CodeForces 339D Xenia and Bit Operations(线段树点修改)

题目链接:

http://codeforces.com/problemset/problem/339/D

解题思路:

题目大意:
     输入n和m分别表示有2^n个数和m个更新,每次更新只把p位置的值改成b,然后输出整个序列运算后的值,但是这个运算比较麻烦, 最下面一层数字两两之间进行或运算得到原来数目一半的数字,然后剩下的再两两之间进行异或运算,再得到一半,然后再或,再异或。。。。。。直到得到一个数字为止,这个数字就是每次询问的结果。

算法思想:
     如果只有一种运算,就是简单的线段树点更新,区间查询问题。然而现在,我们要确定什么时候用or 什么时候用xor, 不过想想看,最下面一层是用or, 总共有n层,因为or和xor是交替进行的,所以我们就可以用n确定每层的运算,然后在建树和更新的时候分情况讨论就可以了。

AC代码:

#include <iostream>
#include <cstdio>
using namespace std;

const int maxn = 1<<17+5;
struct node{
    int l,r;
    int sum;
}tree[maxn<<2];
int a[maxn];

void build(int id,int l,int r,int op){
    tree[id].l = l;
    tree[id].r = r;
    if(l == r){
        tree[id].sum = a[l];
        return;
    }
    int mid = (l+r)>>1;
    build(id<<1,l,mid,-op);
    build(id<<1|1,mid+1,r,-op);
    if(op == 1)
        tree[id].sum = tree[id<<1].sum^tree[id<<1|1].sum;
    else
        tree[id].sum = tree[id<<1].sum|tree[id<<1|1].sum;
}

void update(int id,int x,int val,int op){
    if(tree[id].l == x && tree[id].r == x){
        tree[id].sum = val;
        return;
    }
    int mid = (tree[id].l+tree[id].r)>>1;
    if(x <= mid)
        update(id<<1,x,val,-op);
    else
        update(id<<1|1,x,val,-op);
    if(op == 1)
        tree[id].sum = tree[id<<1].sum^tree[id<<1|1].sum;
    else
        tree[id].sum = tree[id<<1].sum|tree[id<<1|1].sum;
}

int query(int id,int l,int r){
    if(tree[id].l == l && tree[id].r == r){
        return tree[id].sum;
    }
    int mid = (tree[id].l+tree[id].r)>>1;
    if(r <= mid)
        return query(id<<1,l,r);
    if(l > mid)
        return query(id<<1|1,l,r);
    return query(id<<1,l,mid)^query(id<<1|1,mid+1,r);
}

int main(){
    int n,m;
    while(~scanf("%d%d",&n,&m)){
        int num = 1<<n,op;
        for(int i = 1; i <= num; i++)
            scanf("%d",&a[i]);
        if(n&1)
            op = -1;//或
        else
            op = 1;//异或
        build(1,1,num,op);
        int a,b;
        while(m--){
            scanf("%d%d",&a,&b);
            update(1,a,b,op);
            printf("%d\n",query(1,1,num));
        }
    }
    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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