Leetcode 240. Search a 2D Matrix II

https://leetcode.com/problems/search-a-2d-matrix-ii/

Medium

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.

---

• 三種解法
  • 1. 從右上角開始找，i.e. 當前行最大，當前列最小的開始。由於橫豎都是升序，因此若是target > current，必然不在當前行；若是target < current，必然不在當前列。
  • 2. Python any() function
    • https://docs.python.org/3/library/functions.html#any
  • 3. 對每一行進行二分查找。記得Python3要用整除//, i.e. middle = (left + right) // 2。
  • https://leetcode.com/problems/search-a-2d-matrix-ii/discuss/66140/My-concise-O(m%2Bn)-Java-solution
  • https://leetcode.com/problems/search-a-2d-matrix-ii/discuss/66163/C%2B%2B-two-solutions-(O(m%2Bn)-O(mlogn))

 1 class Solution:
 2     def searchMatrix(self, matrix, target):
 3         """
 4         :type matrix: List[List[int]]
 5         :type target: int
 6         :rtype: bool
 7         """
 8         if not matrix or len(matrix) == 0 or len(matrix[0]) == 0:
 9             return False
10         
11         row, column = 0, len(matrix[0]) - 1
12         
13         while row < len(matrix) and column >= 0:
14             if target == matrix[row][column]:
15                 return True
16             elif target < matrix[row][column]:
17                 column -= 1
18             else:
19                 row += 1
20         
21         return False
22     
23     def searchMatrix2(self, matrix, target):
24         """
25         :type matrix: List[List[int]]
26         :type target: int
27         :rtype: bool
28         """
29         return any(target in row for row in matrix)
30     
31     def searchMatrix3(self, matrix, target):
32         """
33         :type matrix: List[List[int]]
34         :type target: int
35         :rtype: bool
36         """
37         if not matrix or len(matrix) == 0 or len(matrix[0]) == 0:
38             return False
39         
40         def helper(nums, target):
41             left, right = 0, len(nums) - 1
42             
43             while left <= right:
44                 # remember to use // 2
45                 middle = (left + right) // 2
46 
47                 if target == nums[middle]:
48                     return True
49                 elif target < nums[middle]:
50                     right = middle - 1
51                 else:
52                     left = middle + 1
53             
54             return False
55         
56         for row in matrix:
57             if helper(row, target):
58                 return True
59         
60         return False

View Python Code