Codeforces 463D Gargari and Permutations

本文探讨了如何解决给定1到n的k个排列时寻找最长公共子序列的问题,通过使用动态规划方法,实现了一种有效求解策略。

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题意:给定1到n的k个排列。求最长公共子序列的长度。

这题是看了官方题解,才会的。

#include <iostream>
#include <cstdio>
using namespace std;
int n,k;
int position[5][1000];//记录position[i][j]记录第i行中,数字j出现的位置。 
int a[5][1000];//记录数列 
int dp[1000];//dp[i]表示,以下标i结尾的最长公共子序列长度。 
int main(void)
{
	while(cin>>n>>k){
		for(int i=0;i<k;i++){
			for(int j=0;j<n;j++){
				scanf("%d",&a[i][j]);
				position[i][--a[i][j]]=j;
			}
		}
		int ans=0;
		for(int j=0;j<n;++j){//对于 j 
			int maxn=0;
			for(int p=0;p <j;++p){//对于 以(j之前的每个点) 结尾的最长序列,判断j可不可以加进去 
				int i;
				for(i=1;i<k&&position[i][a[0][p]]<position[i][a[0][j]];++i) ; 
				if(i==k&&dp[p]>maxn){//求这些可以加进去的点中,dp值最大的一个 
						maxn=dp[p];// 
				}
			}
			dp[j]=maxn+1;//本点dp值=最大dp值加上1
			ans=max(ans,dp[j]);//求每一点dp值最大的一个。
		}
		printf("%d\n",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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