Codeforces 799C. Fountains

本文介绍了一种算法,帮助玩家在有限的游戏币下选择最优的道具组合以最大化游戏体验。通过分别处理不同货币类型的物品,并利用动态规划思想进行优化。
C. Fountains
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
Arkady plays Gardenscapes a lot. Arkady wants to build two new fountains. There are n available fountains, for each fountain its beauty and cost are known. There are two types of money in the game: coins and diamonds, so each fountain cost can be either in coins or diamonds. No money changes between the types are allowed.

Help Arkady to find two fountains with maximum total beauty so that he can buy both at the same time.

Input
The first line contains three integers n, c and d (2 ≤ n ≤ 100000, 0 ≤ c, d ≤ 100000) — the number of fountains, the number of coins and diamonds Arkady has.

The next n lines describe fountains. Each of these lines contain two integers bi and pi (1 ≤ bi, pi ≤ 100000) — the beauty and the cost of the i-th fountain, and then a letter "C" or "D", describing in which type of money is the cost of fountain i: in coins or in diamonds, respectively.

Output
Print the maximum total beauty of exactly two fountains Arkady can build. If he can't build two fountains, print 0.

Examples
input
3 7 6
10 8 C
4 3 C
5 6 D
output
9
input
2 4 5
2 5 C
2 1 D
output
0
input
3 10 10
5 5 C
5 5 C
10 11 D
output
10
Note
In the first example Arkady should build the second fountain with beauty 4, which costs 3 coins. The first fountain he can't build because he don't have enough coins. Also Arkady should build the third fountain with beauty 5 which costs 6 diamonds. Thus the total beauty of built fountains is 9.

In the second example there are two fountains, but Arkady can't build both of them, because he needs 5 coins for the first fountain, and Arkady has only 4 coins.

考虑建了一个C一个D的情况 答案就是C,D中取满足cost的最大值即可
CC的情况 , 按cost升序排序,维护sc[i]=cost小于等于i的情况下,收益最大的值
枚举每对{bi,pi}并依次插入sc中即可 CC的最大值就算sc[min(c-i,i)]+当前收益
DD同理

#include<stdio.h>
#include <iostream>
#include<stdlib.h>
#include<algorithm>
#include<vector>
#include<deque>
#include<map>
#include<set>
#include<queue>
#include<math.h>
#include<string.h>
#include<string>

using namespace std;
#define ll long long
#define pii pair<int,int>

const int inf = 1e9 + 7;

const int N = 1e5+5;

vector<pii>cf,df;
int sc[N];
int sd[N];

int slove(int n,int c,int d){
    sort(cf.begin(),cf.end());
    sort(df.begin(),df.end());
    int cc=-inf;
    int lastIdx=0;
    for(int i=0;i<cf.size();++i){
        int cost=cf[i].first;
        int score=cf[i].second;
        for(int j=lastIdx+1;j<=cost;++j){
            sc[j]=max(sc[j],sc[j-1]);
        }
        int x=min(c-cost,cost);
        if(x>=0){
            cc=max(cc,sc[x]+score);
        }
        sc[cost]=max(sc[cost],score);
        lastIdx=cost;
    }
    for(int i=lastIdx+1;i<=c;++i){
        sc[i]=max(sc[i],sc[i-1]);
    }
    int dd=-inf;
    lastIdx=0;
    for(int i=0;i<df.size();++i){
        int cost=df[i].first;
        int score=df[i].second;
        for(int j=lastIdx+1;j<=cost;++j){
            sd[j]=max(sd[j],sd[j-1]);
        }
        int x=min(d-cost,cost);
        if(x>=0){
            dd=max(dd,sd[x]+score);
        }
        sd[cost]=max(sd[cost],score);
        lastIdx=cost;
    }
    for(int i=lastIdx+1;i<=d;++i){
        sd[i]=max(sd[i],sd[i-1]);
    }
    int cd=sc[c]+sd[d];
    return max(cc,max(dd,max(0,cd)));
}

int main()
{
    //freopen("/home/lu/Documents/r.txt","r",stdin);
    //freopen("/home/lu/Documents/w.txt","w",stdout);
    int n,c,d;
    while(~scanf("%d%d%d",&n,&c,&d)){
        fill(sc,sc+c+1,-inf);
        fill(sd,sd+d+1,-inf);
        cf.clear();
        df.clear();
        int score,cost;
        char ch;
        for(int i=0;i<n;++i){
            scanf("%d%d%*c%c",&score,&cost,&ch);
            if(ch=='C'){
                cf.push_back({cost,score});
            }
            else{
                df.push_back({cost,score});
            }
        }
        printf("%d\n",slove(n,c,d));
    }
    return 0;
}
### Codeforces Div.2 比赛难度介绍 Codeforces Div.2 比赛主要面向的是具有基础编程技能到中级水平的选手。这类比赛通常吸引了大量来自全球不同背景的参赛者,包括大学生、高中生以及一些专业人士。 #### 参加资格 为了参加 Div.2 比赛,选手的评级应不超过 2099 分[^1]。这意味着该级别的竞赛适合那些已经掌握了一定算法知识并能熟练运用至少一种编程语言的人群参与挑战。 #### 题目设置 每场 Div.2 比赛一般会提供五至七道题目,在某些特殊情况下可能会更多或更少。这些题目按照预计解决难度递增排列: - **简单题(A, B 类型)**: 主要测试基本的数据结构操作和常见算法的应用能力;例如数组处理、字符串匹配等。 - **中等偏难题(C, D 类型)**: 开始涉及较为复杂的逻辑推理能力和特定领域内的高级技巧;比如图论中的最短路径计算或是动态规划入门应用实例。 - **高难度题(E及以上类型)**: 对于这些问题,则更加侧重考察深入理解复杂概念的能力,并能够灵活组合多种方法来解决问题;这往往需要较强的创造力与丰富的实践经验支持。 对于新手来说,建议先专注于理解和练习前几类较容易的问题,随着经验积累和技术提升再逐步尝试更高层次的任务。 ```cpp // 示例代码展示如何判断一个数是否为偶数 #include <iostream> using namespace std; bool is_even(int num){ return num % 2 == 0; } int main(){ int number = 4; // 测试数据 if(is_even(number)){ cout << "The given number is even."; }else{ cout << "The given number is odd."; } } ```
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