Description

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.

Solutions

　　右上角向下向左遍历。

# Time: O(nlogn)
# Space: O(nlogn)
class Solution:
    def searchMatrix(self, matrix, target):
        """
        :type matrix: List[List[int]]
        :type target: int
        :rtype: bool
        """
        if not matrix or not matrix[0]:
            return False
        
        r = len(matrix)
        for i in range(r):
            if matrix[i][-1] < target:
                continue
            if self.binary_search(matrix[i], target):
                return True
        return False
    
    def binary_search(self, nums, target):
        if not nums:
            return False
        l, r = 0, len(nums) - 1
        while l <= r:
            mid = l + (r - l) // 2
            if nums[mid] == target:
                return True
            elif nums[mid] > target:
                r = mid - 1
            else:
                l = mid + 1
        return False

# 129/129 cases passed (32 ms)
# Your runtime beats 82.94 % of python3 submissions
# Your memory usage beats 88.89 % of python3 submissions (17.4 MB)

2. Trick

# Time: O(m+n)
# Space: O(1)
class Solution:
    def searchMatrix(self, matrix, target):
        if not matrix or not matrix[0]:
            return False
        
        r, c = 0, len(matrix[0]) - 1
        while r < len(matrix) and c >= 0:
            if matrix[r][c] == target:
                return True
            elif matrix[r][c] > target:
                c -= 1
            else:
                r += 1
        return False

# 129/129 cases passed (40 ms)
# Your runtime beats 36.96 % of python3 submissions
# Your memory usage beats 92.59 % of python3 submissions (17.4 MB)

References

  1. 240. Search a 2D Matrix II