrix[x][mid] < target:
                l = mid+1
            else:
                return True
        return False