Convert all substrings of length ‘k’ from base ‘b’ to decimal

A string defining a valid number is given. Output all the base conversions of substrings of length ‘k’ from base ‘b’ to base 10.

Examples:

Input :  str = "12212", 
      k = 3, b = 3.
Output : 17 25 23
Explanation :
All the substrings of length 'k' are : 122, 221, 212.
Base conversion can be computed using the formula.

Method 1 (Simple)

A simple approach is to use simple base conversion technique. For a base b number str, its decimal equivalent is str[0]*b0 + str[1]*b1 + str[2]*b2 + … + str[n-1]*bn-1

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// Simple C++ program to convert all substrings from
// decimal to given base.
#include <bits/stdc++.h>
using namespace std;
  
int substringConversions(string str, int k, int b)
{
    for (int i=0; i + k <= str.size(); i++)
    {
        // Saving substring in sub
        string sub = str.substr(i, k);        
          
        // Evaluating decimal for current substring
        // and printing it.
        int sum = 0, counter = 0;
        for (int i = sub.size() - 1; i >= 0; i--)
        {
            sum = sum + ((sub.at(i) - '0') * pow(b, counter));
            counter++;
        }        
        cout << sum << " ";
    }
}
  
// Driver code
int main()
{
    string str = "12212";
    int b = 3, k = 3;
    substringConversions(str, b, k);    
    return 0;
}

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Output:


17 25 23



Time Complexity : O(n*k)


Method 2 (Using sliding window)


We can use Sliding Window technique to solve it in linear time. Every time we slide the window, we will subtract the weight of first element i.e. (element * pow(b, k-1) ). Now multiplying the previous sum with ‘b’ will increase weight of every element 3 times which is required. Also we will simply add the new element in window because its weight will be element * pow(b, 0). 


Below is the implementation :




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// Efficient C++ program to convert all substrings from 


// decimal to given base. 


#include <bits/stdc++.h> 


using namespace std; 


  


int substringConversions(string str, int k, int b) 


{ 


   int i = 0, sum = 0, counter = k-1; 


  


    // Computing the decimal of first window 


    for (i; i < k; i++) 


    { 


        sum = sum + ((str.at(i) - '0') * pow(b, counter)); 


        counter--; 


    } 


    cout << sum << " "; 


      


    // prev stores the pervious decimal 


    int prev = sum; 


             


    // Computing decimal equivalents of all other windows 


    sum = 0, counter = 0; 


    for (i; i < str.size(); i++) 


    { 


        // Subtracting weight of the element pushed out of window 


        sum = prev - ((str.at(i - k) - '0') * pow(b, k-1)); 


          


        // Multiplying the decimal by base to formulate other window  


        sum = sum * b; 


          


        // Adding the new element of window to sum 


        sum = sum + (str.at(i) - '0'); 


          


        // Decimal of current window 


        cout << sum << " "; 


          


        // Updating prev 


        prev = sum; 


          


        counter++; 


    } 


} 


  


// Driver code 


int main() 


{ 


    string str = "12212"; 


    int b = 3, k = 3; 


    substringConversions(str, b, k);     


    return 0; 


} 



















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Python3





# Simple Python3 program to convert all

# substrings from decimal to given base.

import math as mt


def substringConversions(str1, k, b):


	for i in range(0, len(str1) – k + 1):


		# Saving subin sub

		sub = str1[i:k + i]


		# Evaluating decimal for current

		# substring and printing it.

		Sum = 0

		counter = 0

		for i in range(len(sub) – 1, -1, -1):

			Sum = (Sum + ((ord(sub[i]) – ord(‘0’)) *

			               pow(b, counter)))

			counter += 1


		print(Sum, end = ” “)


# Driver code

str1 = “12212”

b = 3

k = 3

substringConversions(str1, b, k) 


# This code is contributed by

# Mohit Kumar 29




Output:


17 25 23



Time Complexity: O(n)



        
          
          
          
        

            

This article is contributed by Rohit Thapliyal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.


Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



          
          
          
          

            

    

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Improved By :  mohit kumar 29