質問の逆関数の問題をPythonで解いてみた。

　質問の逆関数の問題をPythonで解いてみました。というか、検算してみました。(^_^;

● InvFunc1.py

# coding: UTF-8
# InvFunc1.py
'''
               n
      4n-1+(-1)
 x = ------------
          2
          x+1
 n = Int(-----) = (x+1)//2
           2
'''
from time import time

def main():
    tm = time()  # Timer Start
    M = 100
    R = list(range(1,M+1))  # 自然数1〜100までのリスト
    lX = []
    for n in R:
        x = (4*n-1+(-1)**n)//2
        lX.append(x)
    print(lX)

    lN = []
    for x in lX:
        n = (x+1)//2    # int((x+1)/2)でもよい
        lN.append(n)
    print(lN)
    print(lN==R)
    print("Runtime : %.3f [sec]"%(time()-tm))   # Timer Stop & Disp

if __name__ == '__main__':
    main()

●実行結果

[1, 4, 5, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 56, 57, 60, 61, 64, 65, 68, 69, 72, 73, 76, 77, 80, 81, 84, 85, 88, 89, 92, 93, 96, 97, 100, 101, 104, 105, 108, 109, 112, 113, 116, 117, 120, 121, 124, 125, 128, 129, 132, 133, 136, 137, 140, 141, 144, 145, 148, 149, 152, 153, 156, 157, 160, 161, 164, 165, 168, 169, 172, 173, 176, 177, 180, 181, 184, 185, 188, 189, 192, 193, 196, 197, 200]
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]
True
Runtime : 0.001 [sec]