Codeforces 337D

本文探讨了树的直径概念及其应用。通过分析树内任意一点到标记点子树的距离问题,得出子树直径上的端点为最远点的结论。采用广度优先搜索算法计算子树直径,并遍历所有节点来确定是否存在符合条件的点。

题意略。

思路:

本题着重考察树的直径。如果我们将这些标记点相连,将会得到大树中的一个子树。我之前只知道树内的点到直径上两端点的距离是最远的,其实,在

整个大树中,这个性质同样适用,也即大树上任意一点,到子树中任意一点的距离,其中距离最远者必为子树直径上的端点。

 

如果我从子树的端点接入,那子树中的最远点必然是端点;如果我从非端点接入,那我到最远点的距离是   我到非端点的距离 + 非端点所能达到的最远点的距离

也即我到某个端点的距离。

 

那么我只要看任一个点到子树的两个端点的距离中最大的值,是不是小于等于d,如果是,则有可能存在鬼。

详见代码:

#include<bits/stdc++.h>
#define maxn 100005
using namespace std;

int n,m,d;
int dist[3][maxn];
int mark[maxn];
vector<int> graph[maxn];
queue<int> que;

int bfs(int num,int s){
    while(que.size()) que.pop();
    dist[num][s] = 0;
    que.push(s);
    int ret = -1;
    while(que.size()){
        int temp = que.front();
        que.pop();
        for(int i = 0;i < graph[temp].size();++i){
            int to = graph[temp][i];
            if(dist[num][to] != -1) continue;
            dist[num][to] = dist[num][temp] + 1;
            if(mark[to]){
                if(ret == -1 || dist[num][ret] < dist[num][to]){
                    ret = to;
                }
            }
            que.push(to);
        }
    }
    return ret;
}

int main(){
    scanf("%d%d%d",&n,&m,&d);
    for(int i = 0;i < m;++i){
        int p;
        scanf("%d",&p);
        mark[p] = 1;
    }
    int u,v;
    for(int i = 0;i < n - 1;++i){
        scanf("%d%d",&u,&v);
        graph[u].push_back(v);
        graph[v].push_back(u);
    }
    memset(dist,-1,sizeof(dist));
    int v1 = bfs(0,1);
    int v2 = bfs(1,v1);
    bfs(2,v2);
    int cnt = 0;
    for(int i = 1;i <= n;++i){
        int d1 = dist[1][i],d2 = dist[2][i];
        if(max(d1,d2) <= d) ++cnt;
    }
    printf("%d\n",cnt);
    return 0;
}

 

转载于:https://www.cnblogs.com/tiberius/p/9165788.html

### 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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