1091 N-自守数 (15 point(s)) – PAT乙级真题

如果某个数 K 的平方乘以 N 以后,结果的末尾几位数等于 K,那么就称这个数为“N-自守数”。例如 3×922​​ = 25392,而 25392 的末尾两位正好是 92,所以 92 是一个 3-自守数。

本题就请你编写程序判断一个给定的数字是否关于某个 N 是 N-自守数。

输入格式:
输入在第一行中给出正整数 M(≤20),随后一行给出 M 个待检测的、不超过 1000 的正整数。

输出格式:
对每个需要检测的数字,如果它是 N-自守数就在一行中输出最小的 N 和 NK​2​​ 的值,以一个空格隔开;否则输出 No。注意题目保证 N<10。

输入样例:
3
92 5 233
输出样例:
3 25392
1 25
No

分析:从1-9枚举,判断是否存在N。通过to_string把乘积转成字符串,再通过substr取末尾子串比较即可~

 

PAT 1155 Heap Paths (30 分)- 甲级

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. A common implementation of a heap is the binary heap, in which the tree is a complete binary tree. (Quoted from Wikipedia at https://en.wikipedia.org/wiki/Heap_(data_structure))

One thing for sure is that all the keys along any path from the root to a leaf in a max/min heap must be in non-increasing/non-decreasing order.

Your job is to check every path in a given complete binary tree, in order to tell if it is a heap or not.

Input Specification:
Each input file contains one test case. For each case, the first line gives a positive integer N (1<N≤1,000), the number of keys in the tree. Then the next line contains N distinct integer keys (all in the range of int), which gives the level order traversal sequence of a complete binary tree.

Output Specification:
For each given tree, first print all the paths from the root to the leaves. Each path occupies a line, with all the numbers separated by a space, and no extra space at the beginning or the end of the line. The paths must be printed in the following order: for each node in the tree, all the paths in its right subtree must be printed before those in its left subtree.

Finally print in a line Max Heap if it is a max heap, or Min Heap for a min heap, or Not Heap if it is not a heap at all.

Sample Input 1:
8
98 72 86 60 65 12 23 50
Sample Output 1:
98 86 23
98 86 12
98 72 65
98 72 60 50
Max Heap
Sample Input 2:
8
8 38 25 58 52 82 70 60
Sample Output 2:
8 25 70
8 25 82
8 38 52
8 38 58 60
Min Heap
Sample Input 3:
8
10 28 15 12 34 9 8 56
Sample Output 3:
10 15 8
10 15 9
10 28 34
10 28 12 56
Not Heap

题目大意:给出一颗完全二叉树,打印出从根节点到所有叶节点的路径,打印顺序先右后左,即先序遍历的镜像。然后判断该树是大顶堆、小顶堆或者不是堆~

分析:1.深搜打印出所有路径(从右往左,即先序的镜像),vector保存一路上的节点,通过push和pop回溯,维护路径,index <= n是对只有左叶节点没有右叶节点的点特判
2.判断是否为堆:从第二个节点开始遍历,如果比父节点小,就不是小顶堆,如果比父节点大,就不是大顶堆~

 

PAT 1154 Vertex Coloring (25 分)-甲级

A proper vertex coloring is a labeling of the graph’s vertices with colors such that no two vertices sharing the same edge have the same color. A coloring using at most k colors is called a (proper) k-coloring.

Now you are supposed to tell if a given coloring is a proper k-coloring.

Input Specification:
Each input file contains one test case. For each case, the first line gives two positive integers N and M (both no more than 10
​4
​​ ), being the total numbers of vertices and edges, respectively. Then M lines follow, each describes an edge by giving the indices (from 0 to N−1) of the two ends of the edge.

After the graph, a positive integer K (≤ 100) is given, which is the number of colorings you are supposed to check. Then K lines follow, each contains N colors which are represented by non-negative integers in the range of int. The i-th color is the color of the i-th vertex.

Output Specification:
For each coloring, print in a line k-coloring if it is a proper k-coloring for some positive k, or No if not.

Sample Input:
10 11
8 7
6 8
4 5
8 4
8 1
1 2
1 4
9 8
9 1
1 0
2 4
4
0 1 0 1 4 1 0 1 3 0
0 1 0 1 4 1 0 1 0 0
8 1 0 1 4 1 0 5 3 0
1 2 3 4 5 6 7 8 8 9
Sample Output:
4-coloring
No
6-coloring
No

题目大意:给出一个图(先给出所有边,后给出每个点的颜色),问是否满足:所有的边的两个点的颜色不相同
分析:把所有边存起来,把所有点的颜色存起来(存的过程中放入set统计颜色个数),枚举所有边,检查是否每条边的两点个颜色是否相同,若全不相同,则输出颜色个数,否则输出No~

 

PAT 1153 Decode Registration Card of PAT (25 分)- 甲级

A registration card number of PAT consists of 4 parts:

the 1st letter represents the test level, namely, T for the top level, A for advance and B for basic;
the 2nd – 4th digits are the test site number, ranged from 101 to 999;
the 5th – 10th digits give the test date, in the form of yymmdd;
finally the 11th – 13th digits are the testee’s number, ranged from 000 to 999.
Now given a set of registration card numbers and the scores of the card owners, you are supposed to output the various statistics according to the given queries.

Input Specification:
Each input file contains one test case. For each case, the first line gives two positive integers N (≤10
​4
​​ ) and M (≤100), the numbers of cards and the queries, respectively.

Then N lines follow, each gives a card number and the owner’s score (integer in [0,100]), separated by a space.

After the info of testees, there are M lines, each gives a query in the format Type Term, where

Type being 1 means to output all the testees on a given level, in non-increasing order of their scores. The corresponding Term will be the letter which specifies the level;
Type being 2 means to output the total number of testees together with their total scores in a given site. The corresponding Term will then be the site number;
Type being 3 means to output the total number of testees of every site for a given test date. The corresponding Term will then be the date, given in the same format as in the registration card.
Output Specification:
For each query, first print in a line Case #: input, where # is the index of the query case, starting from 1; and input is a copy of the corresponding input query. Then output as requested:

for a type 1 query, the output format is the same as in input, that is, CardNumber Score. If there is a tie of the scores, output in increasing alphabetical order of their card numbers (uniqueness of the card numbers is guaranteed);
for a type 2 query, output in the format Nt Ns where Nt is the total number of testees and Ns is their total score;
for a type 3 query, output in the format Site Nt where Site is the site number and Nt is the total number of testees at Site. The output must be in non-increasing order of Nt’s, or in increasing order of site numbers if there is a tie of Nt.
If the result of a query is empty, simply print NA.

Sample Input:
8 4
B123180908127 99
B102180908003 86
A112180318002 98
T107150310127 62
A107180908108 100
T123180908010 78
B112160918035 88
A107180908021 98
1 A
2 107
3 180908
2 999
Sample Output:
Case 1: 1 A
A107180908108 100
A107180908021 98
A112180318002 98
Case 2: 2 107
3 260
Case 3: 3 180908
107 2
123 2
102 1
Case 4: 2 999
NA

题目大意:给出一组学生的准考证号和成绩,准考证号包含了等级(乙甲顶),考场号,日期,和个人编号信息,并有三种查询方式
查询一:给出考试等级,找出该等级的考生,按照成绩降序,准考证升序排序
查询二:给出考场号,统计该考场的考生数量和总得分
查询三:给出考试日期,查询改日期下所有考场的考试人数,按照人数降序,考场号升序排序
分析:先把所有考生的准考证和分数记录下来~
1.按照等级查询,枚举选取匹配的学生,然后排序即可
2.按照考场查询,枚举选取匹配的学生,然后计数、求和
3.按日期查询每个考场人数,用unordered_map存储,最后排序汇总~
注意:1.第三个用map存储会超时,用unordered_map就不会超时啦~
2.排序传参建议用引用传参,这样更快,虽然有时候不用引用传参也能通过,但还是尽量用,养成好习惯~