检查数组是否是从 1 到 N 的数字排列

给定一个包含N 个正整数的数组arr ，任务是检查给定的数组 arr 是否表示一个排列。

A sequence of N integers is called a permutation if it contains all integers from 1 to N exactly once.

例子：

Input: arr[] = {1, 2, 5, 3, 2} 
Output: No 
Explanation: 
The given array is not a permutation of numbers from 1 to N, because it contains 2 twice, and 4 is missing for the array to represent a permutation of length 5. 
Input: arr[] = {1, 2, 5, 3, 4} 
Output: Yes 
Explanation: 
Given array contains all integers from 1 to 5 exactly once. Hence, it represents a permutation of length 5. 
 

朴素的方法：显然，给定的数组将仅表示长度为 N 的排列，其中 N 是数组的长度。所以我们必须在给定的数组中搜索从 1 到 N 的每个元素。如果找到所有元素，则数组表示排列，否则不表示排列。
时间复杂度： O(N ² )
有效的方法：
上述方法可以使用一组数据结构进行优化。

1. 遍历给定数组并插入集合数据结构中的每个元素。
2. 另外，找到数组中的最大元素。这个最大元素将是值 N，它代表集合的大小。
3. 遍历数组后，检查集合的大小是否等于 N。
4. 如果集合的大小等于 N，则数组表示排列，否则不表示排列。

下面是上述方法的实现：

C++

// C++ Program to decide if an
// array represents a permutation or not
 
#include 
using namespace std;
 
// Function to check if an
// array represents a permutation or not
bool permutation(int arr[], int n)
{
    // Set to check the count
    // of non-repeating elements
    set hash;
 
    int maxEle = 0;
 
    for (int i = 0; i < n; i++) {
 
        // Insert all elements in the set
        hash.insert(arr[i]);
 
        // Calculating the max element
        maxEle = max(maxEle, arr[i]);
    }
 
    if (maxEle != n)
        return false;
 
    // Check if set size is equal to n
    if (hash.size() == n)
        return true;
 
    return false;
}
 
// Driver code
int main()
{
    int arr[] = { 1, 2, 5, 3, 2 };
    int n = sizeof(arr) / sizeof(int);
 
    if (permutation(arr, n))
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
 
    return 0;
}

Java

// Java Program to decide if an
// array represents a permutation or not
import java.util.*;
 
class GFG{
 
// Function to check if an
// array represents a permutation or not
static boolean permutation(int []arr, int n)
{
    // Set to check the count
    // of non-repeating elements
    Set hash = new HashSet();
 
    int maxEle = 0;
 
    for (int i = 0; i < n; i++) {
 
        // Insert all elements in the set
        hash.add(arr[i]);
 
        // Calculating the max element
        maxEle = Math.max(maxEle, arr[i]);
    }
 
    if (maxEle != n)
        return false;
 
    // Check if set size is equal to n
    if (hash.size() == n)
        return true;
 
    return false;
}
 
// Driver code
public static void main(String args[])
{
    int arr[] = { 1, 2, 5, 3, 2 };
    int n = arr.length;
 
    if (permutation(arr, n))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}
 
// This code is contributed by Surendra_Gangwar

Python3

# Python3 Program to decide if an
# array represents a permutation or not
 
# Function to check if an
# array represents a permutation or not
def permutation(arr, n):
     
        # Set to check the count
    # of non-repeating elements
    s = set()
 
    maxEle = 0;
 
    for i in range(n):
   
        # Insert all elements in the set
        s.add(arr[i]);
 
        # Calculating the max element
        maxEle = max(maxEle, arr[i]);
     
    if (maxEle != n):
        return False
 
    # Check if set size is equal to n
    if (len(s) == n):
        return True;
 
    return False;
 
# Driver code
if __name__=='__main__':
 
    arr = [ 1, 2, 5, 3, 2 ]
    n = len(arr)
 
    if (permutation(arr, n)):
        print("Yes")
    else:
        print("No")
 
# This code is contributed by Princi Singh

C#

// C# Program to decide if an
// array represents a permutation or not
using System;
using System.Collections.Generic;
 
class GFG{
  
// Function to check if an
// array represents a permutation or not
static bool permutation(int []arr, int n)
{
    // Set to check the count
    // of non-repeating elements
    HashSet hash = new HashSet();
  
    int maxEle = 0;
  
    for (int i = 0; i < n; i++) {
  
        // Insert all elements in the set
        hash.Add(arr[i]);
  
        // Calculating the max element
        maxEle = Math.Max(maxEle, arr[i]);
    }
  
    if (maxEle != n)
        return false;
  
    // Check if set size is equal to n
    if (hash.Count == n)
        return true;
  
    return false;
}
  
// Driver code
public static void Main(String []args)
{
    int []arr = { 1, 2, 5, 3, 2 };
    int n = arr.Length;
  
    if (permutation(arr, n))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}
 
// This code is contributed by Princi Singh

Javascript

 
// JavaScript Program to decide if an
// array represents a permutation or not
 
// Function to check if an
// array represents a permutation or not
function permutation(arr, n)
{
    // Set to check the count
    // of non-repeating elements
    let hash =  new Set();
   
    let maxEle = 0;
   
    for (let i = 0; i < n; i++) {
   
        // Insert all elements in the set
        hash.add(arr[i]);
   
        // Calculating the max element
        maxEle = Math.max(maxEle, arr[i]);
    }
   
    if (maxEle != n)
        return false;
   
    // Check if set size is equal to n
    if (hash.length == n)
        return true;
   
    return false;
}
 
// Driver Code
     
    let arr = [ 1, 2, 5, 3, 2 ];
    let n = arr.length;
   
    if (permutation(arr, n))
        document.write("Yes");
    else
        document.write("No");
                   

输出：

No

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