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What is factorial?
In mathematical operations, n! represents the factorial
of n. It is expressed as a mathematical formula:
n!=1*2*3*....*( n-1)*n
An example is provided below: For example, the factorial of 5
# 正确的结果 1*2*3*4*5
The correct result is: 120
The editor provides you with 3 types Different methods to implement factorial operation:
result = 1 # 给定一个初始值 n = 5 for i in range(1, n+1): print("累乘前result: ", result) print("循环数i的值: ", i) result = result * i # 不断地累成result print("累乘后result: ", result) print("------------") result
Result before cumulative multiplication: 1Method 2-Use recursive functionValue of cycle number i: 1
Result after cumulative multiplication: 1
------------
Result before cumulative multiplication: 1
Value of cycle number i : 2
result after cumulative multiplication: 2
------------
result before cumulative multiplication: 2
value of loop number i: 3
cumulative multiplication After result: 6
------------
Result before cumulative multiplication: 6
Value of loop number i: 4
Result after cumulative multiplication: 24
------------
Result before cumulative multiplication: 24
Value of cycle number i: 5
Result after cumulative multiplication: 120
------- -----
The result is: 120
def recursion(n): if n == 0 or n == 1: # 特殊情况 return 1 else: return n * recursion(n-1) # 递归函数rrree
120Method 3 - The reduce function of the third-party library functools
recursion(5)
120Explanation of usage of the reduce function:
# 在python3中reduce函数被移入到functools中;不再是内置函数 from functools import reduce n = 5 reduce(lambda x,y: x*y, range(1,n+1))
reduce(function, iterable[, initializer])
15# 使用自定义函数 from functools import reduce number = range(1,6) # number = [1,2,3,4,5] def add(x,y): return x+y reduce(add, number) # 1+2+3+4+5
15Python implements factorial accumulation Sum-Advanced VersionThe following is an advanced requirement:
How to implement the cumulative sum of factorials?
# 使用匿名函数 from functools import reduce number = range(1,6) reduce(lambda x,y: x+y, number) # 1+2+3+4+5The correct result is 153Method 1-cumulative sum
# 求出下面的阶乘的累加求和 1 + 1*2 + 1*2*3 + 1*2*3*4 + 1*2*3*4*5
120The above is our implementation For the factorial of a single number, put it into a for loop to find the cumulative sum:
# 定义累乘函数 def func(n): result = 1 for i in range(1, n+1): result = result * i # 不断地累成re return result func(5) # 测试案例
153Method 2-Cumulative multiplication recursionIn Use cumulative multiplication and recursive functions simultaneously in one function
# func(1) + func(2) + func(3) + func(4) + func(5) # 调用累乘函数 sum(func(i) for i in range(1,6))
153Method 3-Recursive sum
# 定义累乘函数 def func(n): result = 1 # 定义初始值 for i in range(1, n+1): result = result * i # 不断地累成re # if result == 1 : 等价于下面的条件 if n==0 or n==1: return 1 else: # 下面是关键代码 return result + func(n-1) #在这里实现递归 func(n-1) func(5)
def recursion(n): """ 之前定义的递归函数 """ if n == 0 or n == 1: return 1 else: return n * recursion(n-1)
153Method 4-reduce combined with sum
# recursion(1) + recursion(2) + recursion(3) + recursion(4) + recursion(5) # 调用定义的递归函数 sum(recursion(i) for i in range(1,6))
120Single Call the reduce function twice, combining the for loop and sum to find the sum
from functools import reduce n = 5 reduce(lambda x,y: x*y, range(1,n+1))
153Method 5 - reduce function twice
sum(reduce(lambda x,y: x*y, range(1,n+1)) for n in range(1,6))
[ 1, 2, 6, 24, 120]Pass the above result into the reduce function again as an iterable list. The execution function at this time is the sum of two elements (x y):
[reduce(lambda x,y: x*y, range(1,n+1)) for n in range(1,6)]
153
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