Skip to content
Related Articles

Related Articles

Improve Article

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

  • Difficulty Level : Medium
  • Last Updated : 25 Aug, 2021

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: 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

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 

C++




// 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;
}

Java




// Simple Java program to convert all substrings from
// decimal to given base.
 
class GFG
{
 
static void substringConversions(String str, int k, int b)
{
    for (int i=0; i + k <= str.length(); i++)
    {
        // Saving substring in sub
        String sub = str.substring(i, i+k);    
         
        // Evaluating decimal for current substring
        // and printing it.
        int sum = 0, counter = 0;
        for (int j = sub.length() - 1; j >= 0; j--)
        {
            sum = (int) (sum + ((sub.charAt(j) - '0') *
                                    Math.pow(b, counter)));
            counter++;
        }    
        System.out.print(sum + " ");
    }
}
 
// Driver code
public static void main(String[] args)
{
    String str = "12212";
    int b = 3, k = 3;
    substringConversions(str, b, k);
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Simple Python3 program to convert
# all substrings from decimal to given base.
import math
 
def substringConversions(s, k, b):
     
    l = len(s);
    for i in range(l):
         
        if((i + k) < l + 1):
             
            # Saving substring in sub
            sub = s[i : i + k];    
             
            # Evaluating decimal for current
            # substring and printing it.
            sum, counter = 0, 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
s = "12212";
b, k = 3, 3;
substringConversions(s, b, k);
 
# This code is contributed
# by Princi Singh

C#




// Simple C# program to convert all substrings from
// decimal to given base.
using System;
 
class GFG
{
 
static void substringConversions(String str, int k, int b)
{
    for (int i = 0; i + k <= str.Length; i++)
    {
        // Saving substring in sub
        String sub = str.Substring(i, k);    
         
        // Evaluating decimal for current substring
        // and printing it.
        int sum = 0, counter = 0;
        for (int j = sub.Length - 1; j >= 0; j--)
        {
            sum = (int) (sum + ((sub[j] - '0') *
                                    Math.Pow(b, counter)));
            counter++;
        }    
        Console.Write(sum + " ");
    }
}
 
// Driver code
public static void Main(String[] args)
{
    String str = "12212";
    int b = 3, k = 3;
    substringConversions(str, b, k);
}
}
 
/* This code is contributed by PrinciRaj1992 */

Javascript




<script>
 
// Simple Javascript program to convert
// all substrings from decimal to given base.
function substringConversions(str, k, b)
{
    for(let i = 0; i + k <= str.length; i++)
    {
         
        // Saving substring in sub
        let sub = str.substring(i, i+k);    
           
        // Evaluating decimal for current substring
        // and printing it.
        let sum = 0, counter = 0;
        for(let j = sub.length - 1; j >= 0; j--)
        {
            sum =  (sum + ((sub[j].charCodeAt(0) -
                               '0'.charCodeAt(0)) *
                               Math.pow(b, counter)));
            counter++;
        }    
        document.write(sum + " ");
    }
}
 
// Driver code
let str = "12212";
let b = 3, k = 3;
 
substringConversions(str, b, k);
     
// This code is contributed by patel2127
 
</script>

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 :  

C++




// 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 previous 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;
}

Java




// Efficient Java program to convert
// all substrings from decimal to given base.
import java.util.*;
 
class GFG
{
static void substringConversions(String str,
                                 int k, int b)
{
    int i = 0, sum = 0, counter = k-1;
 
    // Computing the decimal of first window
    for (i = 0; i < k; i++)
    {
        sum = (int) (sum + ((str.charAt(i) - '0') *
                             Math.pow(b, counter)));
        counter--;
    }
    System.out.print(sum + " ");
     
    // prev stores the previous decimal
    int prev = sum;
             
    // Computing decimal equivalents of all other windows
    sum = 0; counter = 0;
    for (; i < str.length(); i++)
    {
        // Subtracting weight of the element
        // pushed out of window
        sum = (int) (prev - ((str.charAt(i - k) - '0') *
                              Math.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.charAt(i) - '0');
         
        // Decimal of current window
        System.out.print(sum + " ");
         
        // Updating prev
        prev = sum;
         
        counter++;
    }
}
 
// Driver code
public static void main(String[] args)
{
    String str = "12212";
    int b = 3, k = 3;
    substringConversions(str, b, k);
}
}
 
// This code is contributed by Rajput-Ji

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

C#




// Efficient C# program to convert
// all substrings from decimal to given base.
using System;
 
class GFG
{
static void substringConversions(String str,
                                 int k, int b)
{
    int i = 0, sum = 0, counter = k-1;
 
    // Computing the decimal of first window
    for (i = 0; i < k; i++)
    {
        sum = (int) (sum + ((str[i] - '0') *
                             Math.Pow(b, counter)));
        counter--;
    }
    Console.Write(sum + " ");
     
    // prev stores the previous decimal
    int prev = sum;
             
    // Computing decimal equivalents
    // of all other windows
    sum = 0; counter = 0;
    for (; i < str.Length; i++)
    {
        // Subtracting weight of the element
        // pushed out of window
        sum = (int) (prev - ((str[i - k] - '0') *
                               Math.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[i] - '0');
         
        // Decimal of current window
        Console.Write(sum + " ");
         
        // Updating prev
        prev = sum;
         
        counter++;
    }
}
 
// Driver code
public static void Main(String[] args)
{
    String str = "12212";
    int b = 3, k = 3;
    substringConversions(str, b, k);
}
}
 
// This code is contributed by Princi Singh

Javascript




<script>
 
// Efficient Javascript program to convert
// all substrings from decimal to given base.
function substringConversions(str, k, b)
{
    let i = 0, sum = 0, counter = k-1;
     
    // Computing the decimal of first window
    for(i = 0; i < k; i++)
    {
        sum =  (sum + ((str[i].charCodeAt(0) -
                           '0'.charCodeAt(0)) *
                           Math.pow(b, counter)));
        counter--;
    }
    document.write(sum + " ");
      
    // prev stores the previous decimal
    let prev = sum;
              
    // Computing decimal equivalents of
    // all other windows
    sum = 0; counter = 0;
    for(; i < str.length; i++)
    {
         
        // Subtracting weight of the element
        // pushed out of window
        sum =  (prev - ((str[i - k].charCodeAt(0) -
                                '0'.charCodeAt(0)) *
                                Math.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[i].charCodeAt(0) -
                        '0'.charCodeAt(0));
          
        // Decimal of current window
        document.write(sum + " ");
          
        // Updating prev
        prev = sum;
          
        counter++;
    }
}
 
// Driver code
let str = "12212";
let b = 3, k = 3;
 
substringConversions(str, b, k);
 
// This code is contributed by unknown2108
 
</script>

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 write.geeksforgeeks.org or mail your article to review-team@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.
 




My Personal Notes arrow_drop_up
Recommended Articles
Page :