1+ """
2+ Problem: Sort an Array
3+
4+ You are given an array of integers `nums`. Your task is to sort the array in ascending order and return it.
5+
6+ Requirements:
7+ - You must not use any built-in sorting functions.
8+ - Your solution should run in O(n log n) time complexity.
9+ - Your solution should use the smallest possible space complexity.
10+
11+ Example 1:
12+ Input: nums = [10, 9, 1, 1, 1, 2, 3, 1]
13+ Output: [1, 1, 1, 1, 2, 3, 9, 10]
14+
15+ Example 2:
16+ Input: nums = [5, 10, 2, 1, 3]
17+ Output: [1, 2, 3, 5, 10]
18+
19+ Constraints:
20+ - 1 <= nums.length <= 50,000
21+ - -50,000 <= nums[i] <= 50,000
22+ """
23+ from typing import List
24+ # Method 1:
25+ class Solution :
26+ def sortArray (self , nums : List [int ]) -> List [int ]:
27+ 28+ n = len (nums )
29+ 30+ for i in range (n - 1 ):
31+ for j in range (n - i - 1 ):
32+ 33+ if nums [j ] > nums [j + 1 ]:
34+ nums [j ] , nums [j + 1 ] = nums [j + 1 ] , nums [j ]
35+ 36+ return nums
37+ 38+ # Method 2:
39+ class Solution :
40+ def sortArray (self , nums : List [int ]) -> List [int ]:
41+ 42+ def merge (left , right ):
43+ new = []
44+ i = 0
45+ j = 0
46+ 47+ while i < len (left ) and j < len (right ):
48+ if left [i ] < right [j ]:
49+ new .append (left [i ])
50+ i += 1
51+ else :
52+ new .append (right [j ])
53+ j += 1
54+ 55+ new .extend (left [i :])
56+ new .extend (right [j :])
57+ return new
58+ 59+ def merge_sort (nums : List [int ]):
60+ if len (nums ) <= 1 :
61+ return nums
62+ 63+ mid = len (nums ) // 2
64+ left_arr = nums [:mid ]
65+ right_arr = nums [mid :]
66+ 67+ left_arr = merge_sort (left_arr )
68+ right_arr = merge_sort (right_arr )
69+ return merge (left_arr , right_arr )
70+ 71+ return merge_sort (nums )
72+ 73+ # Method 3:
74+ class Solution :
75+ def sortArray (self , nums : List [int ]) -> List [int ]:
76+ 77+ def merge_sort (nums ):
78+ 79+ if len (nums ) == 1 :
80+ return nums
81+ 82+ mid = len (nums ) // 2
83+ left_arr = nums [:mid ]
84+ right_arr = nums [mid :]
85+ 86+ left_arr = merge_sort (left_arr )
87+ right_arr = merge_sort (right_arr )
88+ 89+ merge (left_arr ,right_arr ,nums )
90+ return nums
91+ 92+ def merge (left ,right ,nums ):
93+ i = 0
94+ j = 0
95+ k = 0
96+ 97+ while i < len (left ) and j < len (right ):
98+ if left [i ] < right [j ]:
99+ nums [k ] = left [i ]
100+ i += 1
101+ else :
102+ nums [k ] = right [j ]
103+ j += 1
104+ 105+ k += 1
106+ 107+ while i < len (left ):
108+ nums [k ] = left [i ]
109+ i += 1
110+ k += 1
111+ 112+ while j < len (right ):
113+ nums [k ] = right [j ]
114+ j += 1
115+ k += 1
116+ 117+ return merge_sort (nums )
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