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OI-codes/Luogu/UVA307/UVA307.cpp

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#include <iostream>
#include <algorithm>
#include <functional>
#include <numeric>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 70;
int n, m, l, a[N], next[N];
bool flag, vis[N];
void dfs(int now, int last, int rest) {
if (!rest) {
if (now == m) {
flag = true;
return;
}
for (int i = 1; i <= n; i++) {
if (!vis[i]) {
vis[i] = true;
dfs(now + 1, i, l - a[i]);
if (flag) return;
vis[i] = false;
break;
}
}
}
int p = std::lower_bound(a + last + 1, a + n + 1, rest, std::greater<int>()) - a;
for (int i = p; i <= n; i++) {
if (!vis[i]) {
vis[i] = true;
dfs(now, i, rest - a[i]);
vis[i] = false;
if (flag || rest == a[i] || rest == l) return;
i = next[i];
}
}
}
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
while (cin >> n, n) {
flag = false;
std::fill_n(a, N, 0);
std::fill_n(next, N, 0);
std::fill_n(vis, N, false);
vis[1] = true;
for (int i = 1; i <= n; i++) {
cin >> a[i];
}
int sum = std::accumulate(a + 1, a + 1 + n, 0);
std::sort(a + 1, a + 1 + n, std::greater<int>());
for (int i = n; i; i--) {
next[i] = a[i] == a[i + 1] ? next[i + 1] : i;
}
for (l = a[1]; l <= sum / 2; l++) {
if (sum % l) continue;
m = sum / l;
dfs(1, 1, l - a[1]);
if (flag) {
cout << l << endl;
break;
}
}
if (!flag) cout << sum << endl;
}
return 0;
}