ZOJ 2795-Ambiguous permutations

妖狐艹你老母 2022-08-20 13:23 10阅读 0赞

ZOJ Problem Set - 2795

Ambiguous permutations

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Time Limit: 10 Seconds  Memory Limit: 32768 KB

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Some programming contest problems are really tricky: not only do they require a different output format from what you might have expected, but also the sample output does not show the difference. For an example, let us look at permutations.  
A **permutation** of the integers *1* to *n* is an ordering of these integers. So the natural way to represent a permutation is to list the integers in this order. With *n = 5*, a permutation might look like 2, 3, 4, 5, 1.  
However, there is another possibility of representing a permutation: You create a list of numbers where the *i*\-th number is the position of the integer *i* in the permutation. Let us call this second possibility an **inverse permutation**. The inverse permutation for the sequence above is 5, 1, 2, 3, 4.  
An **ambiguous permutation** is a permutation which cannot be distinguished from its inverse permutation. The permutation 1, 4, 3, 2 for example is ambiguous, because its inverse permutation is the same. To get rid of such annoying sample test cases, you have to write a program which detects if a given permutation is ambiguous or not.

**Input Specification**

The input contains several test cases.  
The first line of each test case contains an integer *n* (*1 ≤ n ≤ 100000*). Then a permutation of the integers *1* to *n* follows in the next line. There is exactly one space character between consecutive integers. You can assume that every integer between *1* and *n* appears exactly once in the permutation.  
The last test case is followed by a zero.

**Output Specification**

For each test case output whether the permutation is ambiguous or not. Adhere to the format shown in the sample output.

**Sample Input**

4
    1 4 3 2
    5
    2 3 4 5 1
    1
    1
    0

**Sample Output**

ambiguous
    not ambiguous
    ambiguous

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Source: **University of Ulm Local Contest 2005**

**解题思路：**

**题目大意例如第一个数据：1是第一次输入，在输入的序列中1在第一个，4第二个输入，而2在输入的序列中的第4个。这样的可称为逆序。**

#include<stdio.h>
    #include<string.h>
    #include<algorithm>
    using namespace std;
    int num[100000],pos[100000];
    int main()
    {
    	int T;
    	while(scanf("%d",&T)&&T)
    	{
    		int i,j;
    		for(int i=1;i<=T;i++)
    		{
    			scanf("%d",&num[i]);
    			pos[num[i]]=i;
    		}
    		int wc=1;
    		int flag=1;
    		for(int i=1;i<=T;i++)
    		{
    			if(pos[i]!=num[i])
    			{
    				flag=0;
    				break;
    			}
    		}
    		if(flag==0)
    		{
    			printf("not ambiguous\n");
    		}
    		else
    		{
    			printf("ambiguous\n");
    		}
    	}
    	return 0;
    }