finish 01-homework

2021-10-16 23:35:28 +08:00
parent 1a2d27dc09
commit 001839394c
12 changed files with 369 additions and 0 deletions
@@ -0,0 +1,64 @@
+'''
+Author: SJ2050
+Date: 2021-10-10 23:34:50
+LastEditTime: 2021-10-16 23:23:48
+Version: v0.0.1
+Description: Solution for homework 2.
+Copyright © 2021 SJ2050
+'''
+from itertools import permutations
+
+def combination(arr, n):
+    if n == 0:
+        return [[]]
+
+    l =[]
+    for i in range(0, len(arr)):
+        m = arr[i]
+        remLst = arr[i + 1:]
+
+        for p in combination(remLst, n-1):
+            l.append([m]+p)
+
+    return l
+
+
+def heapPermutation(arr, n, process):
+    if n == 1:
+        process(arr)
+        return
+
+    for i in range(n):
+        heapPermutation(arr, n-1, process)
+        if n & 1:
+            arr[0], arr[n-1] = arr[n-1], arr[0]
+        else:
+            arr[i], arr[n-1] = arr[n-1], arr[i]
+
+
+
+if __name__ == '__main__':
+    nums = [1, 2, 3, 4]
+    m = 3
+    count = 0
+    combs = combination(nums, m)
+
+    def printAndCount(arr):
+        global count
+        count += 1
+
+        for i in range(len(arr)):
+            print(f'{arr[i]}', end='')
+
+        print('')
+
+    print('3-digit nums:')
+    for c in combs:
+        heapPermutation(c, m, printAndCount)
+    print('-'*12)
+    print(f'Total count: {count}')
+
+    # 从一列数中取出三个元素组成三位数的算法复杂度分析:
+    # 首先是组合分析，从一列数中取出三个数的组合个数为n*(n-1)*(n-2)/6，算法时间复杂度为O(n^3).
+    # 接着，对每队组合进行排列，排列算法选用的是heap算法，其时间复杂度为O(n!).
+    # 故总的时间复杂度为: O((n^3)*(3!)) --> O(n^3)