Find the smallest positive number which can not be represented by given digits

Given an array arr[] of size 10 where arr[i] represents the frequency of the digit i. The task is to find the smallest positive number which can not be represented by the given digits.

Examples:

Input: arr[] = {2, 1, 1, 4, 0, 6, 3, 2, 2, 2}
Output: 4
Since the count of 4th digit is 0. So 4 can not be made.



Input : arr[] = {0, 1, 1, 1, 1, 1, 1, 1, 1, 1}
Output : 10
Since the count of 0th digit is 0. So smallest positive integer that can not be made is 10.

Input : arr[] = {2, 2, 1, 2, 1, 1, 3, 1, 1, 1}
Output : 22
To make 22 we require two 2’s but here the count of 2 is only 1.

Approach:

  1. Calculate the min value in the array starting from 1st index and also store it’s index.
  2. Now compare the min value with the value at 0th index.
  3. If its value at 0th index is less than the min value than either 10, 100, 1000 … can’t be expressed.
  4. If its value is greater than min value than iterate the loop up to first min value index and simply print it index value.

Below is the implementation of the above approach:

C++

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// CPP program to find the smallest positive 
// number which can not be represented by given digits
#include<bits/stdc++.h>
using namespace std;
  
// Function to find the smallest positive 
// number which can not be represented by given digits
void expressDigit(int arr[], int n){
      
    int min = 9, index = 0, temp = 0;
      
    // Storing the count of 0 digit
    // or store the value at 0th index
    temp = arr[0];
      
    // Calculates the min value in the array starting 
    // from 1st index and also store it index.
    for(int i = 1; i < 10; i++){
          
        if(arr[i] < min){
            min = arr[i];
            index = i;
        }
    }
      
    // Now compare the min value with the 
    // value at 0th index.
      
    // If its value at 0th index is less than min value
    // than either 10, 100, 1000 ... can't be expressed
    if(temp < min)
    {
        cout << 1;
        for(int i = 1; i <= temp + 1; i++)
            cout << 0;
    }
      
      
    // If it value is greater than min value than
    // iterate the loop upto first min value index 
    // and simply print it index value. 
    else
    {
        for(int i = 0; i < min; i++)
            cout << index;
          
        cout << index;
    }
}
  
// Driver code
int main()
{
    int arr[] = {2, 2, 1, 2, 1, 1, 3, 1, 1, 1};
      
    // Value of N is always 10 as we take digit from 0 to 9
    int N = 10;
      
    // Calling function
    expressDigit(arr, N);
      
    return 0;
      
}

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Java

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// Java program to find the smallest positive 
// number which can not be represented by given digits
import java.util.*;
  
class GFG 
{
  
// Function to find the smallest positive 
// number which can not be represented by given digits
static void expressDigit(int arr[], int n)
{
    int min = 9, index = 0, temp = 0;
      
    // Storing the count of 0 digit
    // or store the value at 0th index
    temp = arr[0];
      
    // Calculates the min value in the array starting 
    // from 1st index and also store it index.
    for(int i = 1; i < 10; i++)
    {
        if(arr[i] < min)
        {
            min = arr[i];
            index = i;
        }
    }
      
    // Now compare the min value with the 
    // value at 0th index.
      
    // If its value at 0th index is less than min value
    // than either 10, 100, 1000 ... can't be expressed
    if(temp < min)
    {
        System.out.print(1);
        for(int i = 1; i <= temp + 1; i++)
            System.out.print(0);
    }
      
    // If it value is greater than min value than
    // iterate the loop upto first min value index 
    // and simply print it index value. 
    else
    {
        for(int i = 0; i < min; i++)
            System.out.print(index);
          
        System.out.print(index);
    }
}
  
// Driver code
public static void main(String[] args) 
{
    int arr[] = {2, 2, 1, 2, 1, 1, 3, 1, 1, 1};
      
    // Value of N is always 10 
    // as we take digit from 0 to 9
    int N = 10;
      
    // Calling function
    expressDigit(arr, N);
}
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python3 program to find the 
# smallest positive number which 
# can not be represented by given digits
  
# Function to find the smallest 
# positive number which can not be
# represented by given digits
def expressDigit(arr, n):
  
    min = 9
    index = 0
  
    temp = 0
  
    # Storing the count of 0 digit
    # or store the value at 0th index
    temp = arr[0]
  
    # Calculates the min value in 
    # the array starting from 
    # 1st index and also store its index.
    for i in range(1, 10):
  
        if(arr[i] < min):
            min = arr[i]
            index = i
  
    # Now compare the min value with the
    # value at 0th index.
  
    # If its value at 0th index is 
    # less than min value than either 
    # 10, 100, 1000 ... can't be expressed
    if(temp < min):
        print(1, end = "")
        for i in range(1, temp + 1):
            print(0, end = "")
  
    # If its value is greater than 
    # min value then iterate the loop 
    # upto first min value index and
    # simply print its index value.
    else:
        for i in range(min):
            print(index, end = "")
  
        print(index)
  
# Driver code
arr = [2, 2, 1, 2, 1
       1, 3, 1, 1, 1]
  
# Value of N is always 10 
# as we take digit from 0 to 9
N = 10
  
# Calling function
expressDigit(arr, N)
  
# This code is contributed by Mohit Kumar

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C#

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// C# program to find the smallest positive 
// number which can not be represented by given digits
using System;
  
class GFG 
{
  
// Function to find the smallest positive 
// number which can not be represented by given digits
static void expressDigit(int []arr, int n)
{
    int min = 9, index = 0, temp = 0;
      
    // Storing the count of 0 digit
    // or store the value at 0th index
    temp = arr[0];
      
    // Calculates the min value in the array starting 
    // from 1st index and also store it index.
    for(int i = 1; i < 10; i++)
    {
        if(arr[i] < min)
        {
            min = arr[i];
            index = i;
        }
    }
      
    // Now compare the min value with the 
    // value at 0th index.
      
    // If its value at 0th index is less than min value
    // than either 10, 100, 1000 ... can't be expressed
    if(temp < min)
    {
        Console.Write(1);
        for(int i = 1; i <= temp + 1; i++)
            Console.Write(0);
    }
      
    // If it value is greater than min value than
    // iterate the loop upto first min value index 
    // and simply print it index value. 
    else
    {
        for(int i = 0; i < min; i++)
            Console.Write(index);
          
        Console.Write(index);
    }
}
  
// Driver code
public static void Main(String[] args) 
{
    int []arr = {2, 2, 1, 2, 1, 1, 3, 1, 1, 1};
      
    // Value of N is always 10 
    // as we take digit from 0 to 9
    int N = 10;
      
    // Calling function
    expressDigit(arr, N);
}
}
  
// This code is contributed by 29AjayKumar

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Output:

22


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