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79 lines (68 loc) · 1.83 KB
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"""
This question is asked by Amazon
Q. How many number of ways are their to climb n stairs. Take a vriation of {1,2} once and finally {1,3,5}
"""
import sys
def num_of_ways(n):
n = int(n)
if n == 0 or n == 1: return 1
return num_of_ways(n-1)+num_of_ways(n-2)
def num_of_ways_iteration(n):
n = int(n)
if n == 0 or n == 1: return 1
num = [None] * (n+1)
num[0] = 1
num[1] = 1
for i in range(2, n+1):
num[i] = num[i-1] + num[i-2]
return num[n]
def num_of_ways_variation(n, X):
'''
The value of item in X shold not exceed value of n
'''
n = int(n)
if n==0: return 1
x = len(X)
if x == 2:
return num_of_ways(n-1)+num_of_ways(n-2)
if x == 3:
return num_of_ways(n-1)+num_of_ways(n-2)+num_of_ways(n-3)
if x == 4:
return num_of_ways(n-1)+num_of_ways(n-2)+num_of_ways(n-3)+num_of_ways(n-4)
def num_of_ways_variation_iteration(n, X):
'''
The value of item in X shold not exceed value of n
'''
n = int(n)
if n==0: return 1
total = 0
for i in X:
if n-i >=0: total+=num_of_ways_variation_iteration(n-i, X)
return total
def efficient_num_of_ways(n, X):
'''
The value of item in X shold not exceed value of n
'''
n = int(n)
if n==0: return 1
total = 0
num = [None] * (n+1)
num[0] = 1
for i in range(1, n+1):
for j in X:
if i-j >=0:
total+=num[i-j]
num[i] = total
return num[n]
if __name__ == "__main__":
'''
Call the fuction form command line
For example:
python recursion.py num_of_ways 4
'''
if sys.argv[3]:
variation = list(map(int, sys.argv[3: ]))
print(variation)
print(globals()[sys.argv[1]](sys.argv[2], variation))
elif sys.argv[2]:
print(globals()[sys.argv[1]](sys.argv[2]))