codeforces 822D My pretty girl Noora

本文探讨了一道复杂的数学题目,并通过分析发现最优解与素数相关。使用埃氏筛法进行质因数分解,并设计了一个简单的动态规划算法来求解问题。代码实现了高效的求解过程。

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传送门

很烦,不会做的尴尬,好神的数学题。

很显然就是求f(x)剩下的暴力,博主表示打表找规律一点没用上(主要是博主菜),首先证明一个东东就是每一轮分女孩的组数一定是素数(这个鬼知道啊!!),考虑合数di = a·b,显然有,然后基本不等式+放缩就有,也就是只要是个合数就一定没素数组数优(2333我怎么可能会想到往素数方面考虑)

然后埃氏筛法质因数分解,设is_prime[i]表示i的最小素因数,主要就是这段代码:

	for(int i=2;i<=Maxn;i++)
		is_prime[i]=i; 
	for(int i=2;i*i<=Maxn;i++)
		if(is_prime[i]==i) 
			for(int j=i*i;j<=Maxn;j+=i)
				is_prime[j]=min((long long)i,is_prime[j]);

最后就是个简单的dp,f[i]=min(f[i],f[i/is_prime[j]]+i*(is_prime[j]-1)/2)这个方程应该很显然。

注意long long!!

代码:

#include<iostream>
#include<stdio.h>
using namespace std;
const int Maxn=5*1e6;
const int oo=2147483647;
const int MOD=1e9+7;
long long f[Maxn],is_prime[Maxn];
void Eratosthenes_sieve()
{
	for(int i=2;i<=Maxn;i++)
		is_prime[i]=i; 
	for(int i=2;i*i<=Maxn;i++)
		if(is_prime[i]==i) 
			for(int j=i*i;j<=Maxn;j+=i)
				is_prime[j]=min((long long)i,is_prime[j]);
}
int main()
{
	int t,l,r,ans=0,p=1;
	scanf("%d%d%d",&t,&l,&r);
	Eratosthenes_sieve();
	for(int i=2;i<=r;i++)
		f[i]=(long long)oo*oo;
	f[1]=0;
	for(int i=2;i<=r;i++)
		for(int j=i;j!=1;j/=is_prime[j])
			f[i]=min(f[i],f[i/is_prime[j]]+i*(is_prime[j]-1)/2)%MOD;
	for(int i=l;i<=r;i++,p=((long long)p*t)%MOD)
		ans=((f[i]%MOD)*p%MOD+ans)%MOD;
	printf("%d",ans);
	return 0;
} 


### Codeforces 1487D Problem Solution The problem described involves determining the maximum amount of a product that can be created from given quantities of ingredients under an idealized production process. For this specific case on Codeforces with problem number 1487D, while direct details about this exact question are not provided here, similar problems often involve resource allocation or limiting reagent type calculations. For instance, when faced with such constraints-based questions where multiple resources contribute to producing one unit of output but at different ratios, finding the bottleneck becomes crucial. In another context related to crafting items using various materials, it was determined that the formula `min(a[0],a[1],a[2]/2,a[3]/7,a[4]/4)` could represent how these limits interact[^1]. However, applying this directly without knowing specifics like what each array element represents in relation to the actual requirements for creating "philosophical stones" as mentioned would require adjustments based upon the precise conditions outlined within 1487D itself. To solve or discuss solutions effectively regarding Codeforces' challenge numbered 1487D: - Carefully read through all aspects presented by the contest organizers. - Identify which ingredient or component acts as the primary constraint towards achieving full capacity utilization. - Implement logic reflecting those relationships accurately; typically involving loops, conditionals, and possibly dynamic programming depending on complexity level required beyond simple minimum value determination across adjusted inputs. ```cpp #include <iostream> #include <vector> using namespace std; int main() { int n; cin >> n; vector<long long> a(n); for(int i=0;i<n;++i){ cin>>a[i]; } // Assuming indices correspond appropriately per problem statement's ratio requirement cout << min({a[0], a[1], a[2]/2LL, a[3]/7LL, a[4]/4LL}) << endl; } ``` --related questions-- 1. How does identifying bottlenecks help optimize algorithms solving constrained optimization problems? 2. What strategies should contestants adopt when translating mathematical formulas into code during competitive coding events? 3. Can you explain why understanding input-output relations is critical before implementing any algorithmic approach? 4. In what ways do prefix-suffix-middle frameworks enhance model training efficiency outside of just tokenization improvements? 5. Why might adjusting sample proportions specifically benefit models designed for tasks requiring both strong linguistic comprehension alongside logical reasoning skills?
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