标签： PAT

Unlike in nowadays, the way that boys and girls expressing their feelings of love was quite subtle in the early years. When a boy A had a crush on a girl B, he would usually not contact her directly in the first place. Instead, he might ask another boy C, one of his close friends, to ask another girl D, who was a friend of both B and C, to send a message to B — quite a long shot, isn’t it? Girls would do analogously.
Here given a network of friendship relations, you are supposed to help a boy or a girl to list all their friends who can possibly help them making the first contact.
Input Specification:
Each input file contains one test case. For each case, the first line gives two positive integers N (1 < N <= 300) and M, being the total number of people and the number of friendship relations, respectively. Then M lines follow, each gives a pair of friends. Here a person is represented by a 4-digit ID. To tell their genders, we use a negative sign to represent girls.
After the relations, a positive integer K (<= 100) is given, which is the number of queries. Then K lines of queries follow, each gives a pair of lovers, separated by a space. It is assumed that the first one is having a crush on the second one.
Output Specification:
For each query, first print in a line the number of different pairs of friends they can find to help them, then in each line print the IDs of a pair of friends.
If the lovers A and B are of opposite genders, you must first print the friend of A who is of the same gender of A, then the friend of B, who is of the same gender of B. If they are of the same gender, then both friends must be in the same gender as theirs. It is guaranteed that each person has only one gender.
The friends must be printed in non-decreasing order of the first IDs, and for the same first ones, in increasing order of the seconds ones.
Sample Input:
10 18
-2001 1001
-2002 -2001
1004 1001
-2004 -2001
-2003 1005
1005 -2001
1001 -2003
1002 1001
1002 -2004
-2004 1001
1003 -2002
-2003 1003
1004 -2002
-2001 -2003
1001 1003
1003 -2001
1002 -2001
-2002 -2003
5
1001 -2001
-2003 1001
1005 -2001
-2002 -2004
1111 -2003
Sample Output:
4
1002 2004
1003 2002
1003 2003
1004 2002
4
2001 1002
2001 1003
2002 1003
2002 1004
0
1
2003 2001
0
分析：1.用数组arr标记两个人是否是朋友（邻接矩阵表示），用v标记所有人的同性朋友（邻接表表示）
2.对于一对想要在一起的A和B，他们需要先找A的所有同性朋友C，再找B的所有同性朋友D，当C和D两人是朋友的时候则可以输出C和D
3.A在寻找同性朋友时，需要避免找到他想要的伴侣B，所以当当前朋友就是B或者B的同性朋友就是A时舍弃该结果
4.输出时候要以4位数的方式输出，所以要%04d
5.如果用int接收一对朋友，-0000和0000对于int来说都是0，将无法得知这个人的性别，也就会影响他找他的同性朋友的那个步骤，所以考虑用字符串接收，因为题目中已经表示会以符号位加四位的方式给出输入，所以只要判断字符串是否大小相等，如果大小相等说明这两个人是同性
6.结果数组因为必须按照第一个人的编号从小到大排序（当第一个相等时按照第二个人编号的从小到大排序），所以要用sort对ans数组排序后再输出结果

Update: 新PAT系统中原代码导致了一个测试点内存超限，使用unordered_map<int, bool> arr 替代二维数组可避免内存超限（2018-05-28更新）

Suppose that all the keys in a binary tree are distinct positive integers. Given the preorder and inorder traversal sequences, you are supposed to output the first number of the postorder traversal sequence of the corresponding binary tree.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (<=50000), the total number of nodes in the binary tree. The second line gives the preorder sequence and the third line gives the inorder sequence. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print in one line the first number of the postorder traversal sequence of the corresponding binary tree.

Sample Input:
7
1 2 3 4 5 6 7
2 3 1 5 4 7 6
Sample Output:
3

分析：一道简单的前序中序转后序，而且只需要知道后序的第一个值，所以可以定义一个变量flag，当post的第一个值已经输出，则flag为true，递归出口处判断flag，可以提前return
ps：经过测试发现没有flag按照正常前序中序转后序也可以AC，但是我在考场上第一次尝试直接转没有提前退出递归的写法并没有能够AC，而是有一部分运行超时，后来增加了flag才AC。可能pat考试时更为严苛，所以对于准备pat考试的小伙伴，建议如果能够缩小运行时间尽量精益求精

Consider a positive integer N written in standard notation with k+1 digits ai as ak…a1a0 with 0 <= ai < 10 for all i and ak > 0. Then N is palindromic if and only if ai = ak-i for all i. Zero is written 0 and is also palindromic by definition.

Non-palindromic numbers can be paired with palindromic ones via a series of operations. First, the non-palindromic number is reversed and the result is added to the original number. If the result is not a palindromic number, this is repeated until it gives a palindromic number. Such number is called a delayed palindrome. (Quoted from https://en.wikipedia.org/wiki/Palindromic_number)

Given any positive integer, you are supposed to find its paired palindromic number.

Input Specification:

Each input file contains one test case which gives a positive integer no more than 1000 digits.

Output Specification:

For each test case, print line by line the process of finding the palindromic number. The format of each line is the following:

A + B = C
where A is the original number, B is the reversed A, and C is their sum. A starts being the input number, and this process ends until C becomes a palindromic number — in this case we print in the last line “C is a palindromic number.”; or if a palindromic number cannot be found in 10 iterations, print “Not found in 10 iterations.” instead.

Sample Input 1:
97152
Sample Output 1:
97152 + 25179 = 122331
122331 + 133221 = 255552
255552 is a palindromic number.
Sample Input 2:
196
Sample Output 2:
196 + 691 = 887
887 + 788 = 1675
1675 + 5761 = 7436
7436 + 6347 = 13783
13783 + 38731 = 52514
52514 + 41525 = 94039
94039 + 93049 = 187088
187088 + 880781 = 1067869
1067869 + 9687601 = 10755470
10755470 + 07455701 = 18211171
Not found in 10 iterations.

分析：1 将字符串倒置与原字符串比较看是否相等可知s是否为回文串
2 字符串s和它的倒置t相加，只需从头到尾相加然后再倒置（记得要处理最后一个进位carry，如果有进位要在末尾+’1’）
3 倒置可采用algorithm头文件里面的函数reverse(s.begin(), s.end())直接对s进行倒置

For a student taking the online course “Data Structures” on China University MOOC (http://www.icourse163.org/), to be qualified for a certificate, he/she must first obtain no less than 200 points from the online programming assignments, and then receive a final grade no less than 60 out of 100. The final grade is calculated by G = (Gmid-termx 40% + Gfinalx 60%) if Gmid-term > Gfinal, or Gfinal will be taken as the final grade G. Here Gmid-term and Gfinal are the student’s scores of the mid-term and the final exams, respectively.

The problem is that different exams have different grading sheets. Your job is to write a program to merge all the grading sheets into one.

Input Specification:

Each input file contains one test case. For each case, the first line gives three positive integers: P , the number of students having done the online programming assignments; M, the number of students on the mid-term list; and N, the number of students on the final exam list. All the numbers are no more than 10,000.

Then three blocks follow. The first block contains P online programming scores Gp’s; the second one contains M mid-term scores Gmid-term’s; and the last one contains N final exam scores Gfinal’s. Each score occupies a line with the format: StudentID Score, where StudentID is a string of no more than 20 English letters and digits, and Score is a nonnegative integer (the maximum score of the online programming is 900, and that of the mid-term and final exams is 100).

Output Specification:

For each case, print the list of students who are qualified for certificates. Each student occupies a line with the format:

StudentID Gp Gmid-term Gfinal G

If some score does not exist, output “-1” instead. The output must be sorted in descending order of their final grades (G must be rounded up to an integer). If there is a tie, output in ascending order of their StudentID’s. It is guaranteed that the StudentID’s are all distinct, and there is at least one qualified student.

Sample Input:
6 6 7
01234 880
a1903 199
ydjh2 200
wehu8 300
dx86w 220
missing 400
ydhfu77 99
wehu8 55
ydjh2 98
dx86w 88
a1903 86
01234 39
ydhfu77 88
a1903 66
01234 58
wehu8 84
ydjh2 82
missing 99
dx86w 81
Sample Output:
missing 400 -1 99 99
ydjh2 200 98 82 88
dx86w 220 88 81 84
wehu8 300 55 84 84

分析：1 因为所有人必须要G编程>=200分，所以用v数组保存所有G编程>=200的人，（一开始gm和gf都为-1），用map映射保存名字所对应v中的下标（为了避免与“不存在”混淆，保存下标+1，当为0时表示该学生的姓名在v中不存在）
2 G期中中出现的名字，如果对应的map并不存在（==0），说明该学生编程成绩不满足条件，则无须保存该学生信息。将存在的人的期中考试成绩更新
3 G期末中出现的名字，也必须保证在map中存在。先更新G期末和G总为新的成绩，当G期末<G期中时再将G总更新为(G期中x 40% + G期末x 60%)
4 将v数组中所有G总满足条件的放入ans数组中，对ans排序（总分递减，总分相同则姓名递增），最后输出ans中的学生信息

地球人习惯使用十进制数，并且默认一个数字的每一位都是十进制的。而在PAT星人开挂的世界里，每个数字的每一位都是不同进制的，这种神奇的数字称为“PAT数”。每个PAT星人都必须熟记各位数字的进制表，例如“……0527”就表示最低位是7进制数、第2位是2进制数、第3位是5进制数、第4位是10进制数，等等。每一位的进制d或者是0（表示十进制）、或者是[2，9]区间内的整数。理论上这个进制表应该包含无穷多位数字，但从实际应用出发，PAT星人通常只需要记住前20位就够用了，以后各位默认为10进制。
在这样的数字系统中，即使是简单的加法运算也变得不简单。例如对应进制表“0527”，该如何计算“6203+415”呢？我们得首先计算最低位：3+5=8；因为最低位是7进制的，所以我们得到1和1个进位。第2位是：0+1+1（进位）=2；因为此位是2进制的，所以我们得到0和1个进位。第3位是：2+4+1（进位）=7；因为此位是5进制的，所以我们得到2和1个进位。第4位是：6+1（进位）=7；因为此位是10进制的，所以我们就得到7。最后我们得到：6203+415=7201。
输入格式：
输入首先在第一行给出一个N位的进制表（0 < N <=20），以回车结束。 随后两行，每行给出一个不超过N位的正的PAT数。
输出格式：
在一行中输出两个PAT数之和。
输入样例：
30527
06203
415
输出样例：
7201

分析：先将要相加的两个字符串S1和S2都扩展到和S等长，然后从后往前按照进制相加到ans中，注意进位carry，最后输出字符串ans，记得不要输出字符串ans前面的0。如果一次都没有输出，最后要输出一个0～

批改多选题是比较麻烦的事情，有很多不同的计分方法。有一种最常见的计分方法是：如果考生选择了部分正确选项，并且没有选择任何错误选项，则得到50%分数；如果考生选择了任何一个错误的选项，则不能得分。本题就请你写个程序帮助老师批改多选题，并且指出哪道题的哪个选项错的人最多。
输入格式：
输入在第一行给出两个正整数N（<=1000）和M（<=100），分别是学生人数和多选题的个数。随后M行，每行顺次给出一道题的满分值（不超过5的正整数）、选项个数（不少于2且不超过5的正整数）、正确选项个数（不超过选项个数的正整数）、所有正确选项。注意每题的选项从小写英文字母a开始顺次排列。各项间以1个空格分隔。最后N行，每行给出一个学生的答题情况，其每题答案格式为“(选中的选项个数 选项1 ……)”，按题目顺序给出。注意：题目保证学生的答题情况是合法的，即不存在选中的选项数超过实际选项数的情况。
输出格式：
按照输入的顺序给出每个学生的得分，每个分数占一行，输出小数点后1位。最后输出错得最多的题目选项的信息，格式为：“错误次数 题目编号（题目按照输入的顺序从1开始编号）-选项号”。如果有并列，则每行一个选项，按题目编号递增顺序输出；再并列则按选项号递增顺序输出。行首尾不得有多余空格。如果所有题目都没有人错，则在最后一行输出“Too simple”。
输入样例1：
3 4
3 4 2 a c
2 5 1 b
5 3 2 b c
1 5 4 a b d e
(2 a c) (3 b d e) (2 a c) (3 a b e)
(2 a c) (1 b) (2 a b) (4 a b d e)
(2 b d) (1 e) (1 c) (4 a b c d)
输出样例1：
3.5
6.0
2.5
2 2-e
2 3-a
2 3-b
输入样例2：
2 2
3 4 2 a c
2 5 1 b
(2 a c) (1 b)
(2 a c) (1 b)
输出样例2：
5.0
5.0
Too simple

分析：错误是指错选或者漏选。用异或运算来判断一个选项和正确选项是否匹配，如果是匹配的，那么异或的结果应当是0；如果不匹配，那么这个选项就是存在错选或者漏选的情况～例如：设a为00001，b为00010，c为00100，d为01000，e为10000，如果给定的正确答案是ac，即10001，那么如果给出的选项也是10001，异或的结果就是0；如果给出的选项是a或者ab，即00001或00011，异或之后不为0，就是错选和漏选的～通过异或操作的结果，再用与运算就可以把错选和漏选的选项找出来～fullscore表示一道题满分的分值；trueopt表示正确的选项，存储的是正确选项二进制的值，二进制由hash给出分别是1,2,4,8,16；cnt是错误的次数，maxcnt是最大错误次数~