Gold Coins

Description

The king pays his loyal knight in gold coins. On the first day of his service, the knight receives one gold coin. On each of the next two days (the second and third days of service), the knight receives two gold coins. On each of the next three days (the fourth, fifth, and sixth days of service), the knight receives three gold coins. On each of the next four days (the seventh, eighth, ninth, and tenth days of service), the knight receives four gold coins. This pattern of payments will continue indefinitely: after receiving N gold coins on each of N consecutive days, the knight will receive N+1 gold coins on each of the next N+1 consecutive days, where N is any positive integer. 

Your program will determine the total number of gold coins paid to the knight in any given number of days (starting from Day 1). 

Input

The input contains at least one, but no more than 21 lines. Each line of the input file (except the last one) contains data for one test case of the problem, consisting of exactly one integer (in the range 1..10000), representing the number of days. The end of the input is signaled by a line containing the number 0.

Output

There is exactly one line of output for each test case. This line contains the number of days from the corresponding line of input, followed by one blank space and the total number of gold coins paid to the knight in the given number of days, starting with Day 1.

Sample Input

10
6
7
11
15
16
100
10000
1000
21
22
0

Sample Output

10 30
6 14
7 18
11 35
15 55
16 61
100 945
10000 942820
1000 29820
21 91
22 98

Description

The king pays his loyal knight in gold coins. On the first day of his service, the knight receives one gold coin. On each of the next two days (the second and third days of service), the knight receives two gold coins. On each of the next three days (the fourth, fifth, and sixth days of service), the knight receives three gold coins. On each of the next four days (the seventh, eighth, ninth, and tenth days of service), the knight receives four gold coins. This pattern of payments will continue indefinitely: after receiving N gold coins on each of N consecutive days, the knight will receive N+1 gold coins on each of the next N+1 consecutive days, where N is any positive integer. 

Your program will determine the total number of gold coins paid to the knight in any given number of days (starting from Day 1). 

Input

The input contains at least one, but no more than 21 lines. Each line of the input file (except the last one) contains data for one test case of the problem, consisting of exactly one integer (in the range 1..10000), representing the number of days. The end of the input is signaled by a line containing the number 0.

Output

There is exactly one line of output for each test case. This line contains the number of days from the corresponding line of input, followed by one blank space and the total number of gold coins paid to the knight in the given number of days, starting with Day 1.

Sample Input

10
6
7
11
15
16
100
10000
1000
21
22
0

Sample Output

10 30
6 14
7 18
11 35
15 55
16 61
100 945
10000 942820
1000 29820
21 91
22 98
   代码:
#include<iostream>
using namespace std;
int main()
{
    int i,j,n,k,ans;
    while(cin>>n&&n>0)
    {
        ans=0;
        for(i=0,j=1;i<n;j++)
        {
            k=j;
            while(k--&&(++i<=n))
                ans+=j;
        }
        cout<<n<<" "<<ans<<endl;
    }
    return 0;
}

A. 纪念品 (Souvenir) A C D E F G H 传统题 1000ms 256MiB Description Xiaowei suddenly acquires a superpower. He knows the daily prices of N N souvenirs for the next T T days. The price of a souvenir refers to the number of gold coins required to buy the souvenir or the number of gold coins that can be earned by selling a souvenir. Every day, Xiaowei can carry out the following two types of transactions any number of times: Choose a souvenir. If he has enough gold coins with him, buy the souvenir at its price for that day. Sell any souvenir he has and earn gold coins equal to the price of the souvenir for that day. The gold coins earned by selling souvenirs on a day can be used to buy souvenirs on the same day too. Similarly, souvenirs purchased on a day can also be sold for gold coins on the same day. After T T days, Xiaowei’s superpower will disappear. Therefore, he will sell all the souvenirs he still has on the T T-th day. Currently, Xiaowei has M M gold coins, and he wants to have as many gold coins as possible after the superpower disappears. What is the maximum number of gold coins he can have? Input Format The first line contains three positive integers T T, N N and M M - the number of days for which Xiaowei knows souvenir prices, the number of souvenirs, and the number of gold coins that Xiaowei currenly has. i i-th of the next T T lines contains N N positive integers P i , 1 , P i , 2 , . . . , P i , N , P i,1 ​ ,P i,2 ​ ,...,P i,N ​ , where P i , j P i,j ​ denotes the price of the j j-th souvenir on the i i-th day. Output Format Print one line containing a positive integer denoting the maximum number of gold coins Xiaowei can have after his superpower disappears. 输入数据 1 6 1 100 50 20 25 20 25 50 输出数据 1 305 The best strategy is: On the second day, spend all 100 100 gold coins to buy 5 5 units of souvenir 1 1. Sell all the 5 5 units of souvenir 1 1 on the third day and get 125 125 gold coins. Buy 6 6 units of souvenir 1 1 on the fourth day. 5 5 gold coins are left. On the sixth day, sell all souvenirs for 300 300 gold coins. On the fourth day there were 5 5 gold coins remaining, so now there are 305 305 gold coins remaining. After the superpower disappears, Xiaowei has 305 305 gold coins, which is the maximum possible. 输入数据 2 3 3 100 10 20 15 15 17 13 15 25 16 输出数据 2 217 The best strategy is: On the first day, spend all the gold coins to buy 10 10 units of souvenir 1 1. Sell all the units of souvenir 1 1 on the next day and get 150 150 gold coins. Buy 8 8 units of souvenir 2 2 and 1 1 unit of souvenir 3 3. 1 1 gold coin is remaining. On the third day, sell all souvenirs and get 216 216 gold coins. On the second day, there was 1 1 gold coin left, so in total there are 217 217 gold coins left. After the superpower disappears, Xiaowei has 217 217 gold coins, which is the maximum possible. Constraints For 10 % 10% of the data, T = 1 T=1. For 30 % 30% of the data, T ≤ 4 , N ≤ 4 , M ≤ 100 , 10 ≤ P i , j ≤ 1001 T≤4,N≤4,M≤100,10≤P i,j ​ ≤1001. For another 15 % 15% of the data, T ≤ 100 , N = 1 T≤100,N=1. For another 15 % 15% of the data, T = 2 , N ≤ 100 T=2,N≤100. For 100 % 100% of the data, T ≤ 100 , N ≤ 100 , M ≤ 10 3 , 1 ≤ P i , j ≤ 10 4 T≤100,N≤100,M≤10 3 ,1≤P i,j ​ ≤10 4 . It is guaranteed that at any time, the number of gold coins that Xiaowei has can't exceed 10 4 10 4 .
10-27
内容概要:本文详细介绍了“秒杀商城”微服务架构的设计与实战全过程,涵盖系统从需求分析、服务拆分、技术选型到核心功能开发、分布式事务处理、容器化部署及监控链路追踪的完整流程。重点解决了高并发场景下的超卖问题,采用Redis预减库存、消息队列削峰、数据库乐观锁等手段保障数据一致性,并通过Nacos实现服务注册发现与配置管理,利用Seata处理跨服务分布式事务,结合RabbitMQ实现异步下单,提升系统吞吐能力。同时,项目支持Docker Compose快速部署和Kubernetes生产级编排,集成Sleuth+Zipkin链路追踪与Prometheus+Grafana监控体系,构建可观测性强的微服务系统。; 适合人群:具备Java基础和Spring Boot开发经验,熟悉微服务基本概念的中高级研发人员,尤其是希望深入理解高并发系统设计、分布式事务、服务治理等核心技术的开发者;适合工作2-5年、有志于转型微服务或提升架构能力的工程师; 使用场景及目标:①学习如何基于Spring Cloud Alibaba构建完整的微服务项目;②掌握秒杀场景下高并发、超卖控制、异步化、削峰填谷等关键技术方案;③实践分布式事务(Seata)、服务熔断降级、链路追踪、统一配置中心等企业级中间件的应用;④完成从本地开发到容器化部署的全流程落地; 阅读建议:建议按照文档提供的七个阶段循序渐进地动手实践,重点关注秒杀流程设计、服务间通信机制、分布式事务实现和系统性能优化部分,结合代码调试与监控工具深入理解各组件协作原理,真正掌握高并发微服务系统的构建能力。
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