Check if the given Prufer sequence is valid or not

Given a Prufer sequence of N integers, the task is to check if the given sequence is a valid Prufer sequence or not.

Examples:

```Input: arr[] = {4, 1, 3, 4}
Output: Valid
The tree is:
2----4----3----1----5
|
6

Input: arr[] = {4, 1, 7, 4}
Output: Invalid
```

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Since we know the Prufer sequence is of length N – 2 where N is the number of vertices. Hence we need to check if the Prufer sequence consists of elements which are in the range [1, N].

Below is the implementation of the above approach:

C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function that returns true if ` `// given Prufer sequence is valid ` `bool` `isValidSeq(``int` `a[], ``int` `n) ` `{ ` `    ``int` `nodes = n + 2; ` ` `  `    ``// Iterate in the Prufer sequence ` `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// If out of range ` `        ``if` `(a[i] < 1 || a[i] > nodes) ` `            ``return` `false``; ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a[] = { 4, 1, 3, 4 }; ` `    ``int` `n = ``sizeof``(a) / ``sizeof``(a[0]); ` `    ``if` `(isValidSeq(a, n)) ` `        ``cout << ``"Valid"``; ` `    ``else` `        ``cout << ``"Invalid"``; ` ` `  `    ``return` `0; ` `} `

Java

 `// Java implementation of the approach ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` ` `  ` `  `// Function that returns true if ` `// given Prufer sequence is valid ` `static` `boolean` `isValidSeq(``int` `[]a, ``int` `n) ` `{ ` `    ``int` `nodes = n + ``2``; ` ` `  `    ``// Iterate in the Prufer sequence ` `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``{ ` ` `  `        ``// If out of range ` `        ``if` `(a[i] < ``1` `|| a[i] > nodes) ` `            ``return` `false``; ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args)  ` `{ ` `    ``int` `a[] = { ``4``, ``1``, ``3``, ``4` `}; ` `    ``int` `n = a.length; ` `    ``if` `(isValidSeq(a, n)) ` `        ``System.out.println( ``"Valid"``); ` `    ``else` `        ``System.out.print( ``"Invalid"``); ` `} ` `} ` ` `  `// This code is contributed by anuj_67.. `

Python3

 `# Python3 implementation of the approach  ` ` `  `# Function that returns true if  ` `# given Prufer sequence is valid  ` `def` `isValidSeq(a, n) :  ` ` `  `    ``nodes ``=` `n ``+` `2``;  ` ` `  `    ``# Iterate in the Prufer sequence  ` `    ``for` `i ``in` `range``(n) : ` ` `  `        ``# If out of range  ` `        ``if` `(a[i] < ``1` `or` `a[i] > nodes) : ` `            ``return` `False``;  ` `     `  `    ``return` `True``;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``a ``=` `[ ``4``, ``1``, ``3``, ``4` `];  ` `     `  `    ``n ``=` `len``(a);  ` `     `  `    ``if` `(isValidSeq(a, n)) : ` `        ``print``(``"Valid"``);  ` `    ``else` `: ` `        ``print``(``"Invalid"``);  ` `         `  `# This code is contributed by AnkitRai01 `

C#

 `// C# implementation of the approach ` `using` `System; ` `     `  `class` `GFG  ` `{ ` ` `  ` `  `// Function that returns true if ` `// given Prufer sequence is valid ` `static` `Boolean isValidSeq(``int` `[]a, ``int` `n) ` `{ ` `    ``int` `nodes = n + 2; ` ` `  `    ``// Iterate in the Prufer sequence ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `    ``{ ` ` `  `        ``// If out of range ` `        ``if` `(a[i] < 1 || a[i] > nodes) ` `            ``return` `false``; ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main (String[] args)  ` `{ ` `    ``int` `[]a = { 4, 1, 3, 4 }; ` `    ``int` `n = a.Length; ` `    ``if` `(isValidSeq(a, n)) ` `        ``Console.WriteLine( ``"Valid"``); ` `    ``else` `    ``Console.WriteLine( ``"Invalid"``); ` `} ` `} ` ` `  `// This code has been contributed by 29AjayKumar `

Output:

```Valid
```

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