題目

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

從矩陣的最右端元素開始考慮，如果它比所求要大，那么在當(dāng)前行查找即可。否則，進(jìn)入下一行。

代碼

class Solution(object):

    def binarySearch(self, nums, l, r, target):
        if l > r:
            return False
        m = l + (r-l)/2
        if nums[m] == target:
            return True
        elif nums[m] > target:
            return self.binarySearch(nums, l, m-1, target)
        else:
            return self.binarySearch(nums, m+1, r, target)

    def searchMatrix(self, matrix, target):
        """
        :type matrix: List[List[int]]
        :type target: int
        :rtype: bool
        """
        if matrix==None or len(matrix)==0:
            return False
        m = len(matrix)
        n = len(matrix[0])
        i = 0
        while i < m:
            if matrix[i][n-1] == target:
                return True
            elif matrix[i][n-1] > target:
                return self.binarySearch(matrix[i], 0, n-1, target)
            else:
                i += 1
        return False