[F3-24] Fibonacci

In [2]:

def fibonacci(n):
    if n <= 2:
        number = 1
    else:
       number = fibonacci(n-1) + fibonacci(n-2)
    return number

In [3]:

fibonacci(3)

Out[3]:

2

In [5]:

fibonacci(4)

Out[5]:

3

Memoization¶

좀 더 빠르게 연산하기 위해 일정 값을 기억하게 하기
중간 계산값을 기억시켜서 다시 계산하는 대신 바로 읽게 하여 시간을 줄임

In [8]:

memory = {1: 1, 2: 1}

def fibonacci(n):
    if n in memory:
        number = memory[n]
    else:
       number = fibonacci(n-1) + fibonacci(n-2)
    return number

fibonacci(2)

Out[8]:

1

In [10]:

memory = {1: 1, 2: 1}

def fibonacci(n):
    if n in memory:
        number = memory[n]
    else:
       number = fibonacci(n-1) + fibonacci(n-2)
       memory[n] = number # fibonacci(n-1)+fibonacci(n-2) 모두 메모리에 저장됨. -> 새로운 키 값을 저장시켜줌
    return number

In [11]:

memory = {1: 1, 2: 1}

def fibonacci(n):
    if n in memory:
        number = memory[n]
    else:
       number = fibonacci(n-1) + fibonacci(n-2)
       memory[n] = number
    return number

print(fibonacci(100))

print(memory)

354224848179261915075
{1: 1, 2: 1, 3: 2, 4: 3, 5: 5, 6: 8, 7: 13, 8: 21, 9: 34, 10: 55, 11: 89, 12: 144, 13: 233, 14: 377, 15: 610, 16: 987, 17: 1597, 18: 2584, 19: 4181, 20: 6765, 21: 10946, 22: 17711, 23: 28657, 24: 46368, 25: 75025, 26: 121393, 27: 196418, 28: 317811, 29: 514229, 30: 832040, 31: 1346269, 32: 2178309, 33: 3524578, 34: 5702887, 35: 9227465, 36: 14930352, 37: 24157817, 38: 39088169, 39: 63245986, 40: 102334155, 41: 165580141, 42: 267914296, 43: 433494437, 44: 701408733, 45: 1134903170, 46: 1836311903, 47: 2971215073, 48: 4807526976, 49: 7778742049, 50: 12586269025, 51: 20365011074, 52: 32951280099, 53: 53316291173, 54: 86267571272, 55: 139583862445, 56: 225851433717, 57: 365435296162, 58: 591286729879, 59: 956722026041, 60: 1548008755920, 61: 2504730781961, 62: 4052739537881, 63: 6557470319842, 64: 10610209857723, 65: 17167680177565, 66: 27777890035288, 67: 44945570212853, 68: 72723460248141, 69: 117669030460994, 70: 190392490709135, 71: 308061521170129, 72: 498454011879264, 73: 806515533049393, 74: 1304969544928657, 75: 2111485077978050, 76: 3416454622906707, 77: 5527939700884757, 78: 8944394323791464, 79: 14472334024676221, 80: 23416728348467685, 81: 37889062373143906, 82: 61305790721611591, 83: 99194853094755497, 84: 160500643816367088, 85: 259695496911122585, 86: 420196140727489673, 87: 679891637638612258, 88: 1100087778366101931, 89: 1779979416004714189, 90: 2880067194370816120, 91: 4660046610375530309, 92: 7540113804746346429, 93: 12200160415121876738, 94: 19740274219868223167, 95: 31940434634990099905, 96: 51680708854858323072, 97: 83621143489848422977, 98: 135301852344706746049, 99: 218922995834555169026, 100: 354224848179261915075}

In [ ]: