BZOJ 4488: [Jsoi2015]最大公约数

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;
}