Check divisibility of binary string by 2^k
Given a binary string and a number k, task is to check whether the binary string is evenly divisible by 2k or not.
Examples :
Input : 11000 k = 2 Output : Yes Explanation : (11000)2 = (24)10 24 is evenly divisible by 2k i.e. 4. Input : 10101 k = 3 Output : No Explanation : (10101)2 = (21)10 21 is not evenly divisible by 2k i.e. 8.
Naive Approach : Compute the binary string into decimal and then simply check whether it is divisible by 2k. But, this approach is not feasible for long binary string as time complexity will be high for computing decimal number from binary string and then dividing it by 2k.
Efficient Approach : In the binary string, check for last k bits. If the all the last k bits are 0, then the binary number is evenly divisible by 2k else it is not evenly divisible. Time complexity using this approach is O(k).
Below is the implementation of the approach.
C++
// C++ implementation to check whether // given binary number is evenly // divisible by 2^k or not #include <bits/stdc++.h> using namespace std; // function to check whether // given binary number is // evenly divisible by 2^k or not bool isDivisible(char str[], int k) { int n = strlen(str); int c = 0; // count of number of 0 from last for (int i = 0; i < k; i++) if (str[n - i - 1] == '0') c++; // if count = k, number is evenly // divisible, so returns true else // false return (c == k); } // Driver program to test above int main() { // first example char str1[] = "10101100"; int k = 2; if (isDivisible(str1, k)) cout << "Yes" << endl; else cout << "No" << "\n"; // Second example char str2[] = "111010100"; k = 2; if (isDivisible(str2, k)) cout << "Yes" << endl; else cout << "No" << endl; return 0; } |
chevron_right
filter_none
Java
// Java implementation to check whether // given binary number is evenly // divisible by 2^k or not class GFG { // function to check whether // given binary number is // evenly divisible by 2^k or not static boolean isDivisible(String str, int k) { int n = str.length(); int c = 0; // count of number of 0 from last for (int i = 0; i < k; i++) if (str.charAt(n - i - 1) == '0') c++; // if count = k, number is evenly // divisible, so returns true else // false return (c == k); } // Driver program to test above public static void main(String args[]) { // first example String str1 = "10101100"; int k = 2; if (isDivisible(str1, k) == true) System.out.println("Yes"); else System.out.println("No"); // Second example String str2 = "111010100"; k = 2; if (isDivisible(str2, k) == true) System.out.println("Yes"); else System.out.println("No"); } } // This code is contributed by JaideepPyne. |
chevron_right
filter_none
Python 3
# Python 3 implementation to check # whether given binary number is # evenly divisible by 2^k or not # function to check whether # given binary number is # evenly divisible by 2^k or not def isDivisible(str, k): n = len(str) c = 0 # count of number of 0 from last for i in range(0, k): if (str[n - i - 1] == '0'): c += 1 # if count = k, number is evenly # divisible, so returns true else # false return (c == k) # Driver program to test above # first example str1 = "10101100"k = 2if (isDivisible(str1, k)): print("Yes") else: print("No") # Second example str2 = "111010100"k = 2if (isDivisible(str2, k)): print("Yes") else: print("No") # This code is contributed by Smitha |
chevron_right
filter_none
C#
// C# implementation to check whether // given binary number is evenly // divisible by 2^k or not using System; class GFG { // function to check whether // given binary number is // evenly divisible by 2^k or not static bool isDivisible(String str, int k) { int n = str.Length; int c = 0; // count of number of 0 from last for (int i = 0; i < k; i++) if (str[n - i - 1] == '0') c++; // if count = k, number is evenly // divisible, so returns true else // false return (c == k); } // Driver program to test above public static void Main() { // first example String str1 = "10101100"; int k = 2; if (isDivisible(str1, k) == true) Console.Write("Yes\n"); else Console.Write("No"); // Second example String str2 = "111010100"; k = 2; if (isDivisible(str2, k) == true) Console.Write("Yes"); else Console.Write("No"); } } // This code is contributed by Smitha. |
chevron_right
filter_none
PHP
<?php // PHP implementation to check whether // given binary number is evenly // function to check whether // given binary number is // evenly divisible by 2^k or not function isDivisible($str, $k) { $n = strlen($str); $c = 0; // count of number // of 0 from last for ($i = 0; $i < $k; $i++) if ($str[$n - $i - 1] == '0') $c++; // if count = k, // number is evenly // divisible, so // returns true else // false return ($c == $k); } // Driver Code // first example $str1 = "10101100"; $k = 2; if (isDivisible($str1, $k)) echo "Yes", "\n"; else echo "No", "\n"; // Second example $str2= "111010100"; $k = 2; if (isDivisible($str2, $k)) echo "Yes", "\n"; else echo "No", "\n"; // This code is contributed by Ajit ?> |
chevron_right
filter_none
Output:
Yes Yes
Time Complexity: O(k)
Recommended Posts:
- Check divisibility in a binary stream
- Python | Check if a given string is binary string or not
- Check the divisibility of Hexadecimal numbers
- To check divisibility of any large number by 999
- Check if binary string multiple of 3 using DFA
- Check if all the 1's in a binary string are equidistant or not
- Check if a binary string contains consecutive same or not
- Check if a binary string contains all permutations of length k
- Check if a binary string has a 0 between 1s or not | Set 1 (General approach)
- Check if it is possible to rearrange a binary string with alternate 0s and 1s
- Check if a binary string has two consecutive occurrences of one everywhere
- Check if an encoding represents a unique binary string
- Check if a binary string has a 0 between 1s or not | Set 2 (Regular Expression Approach)
- Check whether a binary string can be formed by concatenating given N numbers sequentially
- Longest sub string of 0's in a binary string which is repeated K times
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 Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
- Map every character of one string to another such that all occurrences are mapped to the same character
- Find the longest string that can be made up of other strings from the array
- Count of strings in the first array which are smaller than every string in the second array
- Find distinct characters in distinct substrings of a string
- C++ program to compare two Strings using Operator Overloading
