先贴出本人未特判但是AC的代码

#include <iostream>
#include <vector>
#define endl '\n'
using namespace std;

vector<int> final;
int a[10010];

vector<int> mul(vector<int>& A, int b) {
    vector<int> C;
    int t = 0;
    for (int i = 0; i < A.size() || t; i++) {
        if (i < A.size()) {
            t += A[i] * b;
        }
        C.push_back(t % 10);
        t /= 10;
    }
    while (C.size() > 1 && C.back() == 0) {
        C.pop_back();
    }
    return C;
}

int main() {
    int n, total = 0, cnt = 0;
    cin >> n;
    for (int i = 2; total < n; ++i) {
        total += i;
        a[cnt++] = i;
    }
    final.push_back(1);
    for (int i = 0; i < cnt; ++i) {
        if (a[i] == total - n) {
            continue;
        }
        final = mul(final, a[i]);
        cout << a[i] << " ";
    }
    cout << endl;
    for (int i = final.size() - 1; i >= 0; --i) {
        cout << final[i];
    }
    return 0;
}

此代码缺少对于$total - n = 1$情况的特判，当输入$53$时，输出为：

2 3 4 5 6 7 8 9 10
3628800

而$2$加到$10$的值是$54$而非$53$

所以这个代码是错误的，但是OJ并没有提示WA。

下面是重新提交的代码：

#include <iostream>
#include <vector>
#define endl '\n'
using namespace std;

vector<int> final;
int a[10010];

vector<int> mul(vector<int>& A, int b) {
    vector<int> C;
    int t = 0;
    for (int i = 0; i < A.size() || t; i++) {
        if (i < A.size()) {
            t += A[i] * b;
        }
        C.push_back(t % 10);
        t /= 10;
    }
    while (C.size() > 1 && C.back() == 0) {
        C.pop_back();
    }
    return C;
}

int main() {
    int n, total = 0, cnt = 0;
    cin >> n;
    for (int i = 2; total < n; ++i) {
        total += i;
        a[cnt++] = i;
    }
    final.push_back(1);
    if (total - n == 1) {
        a[0] = a[cnt - 1] + 1;
        cnt--;
        sort(a, a + cnt);
    }
    for (int i = 0; i < cnt; ++i) {
        if (a[i] == total - n) {
            continue;
        }
        final = mul(final, a[i]);
        cout << a[i] << " ";
    }
    cout << endl;
    for (int i = final.size() - 1; i >= 0; --i) {
        cout << final[i];
    }
    return 0;
}

当输入$53$时,输出为

3 4 5 6 7 8 9 11 
1995840

才是正确答案

本题可加强任何形如$(\sum_{i = 2}^{n}{i}) - 1$ 的数据