codeforces 706D (字典树)

本文提供 CodeForces 706D 题目的解题思路及代码实现,采用字典树存储二进制表示,解决增添、删除元素及查询集合中与指定值异或结果最大的元素问题。

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题目链接:http://codeforces.com/problemset/problem/706/D

题意:q次操作,可以向多重集中增添,删除,询问异或最大值。

思路:转化为二进制用字典树存储,数字从高位开始,并全部固定位30位。

#include<bits/stdc++.h>
using namespace std;
const int N=2e5 + 5;
int now = 1 ,Trie[N<<5][2] ,num[N<<5];
void Insert(int x)
{
    for(int i = 29 ,cur = 1 ; i >= 0 ;i--)
    {
        int tmp=(x >> i) & 1;
        if(!Trie[cur][tmp])
            Trie[cur][tmp] = ++now;
        cur = Trie[cur][tmp];
        num[cur]++;
    }
}
void Delete(int x)
{
    for(int i = 29 ,cur = 1 ;i >= 0 ;i--)
    {
        cur = Trie[cur][(x>>i)&1];
        num[cur]--;
    }
}
int query(int x)
{
    int ans=0;
    for(int i = 29 ,cur = 1 ;i >= 0 ;i--)
    {
        int tmp = (x >> i) & 1;
        if(num[Trie[cur][tmp^1]])
        {
            ans += (1<<i);
            cur = Trie[cur][tmp^1];
        }
        else
            cur = Trie[cur][tmp];
    }
    return ans;
}
int main()
{
    int q;
    scanf("%d",&q);
    Insert(0);
    char c;
    while(q--)
    {
        int x;
        scanf(" %c %d" ,&c ,&x);
        if(c == '+')
            Insert(x);
        if(c == '-')
            Delete(x);
        if(c == '?')
            printf("%d\n" ,query(x));
    }
    return 0;
}



关于字典树:http://blog.youkuaiyun.com/u011787119/article/details/46991691

### 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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