Find the lexicographically smallest string which satisfies the given condition

Given an array, arr[] of N integers, where arr[i] represents the number of distinct characters in the prefix of length (i + 1) of a string S. The task is to find the lexicographically smallest string (if any exists) that satisfies the given prefix array. The string should be of lowercase English alphabets [a-z]. If no such string exists then print -1.

Examples:

Input: arr[] = {1, 1, 2, 3}
Output: aabc
prefix[0] has 1 distinct character
prefix[1] has 1 distinct character
prefix[2] has 2 distinct characters
prefix[3] has 3 distinct characters
And the string is the smallest possible.



Input: arr[] = {1, 2, 2, 3, 3, 4}
Output: abacad

Input: arr[] = {1, 1, 3, 3}
Output: -1

Approach: The first character of every string will always be ‘a’. Since we have to find the lexicographically smallest string. Therefore, if the number of different characters in the prefix of length i and i + 1 is same, then (i+1)th character will be ‘a’ otherwise it will be a different character from all characters in length i and it will be one greater than the greatest character in the prefix of length i.
For example, if prefix array is {1, 2, 2, 3, 4} then the first character will be ‘a’, the second character will be ‘b’ since number of different character is 2 (it can also be ‘c’ or ‘d’ etc but we have to take lexicographically smallest). Third character will be either ‘a’ or ‘b’ but we take ‘a’ since “aba” is smaller than “abb”.
Similarly, fourth and fifth character will be ‘c’ and ‘d’ respectively. Therefore, the resultant string that satisfies the given prefix array will be “abacd”.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <iostream>
using namespace std;
  
// Function to return the required string
string smallestString(int N, int A[])
{
    // First character will always be 'a'
    char ch = 'a';
  
    // To store the resultant string
    string S = "";
  
    // Since length of the string should be
    // greater than 0 and first element
    // of array should be 1
    if (N < 1 || A[0] != 1) {
        S = "-1";
        return S;
    }
  
    S += ch;
    ch++;
  
    // Check one by one all element of given prefix array
    for (int i = 1; i < N; i++) {
        int diff = A[i] - A[i - 1];
  
        // If the difference between any two
        // consecutive elements of the prefix array
        // is greater than 1 then there will be no such
        // string possible that satisfies the given array
        // Also, string cannot have more than
        // 26 distinct characters
        if (diff > 1 || diff < 0 || A[i] > 26) {
            S = "-1";
            return S;
        }
  
        // If difference is 0 then the (i + 1)th character
        // will be same as the ith character
        else if (diff == 0)
            S += 'a';
  
        // If difference is 1 then the (i + 1)th character
        // will be different from the ith character
        else {
            S += ch;
            ch++;
        }
    }
  
    // Return the resultant string
    return S;
}
  
// Driver code
int main()
{
    int arr[] = { 1, 1, 2, 3, 3 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << smallestString(n, arr);
  
    return 0;
}

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Java

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// Java implementation of the above approach 
class GFG 
      
    // Function to return the required string 
    static String smallestString(int N, int []A) 
    
        // First character will always be 'a' 
        char ch = 'a'
      
        // To store the resultant string 
        String S = ""
      
        // Since length of the string should be 
        // greater than 0 and first element 
        // of array should be 1 
        if (N < 1 || A[0] != 1
        
            S = "-1"
            return S; 
        
      
        S += ch; 
        ch++; 
      
        // Check one by one all element of given prefix array 
        for (int i = 1; i < N; i++) 
        
            int diff = A[i] - A[i - 1]; 
      
            // If the difference between any two 
            // consecutive elements of the prefix array 
            // is greater than 1 then there will be no such 
            // string possible that satisfies the given array 
            // Also, string cannot have more than 
            // 26 distinct characters 
            if (diff > 1 || diff < 0 || A[i] > 26
            
                S = "-1"
                return S; 
            
      
            // If difference is 0 then the (i + 1)th character 
            // will be same as the ith character 
            else if (diff == 0
                S += 'a'
      
            // If difference is 1 then the (i + 1)th character 
            // will be different from the ith character 
            else
            
                S += ch; 
                ch++; 
            
        
      
        // Return the resultant string 
        return S; 
    
      
    // Driver code 
    public static void main(String args[]) 
    
        int []arr = { 1, 1, 2, 3, 3 }; 
        int n = arr.length; 
        System.out.println(smallestString(n, arr)); 
    
  
// This code is contributed by Ryuga

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Python3

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# Function to return the required string
def smallestString(N, A):
      
    # First character will always be 'a'
    ch = 'a'
  
    # To store the resultant string
    S = ""
  
    # Since length of the string should be
    # greater than 0 and first element
    # of array should be 1
    if (N < 1 or A[0] != 1):
        S = "-1"
        return S
  
    S += str(ch)
    ch = chr(ord(ch) + 1)
  
    # Check one by one all element of 
    # given prefix array
    for i in range(1, N):
        diff = A[i] - A[i - 1]
  
        # If the difference between any two
        # consecutive elements of the prefix 
        # array is greater than 1 then there 
        # will be no such string possible that 
        # satisfies the given array. 
        # Also, string cannot have more than
        # 26 distinct characters
        if (diff > 1 or diff < 0 or A[i] > 26):
            S = "-1"
            return S
  
        # If difference is 0 then the 
        # (i + 1)th character will be 
        # same as the ith character
        elif (diff == 0):
            S += 'a'
  
        # If difference is 1 then the 
        # (i + 1)th character will be 
        # different from the ith character
        else:
            S += ch
            ch = chr(ord(ch) + 1)
  
    # Return the resultant string
    return S
  
# Driver code
arr = [1, 1, 2, 3, 3]
n = len(arr)
print(smallestString(n, arr))
  
# This code is contributed 
# by mohit kumar

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C#

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// C# implementation of the approach
using System;
  
class GFG
{
      
// Function to return the required string
static string smallestString(int N, int []A)
{
    // First character will always be 'a'
    char ch = 'a';
  
    // To store the resultant string
    string S = "";
  
    // Since length of the string should be
    // greater than 0 and first element
    // of array should be 1
    if (N < 1 || A[0] != 1) 
    {
        S = "-1";
        return S;
    }
  
    S += ch;
    ch++;
  
    // Check one by one all element of given prefix array
    for (int i = 1; i < N; i++)
    {
        int diff = A[i] - A[i - 1];
  
        // If the difference between any two
        // consecutive elements of the prefix array
        // is greater than 1 then there will be no such
        // string possible that satisfies the given array
        // Also, string cannot have more than
        // 26 distinct characters
        if (diff > 1 || diff < 0 || A[i] > 26) 
        {
            S = "-1";
            return S;
        }
  
        // If difference is 0 then the (i + 1)th character
        // will be same as the ith character
        else if (diff == 0)
            S += 'a';
  
        // If difference is 1 then the (i + 1)th character
        // will be different from the ith character
        else 
        {
            S += ch;
            ch++;
        }
    }
  
    // Return the resultant string
    return S;
}
  
// Driver code
static void Main()
{
    int []arr = { 1, 1, 2, 3, 3 };
    int n = arr.Length;
    Console.WriteLine(smallestString(n, arr));
}
}
  
// This code is contributed by mits

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PHP

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<?PHP
// PHP implementation of the above approach 
// Function to return the required string 
function smallestString($N, $A
    // First character will always be 'a' 
    $ch = 'a'
  
    // To store the resultant string 
    $S = ""
  
    // Since length of the string should be 
    // greater than 0 and first element 
    // of array should be 1 
    if ($N < 1 || $A[0] != 1) 
    
        $S = "-1"
        return $S
    
  
    $S .= $ch
    $ch++; 
  
    // Check one by one all element of given prefix array 
    for ($i = 1; $i < $N; $i++) 
    
        $diff = $A[$i] - $A[$i - 1]; 
  
        // If the difference between any two 
        // consecutive elements of the prefix array 
        // is greater than 1 then there will be no such 
        // string possible that satisfies the given array 
        // Also, string cannot have more than 
        // 26 distinct characters 
        if ($diff > 1 || $diff < 0 || $A[$i] > 26) 
        
            $S = "-1"
            return $S
        
  
        // If difference is 0 then the (i + 1)th character 
        // will be same as the ith character 
        else if ($diff == 0) 
            $S .= 'a'
  
        // If difference is 1 then the (i + 1)th character 
        // will be different from the ith character 
        else
        
            $S .= $ch
            $ch++; 
        
    
  
    // Return the resultant string 
    return $S
  
// Driver code 
$arr = array( 1, 1, 2, 3, 3 ); 
$n = sizeof($arr); 
echo(smallestString($n, $arr)); 
  
// This code is contributed by Code_Mech
?>

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Output:

aabca


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