是否有任何 O(n^2) 算法来生成数组的所有子序列? [英] Is there any O(n^2) algorithm to generate all sub-sequences of an array?

问题描述

我想知道是否有任何 O(n^2) 复杂度算法来生成数组的所有子序列.我知道一个算法，但它需要 O((2^n)*n) 时间.

I was wondering if there is any O(n^2) complexity algorithm for generating all sub-sequences of an array. I know an algorithm but it takes O((2^n)*n) time.

int main() {
    int n; 
    cin >> n;
    vector<int> a(n);
    for(int i = 0; i < n; ++i) 
        cin >> a[i];
    int64_t opsize = pow(2,n);
    for (int counter = 1; counter < opsize; counter++) {
        for (int j = 0; j < n; j++) {
           if (counter & (1 << j))
                 cout << a[j] << " ";
        }
        cout << endl;
    }
}

推荐答案

否

不可能有任何算法的复杂度小于O(2^n)，因为有O(2^n) 个子序列.您需要打印它们中的每一个，因此时间复杂度必须大于或等于 O(2^n).

There cannot be any algorithm of less than O(2^n) complexity simply because there are O(2^n) sub-sequences. You need to print each of them hence the time complexity has to be greater than or equal to O(2^n).

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