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

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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.

Naive approach: A simple approach is to use a 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]*b^n-1

Follow the below steps to implement the above idea:

Define the substringConversions function that takes a string str, an integer k (substring length), and an integer b (target base) as input.
For each substring of length k in str:
a. Extract the substring and save it in the variable sub.
b. Evaluate the decimal value of sub by iterating over each character in sub from right to left:
i. Convert the character to its corresponding digit value using sub.at(i) – ‘0’.
ii. Multiply the digit value by the base raised to the power of its position in the substring, starting from 0 (i.e., the rightmost digit has a power of 0).
iii. Add the result of step ii to a running total sum.
c. Print the final value of sum for the current substring.
End the substringConversions function.

Below is the implementation of the above approach:

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)
Auxiliary Space: O(n)

Efficient approach (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 substring in 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)
Auxiliary Space: O(n)

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