Permutation of first N natural numbers having given array as the prefix maximum array - GeeksforGeeks

11 Aug, 2021
Given an array arr[] consisting of N positive integers, the task is to find the permutation of first N natural numbers such that the given array arr[] is the prefix maximum array of that permutation. If no such permutation exists, then print “-1”.
Examples:
Input: arr[] = {1, 3, 4, 5, 5}Output: 1 3 4 5 2Explanation:The prefix maximum array of the permutation {1, 3, 4, 5, 2} is {1, 3, 4, 5, 5}.
Input: arr[] = {1, 1, 3, 4}Output: -1
Naive Approach: The simplest approach to solve the given problem is to generate all possible permutations of the first N natural numbers and check if there exists any permutation whose prefix maximum array is the array arr[] or not. If any such permutation is found, then print that permutation. Otherwise, print “-1”. 
Time Complexity: O(N * N!)Auxiliary Space: O(1)
Efficient Approach: The above approach can be optimized based on the observation that the first occurrence of every number in the arr[] will be at the same place as that in the required permutation. Therefore, after filling the first occurrence of all the elements at their correct positions, fill the remaining numbers in ascending order. Follow the steps below to solve the problem:
Initialize an array ans[] of size N with all elements as 0 and a vector V[] to store all the unvisited elements in the array.
Initialize a HashMap M to store the index of the first occurrence of elements
Traverse the array arr[] and if arr[i] is not present in M, then store the index of arr[i] in M and update ans[i] to arr[i].
Iterate over the range [1, N] using the variable i and check if i is not present in M, store it in the vector V[].
Traverse the array ans[] and if the value of ans[i] is 0, then update ans[i] to V[j] and increment j by 1.
After completing the above steps, check if the maximum element prefix array is the same as arr[]. If found to be true, then print the array ans[] as the result. Otherwise, print “-1”.
Below is the implementation of the above approach:
C++
Java
Python3
C#
Javascript
// C++ program for the above approach #include <bits/stdc++.h>using namespace std; // Function to check if the maximum// prefix array of ans[] is equal// to array arr[]bool checkPermutation(    int ans[], int a[], int n){    // Initialize a variable, Max    int Max = INT_MIN;     // Traverse the array, ans[]    for (int i = 0; i < n; i++) {         // Store the maximum value        // upto index i        Max = max(Max, ans[i]);         // If it is not equal to a[i],        // then return false        if (Max != a[i])            return false;    }     // Otherwise return false    return true;} // Function to find the permutation of// the array whose prefix maximum array// is same as the given array a[]void findPermutation(int a[], int n){    // Stores the required permutation    int ans[n] = { 0 };     // Stores the index of first    // occurrence of elements    unordered_map<int, int> um;     // Traverse the array a[]    for (int i = 0; i < n; i++) {         // If a[i] is not present        // in um, then store it in um        if (um.find(a[i]) == um.end()) {             // Update the ans[i]            // to a[i]            ans[i] = a[i];            um[a[i]] = i;        }    }     // Stores the unvisited numbers    vector<int> v;    int j = 0;     // Fill the array, v[]    for (int i = 1; i <= n; i++) {         // Store the index        if (um.find(i) == um.end()) {            v.push_back(i);        }    }     // Traverse the array, ans[]    for (int i = 0; i < n; i++) {         // Fill v[j] at places where        // ans[i] is 0        if (ans[i] == 0) {            ans[i] = v[j];            j++;        }    }     // Check if the current permutation    // maximum prefix array is same as    // the given array a[]    if (checkPermutation(ans, a, n)) {         // If true, the print the        // permutation        for (int i = 0; i < n; i++) {            cout << ans[i] << " ";        }    }     // Otherwise, print -1    else        cout << "-1";} // Driver Codeint main(){    int arr[] = { 1, 3, 4, 5, 5 };    int N = sizeof(arr) / sizeof(arr[0]);     // Function Call    findPermutation(arr, N);     return 0;}
// Java program for the above approachimport java.io.*;import java.lang.*;import java.util.*; class GFG{ // Function to check if the maximum// prefix array of ans[] is equal// to array arr[]static boolean checkPermutation(int ans[], int a[],                                int n){         // Initialize a variable, Max    int Max = Integer.MIN_VALUE;     // Traverse the array, ans[]    for(int i = 0; i < n; i++)    {                 // Store the maximum value        // upto index i        Max = Math.max(Max, ans[i]);         // If it is not equal to a[i],        // then return false        if (Max != a[i])            return false;    }     // Otherwise return false    return true;} // Function to find the permutation of// the array whose prefix maximum array// is same as the given array a[]static void findPermutation(int a[], int n){         // Stores the required permutation    int ans[] = new int[n];     // Stores the index of first    // occurrence of elements    HashMap<Integer, Integer> um = new HashMap<>();     // Traverse the array a[]    for(int i = 0; i < n; i++)    {                 // If a[i] is not present        // in um, then store it in um        if (!um.containsKey(a[i]))        {                         // Update the ans[i]            // to a[i]            ans[i] = a[i];            um.put(a[i], i);        }    }     // Stores the unvisited numbers    ArrayList<Integer> v = new ArrayList<>();    int j = 0;     // Fill the array, v[]    for(int i = 1; i <= n; i++)    {                 // Store the index        if (!um.containsKey(i))        {            v.add(i);        }    }     // Traverse the array, ans[]    for(int i = 0; i < n; i++)    {                 // Fill v[j] at places where        // ans[i] is 0        if (ans[i] == 0)        {            ans[i] = v.get(j);            j++;        }    }     // Check if the current permutation    // maximum prefix array is same as    // the given array a[]    if (checkPermutation(ans, a, n))    {                 // If true, the print the        // permutation        for(int i = 0; i < n; i++)        {            System.out.print(ans[i] + " ");        }    }     // Otherwise, print -1    else        System.out.println("-1");} // Driver Codepublic static void main(String[] args){    int arr[] = { 1, 3, 4, 5, 5 };    int N = arr.length;     // Function Call    findPermutation(arr, N);}} // This code is contributed by Kingash
# Python3 program for the above approachimport sys # Function to check if the maximum# prefix array of ans[] is equal# to array arr[]def checkPermutation(ans, a, n):     # Initialize a variable, Max    Max = -sys.maxsize - 1     # Traverse the array, ans[]    for i in range(n):         # Store the maximum value        # upto index i        Max = max(Max, ans[i])         # If it is not equal to a[i],        # then return false        if (Max != a[i]):            return False     # Otherwise return false    return True # Function to find the permutation of# the array whose prefix maximum array# is same as the given array a[]def findPermutation(a, n):     # Stores the required permutation    ans = [0] * n     # Stores the index of first    # occurrence of elements    um = {}     # Traverse the array a[]    for i in range(n):         # If a[i] is not present        # in um, then store it in um        if (a[i] not in um):             # Update the ans[i]            # to a[i]            ans[i] = a[i]            um[a[i]] = i     # Stores the unvisited numbers    v = []    j = 0     # Fill the array, v[]    for i in range(1, n + 1):         # Store the index        if (i not in um):            v.append(i)     # Traverse the array, ans[]    for i in range(n):         # Fill v[j] at places where        # ans[i] is 0        if (ans[i] == 0):            ans[i] = v[j]            j += 1     # Check if the current permutation    # maximum prefix array is same as    # the given array a[]    if (checkPermutation(ans, a, n)):         # If true, the print the        # permutation        for i in range(n):            print(ans[i], end = " ")     # Otherwise, print -1    else:        print("-1") # Driver Codeif __name__ == "__main__":     arr = [ 1, 3, 4, 5, 5 ]    N = len(arr)     # Function Call    findPermutation(arr, N) # This code is contributed by ukasp
// C# program for the above approachusing System;using System.Collections.Generic;  class GFG{     // Function to check if the maximum// prefix array of ans[] is equal// to array arr[]static bool checkPermutation(int[] ans, int[] a,                             int n){         // Initialize a variable, Max    int Max = Int32.MinValue;     // Traverse the array, ans[]    for(int i = 0; i < n; i++)    {                 // Store the maximum value        // upto index i        Max = Math.Max(Max, ans[i]);         // If it is not equal to a[i],        // then return false        if (Max != a[i])            return false;    }         // Otherwise return false    return true;} // Function to find the permutation of// the array whose prefix maximum array// is same as the given array a[]static void findPermutation(int[] a, int n){         // Stores the required permutation    int[] ans = new int[n];     // Stores the index of first    // occurrence of elements    Dictionary<int,               int> um = new Dictionary<int,                                        int>();     // Traverse the array a[]    for(int i = 0; i < n; i++)    {                 // If a[i] is not present        // in um, then store it in um        if (!um.ContainsKey(a[i]))        {                         // Update the ans[i]            // to a[i]            ans[i] = a[i];            um[a[i]] = i;        }    }     // Stores the unvisited numbers    List<int> v = new List<int>();    int j = 0;     // Fill the array, v[]    for(int i = 1; i <= n; i++)    {                 // Store the index        if (!um.ContainsKey(i))        {            v.Add(i);        }    }     // Traverse the array, ans[]    for(int i = 0; i < n; i++)    {                 // Fill v[j] at places where        // ans[i] is 0        if (ans[i] == 0)        {            ans[i] = v[j];            j++;        }    }     // Check if the current permutation    // maximum prefix array is same as    // the given array a[]    if (checkPermutation(ans, a, n))    {                 // If true, the print the        // permutation        for(int i = 0; i < n; i++)        {            Console.Write(ans[i] + " ");        }    }     // Otherwise, print -1    else        Console.Write("-1");} // Driver Codepublic static void Main(){    int[] arr = { 1, 3, 4, 5, 5 };    int N = arr.Length;     // Function Call    findPermutation(arr, N);}} // This code is contributed by sanjoy_62
<script> // JavaScript program for the above approach // Function to check if the maximum// prefix array of ans[] is equal// to array arr[]function checkPermutation(ans,a,n){    // Initialize a variable, Max    let Max = Number.MIN_VALUE;      // Traverse the array, ans[]    for(let i = 0; i < n; i++)    {                  // Store the maximum value        // upto index i        Max = Math.max(Max, ans[i]);          // If it is not equal to a[i],        // then return false        if (Max != a[i])            return false;    }      // Otherwise return false    return true;} // Function to find the permutation of// the array whose prefix maximum array// is same as the given array a[]function findPermutation(a,n){    // Stores the required permutation    let ans = new Array(n);     for(let i=0;i<n;i++)    {        ans[i]=0;    }    // Stores the index of first    // occurrence of elements    let um = new Map();      // Traverse the array a[]    for(let i = 0; i < n; i++)    {                  // If a[i] is not present        // in um, then store it in um        if (!um.has(a[i]))        {                          // Update the ans[i]            // to a[i]            ans[i] = a[i];            um.set(a[i], i);        }    }      // Stores the unvisited numbers    let v = [];    let j = 0;      // Fill the array, v[]    for(let i = 1; i <= n; i++)    {                  // Store the index        if (!um.has(i))        {            v.push(i);        }    }      // Traverse the array, ans[]    for(let i = 0; i < n; i++)    {                  // Fill v[j] at places where        // ans[i] is 0        if (ans[i] == 0)        {            ans[i] = v[j];            j++;        }    }      // Check if the current permutation    // maximum prefix array is same as    // the given array a[]    if (checkPermutation(ans, a, n))    {                  // If true, the print the        // permutation        for(let i = 0; i < n; i++)        {            document.write(ans[i] + " ");        }    }      // Otherwise, print -1    else        document.write("-1");} // Driver Codelet arr=[1, 3, 4, 5, 5];let N = arr.length;// Function CallfindPermutation(arr, N);  // This code is contributed by avanitrachhadiya2155 </script>
1 3 4 5 2
 
Time Complexity: O(N)Auxiliary Space: O(N)
Kingash
sanjoy_62
ukasp
avanitrachhadiya2155
simmytarika5
cpp-unordered_map
Natural Numbers
permutation
prefix
Arrays
Hash
Mathematical
Arrays
Hash
Mathematical
permutation
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