# 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.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Method 1 (Simple)

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

## C++

 `// Simple C++ program to convert all substrings from ` `// decimal to given base. ` `#include ` `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 */`

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 ` `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; ` `} `

## 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 pervious 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 pervious 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 `

Output:

```17 25 23
```

Time Complexity: O(n)

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