算法艺术与信息学竞赛详解：从基础到高级数据结构

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《算法艺术与信息学竞赛题目完全解析》是一份针对ACM竞赛（全称是国际大学生程序设计竞赛）的学习资料，它系统地介绍了算法和数据结构的基础知识，以及它们在实际竞赛中的应用。该文档由一系列问题和实例构成，旨在帮助编程学习者提升技能，解决实际比赛中的挑战。 1. **核心概念**: - **程序与算法的关系**: 提到程序=算法+数据结构，强调算法设计在编写程序中的关键作用。算法是解决问题的具体步骤，而数据结构则是组织和存储数据的方式，两者相辅相成。 2. **基本算法**: - **枚举法**: 用于穷举所有可能的解决方案，适用于问题空间较小的情况。 - **贪心算法**: 在每一步选择中都采取当前看起来最优的选择，但不保证全局最优。 - **递归与分治算法**: 分解复杂问题为更小的部分，递归求解或通过部分解组合得到整体解。 - **递推**: 通过已知结果计算出新的结果，常见于动态规划问题。 3. **数据结构入门**: - **栈和队列**: 基础的数据结构，如火车车厢的进出模式，用于回溯和先进先出操作。 - **串**: 集合元素有序且不可变，用于处理字符串问题。 - **树和二叉树**: 数据结构的基础，如二叉搜索树用于高效查找，树的遍历方法（如前序、中序、后序）也很重要。 - **图及其基本算法**: 关系型数据结构，用于模拟网络连接和路径问题，如最短路径、拓扑排序等。 4. **进阶与应用**: - **并查集**: 一种数据结构，常用于处理集合的合并和查询操作，如连通性问题。 - **堆与变种**: 如最大堆/最小堆，用于优先队列，如任务调度、Dijkstra算法。 - **字典树/前缀树实现**: 用于高效处理字符串搜索和匹配问题，哈希表与二叉搜索树是两种常见实现方式。文档中的题目实例，如Pku1116、Pku1042等，都是具体问题的编码挑战，通过这些实例，读者可以实践和理解算法及数据结构在实际场景中的运用。无论是对于参加信息学竞赛的学生，还是希望提高编程技能的开发者，这份资料都提供了丰富的学习资源和实战练习机会。

算法艺术与信息学竞赛—完全导析 hi.baidu.com/ecbtnrt

else

{ strcpy(temp,BeforeResult[0]);

//记录下 BeforeResult[0],以便 s[n]To01=s[n-1]To00 用

plus(BeforeResult[1],change,AfterResult[0]);

strcpy(BeforeResult[0],AfterResult[0]);

strcpy(BeforeResult[1],temp);

}

for(j=0;j<MAXLEN;j++)

temp[j]='0';

plus(change,change,temp);

strcpy(change,temp);

}

i=0;

while(BeforeResult[0][i]=='0')

i++;//找到第一个不为 0 的位置

while(i<MAXLEN)

{ cout<<BeforeResult[0][i];i++;}

cout<<endl;

}

cin>>total;

}

return 0;

}

void plus(char * num1,char * num2,char * result)//实现 1+num1+num2

{

int i,x,y;

y=1;

for(i=MAXLEN-1;i>=0;i--)

{

x=num1[i]-'0'+num2[i]-'0'+y;

y=x/10;

x=x%10;

result[i]=x+'0';

}

Pku2351--Time Zones

Description

Prior to the late nineteenth century, time keeping was a purely local phenomenon.

Each town would set their clocks to noon when the sun reached its zenith each day. A

clockmaker or town clock would be the "official" time and the citizens would set their

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算法艺术与信息学竞赛—完全导析 hi.baidu.com/ecbtnrt

pocket watches and clocks to the time of the town - enterprising citizens would offer

their services as mobile clock setters, carrying a watch with the accurate time to adjust

the clocks in customer's homes on a weekly basis. Travel between cities meant having

to change one's pocket watch upon arrival.

However, once railroads began to operate and move people rapidly across great

distances, time became much more critical. In the early years of the railroads, the

schedules were very confusing because each stop was based on a different local time.

The standardization of time was essential to efficient operation of railroads.

In 1878, Canadian Sir Sanford Fleming proposed the system of worldwide time zones

that we use today. He recommended that the world be divided into twenty-four time

zones, each spaced 15 degrees of longitude apart. Since the earth rotates once every

24 hours and there are 360 degrees of longitude, each hour the earth rotates

one-twenty-fourth of a circle or 15° of longitude. Sir Fleming's time zones were

heralded as a brilliant solution to a chaotic problem worldwide.

United States railroad companies began utilizing Fleming's standard time zones on

November 18, 1883. In 1884 an International Prime Meridian Conference was held in

Washington D.C. to standardize time and select the Prime Meridian. The conference

selected the longitude of Greenwich, England as zero degrees longitude and

established the 24 time zones based on the Prime Meridian. Although the time zones

had been established, not all countries switched immediately. Though most U.S. states

began to adhere to the Pacific, Mountain, Central, and Eastern time zones by 1895,

Congress didn't make the use of these time zones mandatory until the Standard Time

Act of 1918.

Today, many countries operate on variations of the time zones proposed by Sir

Fleming. All of China (which should span five time zones) uses a single time zone -

eight hours ahead of Coordinated Universal Time (known by the abbreviation UTC -

based on the time zone running through Greenwich at 0° longitude). Russia adheres to

its designated time zones although the entire country is on permanent Daylight Saving

Time and is an hour ahead of their actual zones. Australia uses three time zones - its

central time zone is a half-hour ahead of its designated time zone. Several countries in

the Middle East and South Asia also utilize half-hour time zones.

Since time zones are based on segments of longitude and lines of longitude narrow at

the poles, scientists working at the North and South Poles simply use UTC time.

Otherwise, Antarctica would be divided into 24 very thin time zones!

Time zones have recently been given standard capital-letter abbreviations as follows:

UTC Coordinated Universal Time

GMT Greenwich Mean Time, defined as UTC

BST British Summer Time, defined as UTC+1 hour

IST Irish Summer Time, defined as UTC+1 hour

WET Western Europe Time, defined as UTC

WEST Western Europe Summer Time, defined as UTC+1 hour

CET Central Europe Time, defined as UTC+1

CEST Central Europe Summer Time, defined as UTC+2

EET Eastern Europe Time, defined as UTC+2

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