Given two strings a and b, the task is to count the number of common divisors of both the strings. A string s is a divisor of string t if t can be generated by repeating s a number of times.
Examples:
Input: a = “xaxa”, b = “xaxaxaxa”
Output: 2
The common divisors are “xa” and “xaxa”Input: a = “bbbb”, b = “bbb”
Output:1
The only common divisor is “b”
Approach: For a string s to be a candidate divisor of string t, the following conditions must be fulfilled:
- s must be a prefix of t.
- len(t) % len(s) = 0
Initialize count = 0 and starting from the first character as the ending character of the prefix, check whether the length of the prefix divides the length of both the strings and also if the prefix is same in both the strings. If yes then update count = count + 1. Repeat these steps for all the possible prefixes. Print the value of count in the end.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function that returns true if sub-string// s[0...k] is repeated a number of times// to generate string sint check(string s, int k){ for (int i = 0; i < s.length(); i++) if (s[i] != s[i % k]) return false; return true;}// Function to return the count of common divisorsint countCommonDivisors(string a, string b){ int ct = 0; int n = a.size(), m = b.size(); for (int i = 1; i <= min(n, m); i++) { // If the length of the sub-string // divides length of both the strings if (n % i == 0 && m % i == 0) // If prefixes match in both the strings if (a.substr(0, i) == b.substr(0, i)) // If both the strings can be generated // by repeating the current prefix if (check(a, i) && check(b, i)) ct++; } return ct;}// Driver codeint main(){ string a = "xaxa", b = "xaxaxaxa"; cout << countCommonDivisors(a, b); return 0;} |
Java
// Java implementation of the approach class GFG { // Function that returns true if sub-string // s[0...k] is repeated a number of times // to generate String s static boolean check(String s, int k) { for (int i = 0; i < s.length(); i++) { if (s.charAt(i) != s.charAt(i % k)) { return false; } } return true; } // Function to return the // count of common divisors static int countCommonDivisors(String a, String b) { int ct = 0; int n = a.length(), m = b.length(); for (int i = 1; i <= Math.min(n, m); i++) { // If the length of the sub-string // divides length of both the strings if (n % i == 0 && m % i == 0) { // If prefixes match in both the strings if (a.substring(0, i).equals(b.substring(0, i))) // by repeating the current prefix { // If both the strings can be generated if (check(a, i) && check(b, i)) { ct++; } } } } return ct; } // Driver code public static void main(String[] args) { String a = "xaxa", b = "xaxaxaxa"; System.out.println(countCommonDivisors(a, b)); }} // This code is contributed by PrinciRaj1992 |
Python3
# Python3 implementation of the above approach# Function that returns true if sub-string # s[0...k] is repeated a number of times # to generate String s def check(s, k): for i in range (0, len(s)): if (s[i] != s[i % k]): return False return True# Function to return the# count of common divisors def countCommonDivisors(a, b): ct = 0 n = len(a) m = len(b) for i in range(1, min(n, m) + 1): # If the length of the sub-string # divides length of both the strings if (n % i == 0 and m % i == 0): # If prefixes match in both the strings if (a[0 : i] == b[0 : i]) : # by repeating the current prefix # If both the strings can be generated if (check(a, i) and check(b, i)) : ct = ct + 1 return ct # Driver code a = "xaxa"b = "xaxaxaxa"print(countCommonDivisors(a, b))# This code is contributed by ihritik |
C#
// C# implementation of the above approachusing System;class GFG {// Function that returns true if sub-string // s[0...k] is repeated a number of times // to generate String s static bool check(string s, int k){ for (int i = 0; i < s.Length; i++) { if (s[i] != s[i % k]) { return false; } } return true;}// Function to return the count of// common divisors static int countCommonDivisors(string a, string b) { int ct = 0; int n = a.Length, m = b.Length; for (int i = 1; i <= Math.Min(n, m); i++) { // If the length of the sub-string // divides length of both the strings if (n % i == 0 && m % i == 0) { // If prefixes match in both the strings if (a.Substring(0, i) == (b.Substring(0, i))) // by repeating the current prefix { // If both the strings can be generated if (check(a, i) && check(b, i)) { ct++; } } } } return ct;}// Driver code public static void Main() { string a = "xaxa", b = "xaxaxaxa"; Console.WriteLine(countCommonDivisors(a, b));}} // This code is contributed by ihritik |
Javascript
<script>// Javascript implementation of the approach// Function that returns true if sub-string// s[0...k] is repeated a number of times// to generate string sfunction check(s, k){ for (var i = 0; i < s.length; i++) if (s[i] != s[i % k]) return false; return true;}// Function to return the count of common divisorsfunction countCommonDivisors(a, b){ var ct = 0; var n = a.length, m = b.length; for (var i = 1; i <= Math.min(n, m); i++) { // If the length of the sub-string // divides length of both the strings if (n % i == 0 && m % i == 0) // If prefixes match in both the strings if (a.substring(0, i) == b.substring(0, i)) // If both the strings can be generated // by repeating the current prefix if (check(a, i) && check(b, i)) ct++; } return ct;}// Driver codevar a = "xaxa", b = "xaxaxaxa";document.write( countCommonDivisors(a, b));// This code is contributed by famously.</script> |
Output
2
Complexity Analysis:
- Time Complexity: O(N * M)
- Auxiliary Space: O(1)
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