Codeforces 1187E Tree Painting

本文介绍了解决Codeforces1187ETreePainting问题的一种算法思路,通过换根法来求解最优解。对于每棵树,从树根开始上色,其子节点上色顺序不影响结果。通过枚举所有可能的树根位置,找出能够获得最大点数的方案。

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Codeforces 1187E Tree Painting
思路是换根,对于一棵树,从它的树根开始上色,那么它的下一个上色点只能是它的孩子节点,对于先上哪个孩子节点是不影响的,因为各孩子都已经不连通,所以,对于一棵定根树,从它的树根开始上色,它的答案只有一种。枚举每个节点换成树根的情况,找到能获得的点数的最大值,就是答案。
在某种状态下,把树根(记作A)换到它的一个孩子节点(记作B)时,因为是从B开始上色,对于A所在的与B反向的分支的每一个节点,加上它们的机会又多了一次,而B所在的分支的每个节点,加上他们的机会都减少了一次。

  1. 1作为计算的第一个根,先算出以1为根时每个节点的后代个数,计算出1为根时的答案
  2. 在1为根时计算出的答案的基础上进行换根
  3. 继续递归

需要注意用long long 不然会爆

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=2e5+7;
ll ch[N];
ll vis[N];
vector<int> vec[N];
int n;
void init(){
    cin>>n;
    for(int i=0;i<n-1;i++){
        int a,b;
        cin>>a>>b;
        vec[a].push_back(b);
        vec[b].push_back(a);
    }
}

ll cal(int idx,int former){
    ll sum=1;
    for(int i=0;i<vec[idx].size();i++){
        if(vec[idx][i]!=former)
            sum+=cal(vec[idx][i],idx);
    }
    return ch[idx]=sum;
}

void dfs(int idx,int former){
    if(idx!=1)
    vis[idx]=vis[former]-ch[idx]+(n-ch[idx]);
    for(int i=0;i<vec[idx].size();i++){
        if(vec[idx][i]!=former&&!vis[vec[idx][i]])
            dfs(vec[idx][i],idx);
    }
}

int main(){
    init();
    cal(1,1);
    ll aa=0;
    for(int i=1;i<=n;i++){
        aa+=ch[i];
    }
    vis[1]=aa;
    dfs(1,1);
    ll m=0;
    for(int i=1;i<=n;i++){
        if(m<vis[i])
            m=vis[i];
    }
    cout<<m<<endl;
    return 0;
}
### Codeforces 887E Problem Solution and Discussion The problem **887E - The Great Game** on Codeforces involves a strategic game between two players who take turns to perform operations under specific rules. To tackle this challenge effectively, understanding both dynamic programming (DP) techniques and bitwise manipulation is crucial. #### Dynamic Programming Approach One effective method to approach this problem utilizes DP with memoization. By defining `dp[i][j]` as the optimal result when starting from state `(i,j)` where `i` represents current position and `j` indicates some status flag related to previous moves: ```cpp #include <bits/stdc++.h> using namespace std; const int MAXN = ...; // Define based on constraints int dp[MAXN][2]; // Function to calculate minimum steps using top-down DP int minSteps(int pos, bool prevMoveType) { if (pos >= N) return 0; if (dp[pos][prevMoveType] != -1) return dp[pos][prevMoveType]; int res = INT_MAX; // Try all possible next positions and update 'res' for (...) { /* Logic here */ } dp[pos][prevMoveType] = res; return res; } ``` This code snippet outlines how one might structure a solution involving recursive calls combined with caching results through an array named `dp`. #### Bitwise Operations Insight Another critical aspect lies within efficiently handling large integers via bitwise operators instead of arithmetic ones whenever applicable. This optimization can significantly reduce computation time especially given tight limits often found in competitive coding challenges like those hosted by platforms such as Codeforces[^1]. For detailed discussions about similar problems or more insights into solving strategies specifically tailored towards contest preparation, visiting forums dedicated to algorithmic contests would be beneficial. Websites associated directly with Codeforces offer rich resources including editorials written after each round which provide comprehensive explanations alongside alternative approaches taken by successful contestants during live events. --related questions-- 1. What are common pitfalls encountered while implementing dynamic programming solutions? 2. How does bit manipulation improve performance in algorithms dealing with integer values? 3. Can you recommend any online communities focused on discussing competitive programming tactics? 4. Are there particular patterns that frequently appear across different levels of difficulty within Codeforces contests?
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