Python中子序列递归的总和

Question

Over the weekend I was working on the Ad Infinitum challenge on HackerRank.

One problem was to calculate the sum of all subsequences of a finite sequence, if each subsequence is thought of as an integer.

For example, sequence 4,5,6 would give answer 4 + 5 + 6 + 45 + 46 + 56 + 456 = 618.

I found a recursion and wrote the Python code below. It solved 5/13 test cases.

The remaining 8/13 test cases had runtime errors.

I was hoping someone could spy where in the code the inefficiencies lie, and how they can be sped up. Or, help me decide that it must be that my recursion is not the best strategy.

# Input is a list, representing the given sequence, e.g. L = [4,5,6]

def T(L): 
    limit = 10**9 + 7  # answer is returned modulo 10**9 + 7
    N = len(L)
    if N == 1: 
        return L[0]
    else:
        last = L[-1] 
        K = L[:N-1]
        ans =  T(K)%limit + 10*T(K)%limit + (last%limit)*pow(2,N-1,limit)
        return ans%limit

Answer 1

Well, you want the combinations:

from itertools import combinations

def all_combinations(iterable):
    for r in range(len(digits)):
        yield from combinations(digits, r+1)

And you want to convert them to integers:

def digits_to_int(digits):
    return sum(10**i * digit for i, digit in enumerate(reversed(digits)))

And you want to sum them:

sum(map(digits_to_int, all_combinations([4, 5, 6])))

Then focus on speed.

Answer 2

Assuming you mean continuous subsequence.

test = [4, 5, 6]

def coms(ilist):
    olist = []
    ilist_len = len(ilist)
    for win_size in range(ilist_len, 0, -1):
        for offset in range((ilist_len - win_size) + 1):
            subslice = ilist[offset: offset + win_size]
            sublist  = [value * (10 ** power) for (power, value) in enumerate(reversed(subslice))]
            olist.extend(sublist)
    return olist

print sum(coms(test))

Answer 3

This is my submission for the same problem (Manasa and Sub-sequences). https://www.hackerrank.com/contests/infinitum-may14/challenges/manasa-and-sub-sequences

I hope this will help you to think of a better way.

ans = 0
count = 0
for item in raw_input():
    temp = (ans * 10 + (count + 1)*(int(item)))%1000000007
    ans = (ans + temp)%1000000007
    count = (count*2 + 1)%1000000007

print ans