分类： Code

The “travelling salesman problem” asks the following question: “Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?” It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science. (Quoted from “https://en.wikipedia.org/wiki/Travelling_salesman_problem”.)

In this problem, you are supposed to find, from a given list of cycles, the one that is the closest to the solution of a travelling salesman problem.

Input Specification:
Each input file contains one test case. For each case, the first line contains 2 positive integers N (2<N≤200), the number of cities, and M, the number of edges in an undirected graph. Then M lines follow, each describes an edge in the format City1 City2 Dist, where the cities are numbered from 1 to N and the distance Dist is positive and is no more than 100. The next line gives a positive integer K which is the number of paths, followed by K lines of paths, each in the format:

n C1 C2 ……Cn​​

where n is the number of cities in the list, and C​i‘s are the cities on a path.

Output Specification:
For each path, print in a line Path X: TotalDist (Description) where X is the index (starting from 1) of that path, TotalDist its total distance (if this distance does not exist, output NA instead), and Description is one of the following:

TS simple cycle if it is a simple cycle that visits every city;
TS cycle if it is a cycle that visits every city, but not a simple cycle;
Not a TS cycle if it is NOT a cycle that visits every city.
Finally print in a line Shortest Dist(X) = TotalDist where X is the index of the cycle that is the closest to the solution of a travelling salesman problem, and TotalDist is its total distance. It is guaranteed that such a solution is unique.

Sample Input:
6 10
6 2 1
3 4 1
1 5 1
2 5 1
3 1 8
4 1 6
1 6 1
6 3 1
1 2 1
4 5 1
7
7 5 1 4 3 6 2 5
7 6 1 3 4 5 2 6
6 5 1 4 3 6 2
9 6 2 1 6 3 4 5 2 6
4 1 2 5 1
7 6 1 2 5 4 3 1
7 6 3 2 5 4 1 6
Sample Output:
Path 1: 11 (TS simple cycle)
Path 2: 13 (TS simple cycle)
Path 3: 10 (Not a TS cycle)
Path 4: 8 (TS cycle)
Path 5: 3 (Not a TS cycle)
Path 6: 13 (Not a TS cycle)
Path 7: NA (Not a TS cycle)
Shortest Dist(4) = 8

题目大意：给出一条路径，判断这条路径是这个图的旅行商环路、简单旅行商环路还是非旅行商环路～

分析：如果给出的路径存在某两个连续的点不可达或者第一个结点和最后一个结点不同或者这个路径没有访问过图中所有的点，那么它就不是一个旅行商环路(flag = 0)～如果满足了旅行商环路的条件，那么再判断这个旅行商环路是否是简单旅行商环路，即是否访问过n+1个结点（源点访问两次）～最后输出这些旅行商环路中经过的路径最短的路径编号和路径长度～

When shipping goods with containers, we have to be careful not to pack some incompatible goods into the same container, or we might get ourselves in serious trouble. For example, oxidizing agent （氧化剂） must not be packed with flammable liquid （易燃液体）, or it can cause explosion.

Now you are given a long list of incompatible goods, and several lists of goods to be shipped. You are supposed to tell if all the goods in a list can be packed into the same container.

Input Specification:
Each input file contains one test case. For each case, the first line gives two positive integers: N (≤10^4), the number of pairs of incompatible goods, and M (≤100), the number of lists of goods to be shipped.

Then two blocks follow. The first block contains N pairs of incompatible goods, each pair occupies a line; and the second one contains M lists of goods to be shipped, each list occupies a line in the following format:

K G[1] G[2] … G[K]
where K (≤1,000) is the number of goods and G[i]’s are the IDs of the goods. To make it simple, each good is represented by a 5-digit ID number. All the numbers in a line are separated by spaces.

Output Specification:
For each shipping list, print in a line Yes if there are no incompatible goods in the list, or No if not.

Sample Input:
6 3
20001 20002
20003 20004
20005 20006
20003 20001
20005 20004
20004 20006
4 00001 20004 00002 20003
5 98823 20002 20003 20006 10010
3 12345 67890 23333
Sample Output:
No
Yes
Yes

题目大意：集装箱运输货物时，我们必须特别小心，不能把不相容的货物装在一只箱子里。比如氧化剂绝对不能跟易燃液体同箱，否则很容易造成爆炸。给定一张不相容物品的清单，需要你检查每一张集装箱货品清单，判断它们是否能装在同一只箱子里。对每箱货物清单，判断是否可以安全运输。如果没有不相容物品，则在一行中输出 Yes，否则输出 No～

分析：用map存储每一个货物的所有不兼容货物～在判断给出的一堆货物是否是相容的时候，判断任一货物的不兼容货物是否在这堆货物中～如果存在不兼容的货物，则这堆货物不能相容～如果遍历完所有的货物，都找不到不兼容的两个货物，则这堆货物就是兼容的～

以下文字摘自《灵机一动·好玩的数学》：“狼人杀”游戏分为狼人、好人两大阵营。在一局“狼人杀”游戏中，1 号玩家说：“2 号是狼人”，2 号玩家说：“3 号是好人”，3 号玩家说：“4 号是狼人”，4 号玩家说：“5 号是好人”，5 号玩家说：“4 号是好人”。已知这 5 名玩家中有 2 人扮演狼人角色，有 2 人说的不是实话，有狼人撒谎但并不是所有狼人都在撒谎。扮演狼人角色的是哪两号玩家？

本题是这个问题的升级版：已知 N 名玩家中有 2 人扮演狼人角色，有 2 人说的不是实话，有狼人撒谎但并不是所有狼人都在撒谎。要求你找出扮演狼人角色的是哪几号玩家？

输入格式：
输入在第一行中给出一个正整数 N（5≤N≤100）。随后 N 行，第 i 行给出第 i 号玩家说的话（1≤i≤N），即一个玩家编号，用正号表示好人，负号表示狼人。

输出格式：
如果有解，在一行中按递增顺序输出 2 个狼人的编号，其间以空格分隔，行首尾不得有多余空格。如果解不唯一，则输出最小序列解 —— 即对于两个序列 A=a[1],…,a[M] 和 B=b[1],…,b[M]，若存在 0≤k[k+1]<b[k+1]，则称序列 A 小于序列 B。若无解则输出 No Solution。

输入样例 1：
5
-2
+3
-4
+5
+4
输出样例 1：
1 4
输入样例 2：
6
+6
+3
+1
-5
-2
+4
输出样例 2（解不唯一）：
1 5
输入样例 3：
5
-2
-3
-4
-5
-1
输出样例 3：
No Solution

分析：每个人说的数字保存在v数组中，i从1～n、j从i+1～n遍历，分别假设i和j是狼人，a数组表示该人是狼人还是好人，等于1表示是好人，等于-1表示是狼人。k从1～n分别判断k所说的话是真是假，k说的话和真实情况不同（即v[k] * a[abs(v[k])] < 0）则表示k在说谎，则将k放在lie数组中；遍历完成后判断lie数组，如果说谎人数等于2并且这两个说谎的人一个是好人一个是狼人（即a[lie[0]] + a[lie[1]] == 0）表示满足题意，此时输出i和j并return，否则最后的时候输出No Solution～

做作业的时候，邻座的小盆友问你：“五乘以七等于多少？”你应该不失礼貌地围笑着告诉他：“五十三。”本题就要求你，对任何一对给定的正整数，倒着输出它们的乘积。

输入格式：
输入在第一行给出两个不超过 1000 的正整数 A 和 B，其间以空格分隔。

输出格式：
在一行中倒着输出 A 和 B 的乘积。

输入样例：
5 7
输出样例：
53

分析：a 和 b的乘积转换成字符串，再将字符串反转，最后将反转过的字符串转换成数字～