4488: [Jsoi2015] 最大公约数
思路: 容易发现以某个位置 \(i\) 为结尾所有后缀的 \(gcd\) 个数不超过 \(log(a[i])\).
(怎么发现? 将数写成质因子幂次乘积的形式, 然后 \(gcd\) 每次减小一个质因子, 最多减少 \(log\) 次) 然后就可以用 \(map\) 维护每个 \(gcd\) 的最左端端点.
代码:
- #pragma GCC optimize(2)
- #pragma GCC optimize(3)
- #pragma GCC optimize(4)
- #include<bits/stdc++.h>
- using namespace std;
- #define fi first
- #define se second
- #define pi acos(-1.0)
- #define LL long long
- //#define mp make_pair
- #define pb push_back
- #define ls rt<<1, l, m
- #define rs rt<<1|1, m+1, r
- #define ULL unsigned LL
- #define pll pair<LL, LL>
- #define pii pair<int, int>
- #define piii pair<pii, int>
- #define mem(a, b) memset(a, b, sizeof(a))
- #define fio iOS::sync_with_stdio(false);cin.tie(0);cout.tie(0);
- #define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
- //head
- const int N = 1e5 + 5;
- LL a[N];
- map<LL, int> mp, _p;
- int n;
- int main() {
- scanf("%d", &n);
- for (int i = 1; i <= n; ++i) scanf("%lld", &a[i]);
- LL ans = 0;
- for (int i = 1; i <= n; ++i) {
- ans = max(ans, a[i]);
- for (map<LL, int>::iterator it = mp.begin(); it != mp.end(); ++it) {
- LL g = __gcd(a[i], (*it).fi);
- ans = max(ans, g*(i-(*it).se+1));
- if(_p.find(g) == _p.end()) _p[g] = (*it).se;
- }
- if(_p.find(a[i]) == _p.end()) _p[a[i]] = i;
- mp = _p;
- _p.clear();
- }
- printf("%lld\n", ans);
- return 0;
- }
来源: http://www.bubuko.com/infodetail-3136326.html