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]*bn-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 codeint 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 codepublic 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 mathdef 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 codes = "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 codepublic 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 codelet 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 codeint 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 codepublic 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 mtdef 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 codestr1 = "12212"b = 3k = 3substringConversions(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 codepublic 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 codelet 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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