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  1. Prepare
  2. Algorithms
  3. Recursion
  4. The Power Sum
  5. Discussions

The Power Sum

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352 Discussions

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  • vutrantrung14821
     + 0 comments
    def h(i,S,X,N):
    e=0
    for j in range(i+1,int(X**1/N)+1):
        if S+j**N<X:
            e=e+h(j,S+j**N,X,N)
        elif S+j**N==X:
            e+=1
        else:
            continue
    return e



def powerSum(X, N):
    a=0
    for i in range(1,int(X**1/N)+1):
        S=i**N
        if S < X:
            a += h(i, S, X, N)
        elif S == X:
            a += 1
    return a

  • ilovemylittlecr1
     + 0 comments

    The most intuitive solution you will ever find in this entire discussion. Plus, the run time speed surpassed editorial solution.

    include

    using namespace std;

    int ipow(const int& b, const int& e){ if(e == 0) return 1; return b * pow(b, e - 1); }

    int recursion_ans(const vector& vec, const int& index, const int& remaining){ if(remaining == 0) return 1; if(index < 0 || remaining < 0) return 0;

    return recursion_ans(vec, index - 1, remaining - vec[index]) + 
        recursion_ans(vec, index - 1, remaining);

    }

    int main(){ int X, N; cin >> X >> N;

    vector<int> vec;

int i = 1;
while(i){
    int value = ipow(i, N); ++i;
    if(value > X) break;
    vec.push_back(value);
}

cout << recursion_ans(vec, vec.size() - 1, X);

return 0;

    }

  • jmcparland
     + 0 comments

    Haskell

    Function wwo -- "with or without"

    module Main where

vals :: Int -> Int -> [Int]
vals n k = reverse $ takeWhile (<= n) [x ^ k | x <- [1 ..]]

wwo :: Int -> [Int] -> Int
wwo n xs
  | n == 0 = 1
  | n < 0 = 0
  | null xs = 0
  | otherwise = wwo n (tail xs) + wwo (n - head xs) (tail xs)

main :: IO ()
main = do
  n <- readLn :: IO Int
  k <- readLn :: IO Int
  print $ wwo n (vals n k)

  • SI006677Abhishek
     + 1 comment

    int findPows(int X, int num, int N) {

    int val = X - pow(num, N);
if (val < 0) {
    return 0;  
}
if (val == 0) {
    return 1;  
}

return findPows(val, num + 1, N) + findPows(X, num + 1, N);

    }

    int powerSum(int X, int N) { return findPows(X, 1, N); }

  • dehaka
     + 0 comments

    knapsack, O(X * X^(1/N))

    int powerSum(int X, int N) {
    int L = pow(X, 1.0/N);
    vector<vector<int>> cache(X+1, vector<int>(L+1));
    for (int j=0; j <= L; j++) cache[0][j] = 1;
    for (int i=1; i <= X; i++) {
        for (int j=1; j <= L; j++) {
            if (i < pow(j, N)) cache[i][j] = cache[i][j-1];
            else cache[i][j] = cache[i][j-1] + cache[i - pow(j, N)][j-1];
        }
    }
    return cache[X][L];
}