CodeForces 364D Ghd (随机)_ghd codeforces

本文链接：https://blog.youkuaiyun.com/u013654696/article/details/51682912

本文分享了一段使用C++实现的复杂算法竞赛代码，该算法通过随机选取元素并进行最大公约数运算来求解最优解。代码运用了标准模板库(set、sort等)，并详细展示了如何高效地处理大量整数的运算。

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#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cstdlib>
#include <set>
using namespace std;


#define N 1000020
#define LL long long


int n;
LL a[N], b[N];
LL ans;
LL san[N];
int cnt, c[N], d[N];

set<LL> s;

LL gcd(LL a, LL b) {
	while(a && b && (a >= b? a %= b: b %= a));
	return a + b;
}

int haxi(LL x) {
	return lower_bound(san + 1, san + cnt + 1, x) - san;
}
void calc(int x) {
	cnt = 0;
	for(int i = 1; i <= n; ++i) {
		b[i] = gcd(a[i], a[x]);
	}
	for(int i = 1; 1LL * i * i <= a[x]; ++i) {
		if(a[x] % i) continue;
		san[++cnt] = i;
		if(1LL * i * i != a[x]) san[++cnt] = a[x] / i;
	}
	sort(san + 1, san + cnt + 1);
	cnt = unique(san + 1, san + cnt + 1) - san - 1;
	for(int i = 1; i <= cnt; ++i) c[i] = d[i] = 0;

	for(int i = 1; i <= n; ++i) c[haxi(b[i])]++;
	for(int i = 1; i <= cnt; ++i) {
		if(san[i] <= ans) continue;
		for(int j = i; j <= cnt; ++j) {
			if(san[j] % san[i] == 0) d[i] += c[j];
		}
	}
	for(int i = 1; i <= cnt; ++i) {
		if(d[i] * 2 >= n) ans = max(ans, san[i]);
	}
}





int main() {
	scanf("%d", &n);
	for(int i = 1; i <= n; ++i) scanf("%I64d", &a[i]);

	ans = 1;
	srand(233);
	for(int x = 1, cnt = 0; x <= 12 && cnt <= 1000020; ++x, ++cnt) {
		int v = 1LL * rand() * rand() % n + 1;
		if(s.count(a[v])) {
			--x;
			continue;
		}
		s.insert(a[v]);
		calc(v);
	}
	printf("%I64d\n", ans);
	return 0;
}