Codeforces 496D

本文介绍了一种高效算法,用于分析一系列比赛中选手得分的情况。通过遍历不同得分阈值,算法可以找出所有可能的比赛胜利条件,即获胜所需得分及赢得的比赛数量。

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题意


进行若干场比赛,每次比赛两人对决,赢的人得到1分,输的人不得分,先得到t分的人获胜,开始下场比赛,某个人率先赢下s场比赛时,游戏结束。
现在给出n次对决的输赢情况,问可能的s和t有多少种,并按s递增的方式输出


解析


若使用暴力,10000*10000的时间复杂度会超时,所以要另寻他法。
由于一个人满足t分一局比赛就结束,当一个人赢了s局,比赛结束。
所以我们要遍历t,但是每当一个人达到t分,我们就要舍弃另一个人的分数,下一局便从这个人位置的pos+1,开始算,所以我们要记录这两个人达到t分的位置。之后用每个t分的整数倍去找每个人赢了几局。但要记录是否一个人刚好把最后一场比完后,比赛结束了。


代码

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
#include<cmath>
#include<cstdlib>
#include<vector>
using namespace std;
const int maxn = 200000+10;
int p[maxn], g[maxn];
typedef pair<int, int> P;
vector<P>ve;
int main() {
    int n;
    while (~scanf("%d", &n)) {
        int a, b;
        a = b = 0;
        memset(p, 0, sizeof(p));
        memset(g, 0, sizeof(g));
        ve.clear();

        for (int i=1; i<=n; i++) {
            int x;
            scanf("%d", &x);
            if (x == 1)
                a++, p[a] = i;
            else
                b++, g[b] = i;
        }

        int P, G, maxt, j;
        for (int i=1; i<=2*n; i++) {
            if (p[i] == 0)
                p[i] = n+1;

            if (g[i] == 0)
                g[i] = n+1;
        }

        for (int i=1; i<=n; i++) {
            P = G = maxt = 0;
            j = a = b = 0;

            while (j<n) {
                if (p[i+a] < g[i+b]) {
                    P++;
                    maxt = P;
                    j = p[i+a];
                    a += i;
                    b = j-a;
                }
                else {
                    G++;
                    maxt = G;
                    j = g[i+b];
                    b += i;
                    a = j-b;
                }
                //cout<<j<<endl;
            }
            if (j == n && P != G && max(P, G) == maxt) {
                ve.push_back(make_pair(maxt, i));
            }
        }
        sort(ve.begin(), ve.end());
        printf("%d\n", (int)ve.size());
        for (int i=0; i<ve.size(); i++) {
            printf("%d %d\n", ve[i].first, ve[i].second);
        }
    }
    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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