Count of N-Digit Numbers Not Having Given Prefixes

Here the problem is to determine the total number of strings of the length N containing characters '0' through '9' provided an integer N with an array of string prefixes pre[]. such that none of the strings can contain the provided prefixes. The aim of this article is to implement a program to find the count of N digit numbers not having given prefixes.

A collection of various strings is referred to as an array in the C programming language because an array is a linear grouping of data pieces of a similar type.

As we already know, the string is a character-by-character, one-dimensional array that ends with an empty or a null character.

Sample Example 1

Let us take the Input N = 2,

The given prefix, pre = {"1"}

Output obtained: 90

Explanation

All the 2 digit strings excluding {"01","10","11", "12", "13", "14", "15", "16", "17", "18", "19", "21", "31", "41", "51", "61", "71", "81", "91"} are valid here.

Sample Example 2

Let us take the Input N = 3,

The given prefix, pre = {"56"}

Output obtained: 990

Explanation

All the 3 digit strings excluding {"560", "561", "562", "563", "564", "565", "566", "567", "568", "569"} are valid here.

Sample Example 3

Let us take the Input N = 1,

The given prefix, pre = {"6"}

Output obtained: 9

Explanation

All the 1 digit strings excluding {"6"} are valid here.

Problem Statement

Implement a program to find the count of N digit numbers not having given prefixes.

Approach

In Order to find the count of N digit numbers not having given prefixes, we use the following methodology.

The approach to solve this problem and to find the count of N digit numbers not having given prefixes

Given that there are 10 character options for each position in a string, there are a total of (10N) potential strings. Instead of computing the total number of wanted strings, subtract the total number of unwanted strings. Merging prefixes with identical initial character as the longer prefix prior to iterating through the prefixes may result in the removal of certain repetitions.

Algorithm

The algorithm to to find the count of N digit numbers not having given prefixes given below

• Step 1 ? Start

• Step 2 ? Define function to calculate total strings of length N without the given prefixes

• Step 3 ? Calculate the total strings present

• Step 4 ? Make an array and counter a and aCount respectively and insert these prefixes with same

• Step 5 ? Make a new array of prefixes strings

• Step 6 ? Iterating for each of the starting character

• Step 7 ? Iterate over the array to calculate minimum size prefix

• Step 8 ? now take all these minimum prefixes in the new array of prefixes

• Step 9 ? Iterating over the new prefixes

• Step 10 ? Deduct the unwanted strings

• Step 11 ? Print the result obtained

• Step 12 ? Stop

Example: C Program

Here is the C program implementation of the above written algorithm to find the count of N digit numbers not having given prefixes.

#include <stdio.h>
#include <math.h>
#include <string.h>
#define MAX_LENGTH 10

// Function to calculate total strings of length N without the given prefixes
int totalStrings(int N, char pre[][MAX_LENGTH], int pre_Count){

   // Calculate total strings present
   int total = (int)(pow(10, N) + 0.5);
   
   // Make an array and counter a and aCount respectively and insert these prefixes with same character in the array
   char a[10][MAX_LENGTH];
   int aCount[10] = {0};
   for (int i = 0; i < pre_Count; i++)    {
      int index = pre[i][0] - '0';
      strcpy(a[index] + aCount[index] * MAX_LENGTH, pre[i]);
      aCount[index]++;
   }
   
   // Make a new array of prefixes strings
   char new_pre[pre_Count][MAX_LENGTH];
   int new_pre_count = 0;
   
   // Iterating for  each of the starting //character
   for (int x = 0; x < 10; x++){
      int m = N;
      
      // Iterate over the array to calculate minimum size prefix
      for (int j = 0; j < aCount[x]; j++){
         int p_length = strlen(a[x] + j * MAX_LENGTH);
         m = (m < p_length) ? m : p_length;
      }
      
      // now take all these minimum prefixes in the new array of prefixes
      for (int j = 0; j < aCount[x]; j++){
         int p_length = strlen(a[x] + j * MAX_LENGTH);
         if (p_length <= m){
            strcpy(new_pre[new_pre_count], a[x] + j * MAX_LENGTH);
            new_pre_count++;
         }
      }
   }
   
   // Iterating through the new prefixes
   for (int i = 0; i < new_pre_count; i++){
   
      // Subtract the unwanted strings
      total -= (int)(pow(10, N - strlen(new_pre[i])) + 0.5);
   }
   return total;
}

// The main function
int main(){
   int N = 5;
   char pre[][MAX_LENGTH] = {"1", "0", "2"};
   int pre_Count = sizeof(pre) / sizeof(pre[0]);
   printf("%d\n", totalStrings(N, pre, pre_Count));
   return 0;
}

Output

70000

Conclusion

Likewise, we can to find the count of N digit numbers not having given prefixes.

The challenge of obtaining the program to find the count of N digit numbers not having given prefixes is resolved in this article.

Here C programming code as well as the algorithm to find the count of N digit numbers not having given prefixes are provided.