Given two numbers as strings, find if one is a power of other

• Difficulty Level : Medium
• Last Updated : 19 Aug, 2022

Given two large numbers as strings, find if one is the power of another.

Examples:

```Input : a = "374747", b = "52627712618930723"
Output : YES
Explanation : 374747^3 = 52627712618930723

Input : a = "2", b = "4099"
Output : NO```

Prerequisite: Multiply two large numbers represented as string The approach is simple. First, find smaller of the two strings and then multiply it with itself until it becomes equal to or greater than the larger string. If they are equal, return true, else return false. Below is the implementation of above approach

Implementation:

C++

 `// CPP program to check if one number is``// power of other``#include ``using` `namespace` `std;` `bool` `isGreaterThanEqualTo(string s1, string s2)``{``    ``if` `(s1.size() > s2.size())``        ``return` `true``;` `    ``return` `(s1 == s2);``}` `string multiply(string s1, string s2)``{``    ``int` `n = s1.size();``    ``int` `m = s2.size();` `    ``vector<``int``> result(n + m, 0);` `    ``// Multiply the numbers. It multiplies``    ``// each digit of second string to each``    ``// digit of first and stores the result.``    ``for` `(``int` `i = n - 1; i >= 0; i--)``        ``for` `(``int` `j = m - 1; j >= 0; j--)``            ``result[i + j + 1] +=``               ``(s1[i] - ``'0'``) * (s2[j] - ``'0'``);` `    ``// If the digit exceeds 9, add the``    ``// cumulative carry to previous digit.``    ``int` `size = result.size();``    ``for` `(``int` `i = size - 1; i > 0; i--) {``        ``if` `(result[i] >= 10) {``            ``result[i - 1] += result[i] / 10;``            ``result[i] = result[i] % 10;``        ``}``    ``}` `    ``int` `i = 0;``    ``while` `(i < size && result[i] == 0)``        ``i++;` `    ``// if all zeroes, return "0".``    ``if` `(i == size)``        ``return` `"0"``;` `    ``string temp;` `    ``// Remove starting zeroes.``    ``while` `(i < size) {``        ``temp += (result[i] + ``'0'``);``        ``i++;``    ``}``    ``return` `temp;``}` `// Removes Extra zeroes from front of a string.``string removeLeadingZeores(string s)``{``    ``int` `n = s.size();` `    ``int` `i = 0;``    ``while` `(i < n && s[i] == ``'0'``)``        ``i++;` `    ``if` `(i == n)``        ``return` `"0"``;` `    ``string temp;``    ``while` `(i < n)``        ``temp += s[i++];` `    ``return` `temp;``}` `bool` `isPower(string s1, string s2)``{``    ``// Make sure there are no leading zeroes``    ``// in the string.``    ``s1 = removeLeadingZeores(s1);``    ``s2 = removeLeadingZeores(s2);` `    ``if` `(s1 == ``"0"` `|| s2 == ``"0"``)``        ``return` `false``;` `    ``if` `(s1 == ``"1"` `&& s2 == ``"1"``)``        ``return` `true``;` `    ``if` `(s1 == ``"1"` `|| s2 == ``"1"``)``        ``return` `true``;` `    ``// Making sure that s1 is smaller.``    ``// If it is greater, we recur we``    ``// reversed parameters.``    ``if` `(s1.size() > s2.size())``        ``return` `isPower(s2, s1);` `    ``string temp = s1;``    ``while` `(!isGreaterThanEqualTo(s1, s2))``        ``s1 = multiply(s1, temp);` `    ``return` `s1 == s2;``}` `int` `main()``{``    ``string s1 = ``"374747"``, s2 = ``"52627712618930723"``;``    ``cout << (isPower(s1, s2) ? ``"YES\n"` `: ``"NO\n"``);` `    ``s1 = ``"4099"``, s2 = ``"2"``;``    ``cout << (isPower(s1, s2) ? ``"YES\n"` `: ``"NO\n"``);` `    ``return` `0;``}`

Java

 `// Java program to check if one number is``// power of other``import` `java.util.*;` `class` `new_file``{``    ``static` `boolean` `isGreaterThanEqual(String s1,``                                      ``String s2)``    ``{``        ``if` `(s1.length() > s2.length())``            ``return` `true``;``        ``if` `(s1.compareTo(s2) == ``0``)``            ``return` `true``;``        ``return` `false``;``    ``}` `    ``static` `String multiply(String s1, String s2)``    ``{``        ``int` `n = s1.length();``        ``int` `m = s2.length();` `        ``int``[] result = ``new` `int``[n + m];` `        ``// Multiply the numbers. It multiplies``        ``// each digit of second string to each``        ``// digit of first and stores the result.``        ``for` `(``int` `i = n - ``1``; i >= ``0``; i--)``            ``for` `(``int` `j = m - ``1``; j >= ``0``; j--)``                ``result[i + j + ``1``] += (s1.charAt(i) - ``'0'``) *``                                     ``(s2.charAt(j) - ``'0'``);` `        ``// If the digit exceeds 9, add the``        ``// cumulative carry to previous digit.``        ``int` `size = result.length;``        ``for` `(``int` `i = size - ``1``; i > ``0``; i--)``        ``{``            ``if` `(result[i] >= ``10``)``            ``{``                ``result[i - ``1``] += result[i] / ``10``;``                ``result[i] = result[i] % ``10``;``            ``}``        ``}` `        ``int` `i = ``0``;``        ``while` `(i < size && result[i] == ``0``)``            ``i++;` `        ``// if all zeroes, return "0".``        ``if` `(i == size)``            ``return` `"0"``;` `        ``String temp = ``""``;` `        ``// Remove starting zeroes.``        ``while` `(i < size)``        ``{``            ``temp += Integer.toString(result[i]);``            ``i++;``        ``}``        ``return` `temp;``    ``}` `    ``// Removes Extra zeroes from front of a string.``    ``static` `String removeLeadingZeores(String s)``    ``{``        ``int` `n = s.length();``        ``int` `i = ``0``;``        ``while` `(i < n && s.charAt(i) == ``'0'``)``            ``i++;``        ``if` `(i == n)``            ``return` `"0"``;``        ``String temp = ``""``;``        ``while` `(i < n)``        ``{``            ``temp += s.charAt(i);``            ``i++;``        ``}` `        ``return` `temp;``    ``}` `    ``static` `boolean` `isPower(String s1, String s2)``    ``{` `        ``// Make sure there are no leading zeroes``        ``// in the string.``        ``s1 = removeLeadingZeores(s1);``        ``s2 = removeLeadingZeores(s2);``        ``if` `(s1 == ``"0"` `|| s2 == ``"0"``)``            ``return` `false``;``        ``if` `(s1 == ``"1"` `&& s2 == ``"1"``)``            ``return` `true``;``        ``if` `(s1 == ``"1"` `|| s2 == ``"1"``)``            ``return` `true``;` `        ``// Making sure that s1 is smaller.``        ``// If it is greater, we recur we``        ``// reversed parameters.``        ``if` `(s1.length() > s2.length())``            ``return` `isPower(s2, s1);` `        ``String temp = ``new` `String(s1);``        ``while` `(!isGreaterThanEqual(s1, s2))``            ``s1 = multiply(s1, temp);` `        ``if` `(s1.compareTo(s2) == ``0``)``            ``return` `true``;``        ``return` `false``;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``String s1 = ``"374747"``, s2 = ``"52627712618930723"``;``        ``if` `(isPower(s1, s2))``            ``System.out.println(``"Yes"``);``        ``else``            ``System.out.println(``"No"``);` `        ``s1 = ``"4099"``;``        ``s2 = ``"2"``;` `        ``if` `(isPower(s1, s2))``            ``System.out.println(``"Yes"``);``        ``else``            ``System.out.println(``"No"``);``    ``}``}` `// This code is contributed by``// sanjeev2552`

Python3

 `# Python3 program to check if one``# number is a power of other``def` `isGreaterThanEqualTo(s1, s2):` `    ``if` `len``(s1) > ``len``(s2):``        ``return` `True` `    ``return` `s1 ``=``=` `s2` `def` `multiply(s1, s2):` `    ``n, m ``=` `len``(s1), ``len``(s2)``    ``result ``=` `[``0``] ``*` `(n ``+` `m)` `    ``# Multiply the numbers. It multiplies``    ``# each digit of second string to each``    ``# digit of first and stores the result.``    ``for` `i ``in` `range``(n ``-` `1``, ``-``1``, ``-``1``):``        ``for` `j ``in` `range``(m ``-` `1``, ``-``1``, ``-``1``):``            ``result[i ``+` `j ``+` `1``] ``+``=` `(``int``(s1[i]) ``*``                                  ``int``(s2[j]))` `    ``# If the digit exceeds 9, add the``    ``# cumulative carry to previous digit.``    ``size ``=` `len``(result)``    ``for` `i ``in` `range``(size ``-` `1``, ``0``, ``-``1``):``        ``if` `result[i] >``=` `10``:``            ``result[i ``-` `1``] ``+``=` `result[i] ``/``/` `10``            ``result[i] ``=` `result[i] ``%` `10` `    ``i ``=` `0``    ``while` `i < size ``and` `result[i] ``=``=` `0``:``        ``i ``+``=` `1` `    ``# If all zeroes, return "0".``    ``if` `i ``=``=` `size:``        ``return` `"0"` `    ``temp ``=` `""``    ` `    ``# Remove starting zeroes.``    ``while` `i < size:``        ``temp ``+``=` `str``(result[i])``        ``i ``+``=` `1``    ` `    ``return` `temp` `# Removes Extra zeroes from front of a string.``def` `removeLeadingZeores(s):` `    ``n, i ``=` `len``(s), ``0` `    ``while` `i < n ``and` `s[i] ``=``=` `'0'``:``        ``i ``+``=` `1` `    ``if` `i ``=``=` `n:``        ``return` `"0"` `    ``temp ``=` `""``    ``while` `i < n:``        ``temp ``+``=` `s[i]``        ``i ``+``=` `1``        ` `    ``return` `temp` `def` `isPower(s1, s2):` `    ``# Make sure there are no leading``    ``# zeroes in the string.``    ``s1 ``=` `removeLeadingZeores(s1)``    ``s2 ``=` `removeLeadingZeores(s2)` `    ``if` `s1 ``=``=` `"0"` `or` `s2 ``=``=` `"0"``:``        ``return` `False` `    ``if` `s1 ``=``=` `"1"` `and` `s2 ``=``=` `"1"``:``        ``return` `True` `    ``if` `s1 ``=``=` `"1"` `and` `s2 ``=``=` `"1"``:``        ``return` `True` `    ``# Making sure that s1 is smaller.``    ``# If it is greater, we recur we``    ``# reversed parameters.``    ``if` `len``(s1) > ``len``(s2):``        ``return` `isPower(s2, s1)` `    ``temp ``=` `s1``    ``while` `not` `isGreaterThanEqualTo(s1, s2):``        ``s1 ``=` `multiply(s1, temp)` `    ``return` `s1 ``=``=` `s2` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``s1, s2 ``=` `"374747"``, ``"52627712618930723"``    ``if` `isPower(s1, s2):``        ``print``(``"YES"``)``    ``else``:``        ``print``(``"NO"``)``        ` `    ``s1, s2 ``=` `"4099"``, ``"2"``    ``if` `isPower(s1, s2):``        ``print``(``"YES"``)``    ``else``:``        ``print``(``"NO"``)``    ` `# This code is contributed by Rituraj Jain`

C#

 `// C# program to check if one number is``// power of other``using` `System;` `public` `class` `new_file``{``    ``static` `bool` `isGreaterThanEqual(String s1,``                                    ``String s2)``    ``{``        ``if` `(s1.Length > s2.Length)``            ``return` `true``;``        ``if` `(s1.CompareTo(s2) == 0)``            ``return` `true``;``        ``return` `false``;``    ``}` `    ``static` `String multiply(String s1, String s2)``    ``{``        ``int` `n = s1.Length;``        ``int` `m = s2.Length;``        ``int` `i = 0;``        ``int``[] result = ``new` `int``[n + m];` `        ``// Multiply the numbers. It multiplies``        ``// each digit of second string to each``        ``// digit of first and stores the result.``        ``for` `(i = n - 1; i >= 0; i--)``            ``for` `(``int` `j = m - 1; j >= 0; j--)``                ``result[i + j + 1] += (s1[i] - ``'0'``) *``                                    ``(s2[j] - ``'0'``);` `        ``// If the digit exceeds 9, add the``        ``// cumulative carry to previous digit.``        ``int` `size = result.Length;``        ``for` `(i = size - 1; i > 0; i--)``        ``{``            ``if` `(result[i] >= 10)``            ``{``                ``result[i - 1] += result[i] / 10;``                ``result[i] = result[i] % 10;``            ``}``        ``}` `        ``i = 0;``        ``while` `(i < size && result[i] == 0)``            ``i++;` `        ``// if all zeroes, return "0".``        ``if` `(i == size)``            ``return` `"0"``;` `        ``String temp = ``""``;` `        ``// Remove starting zeroes.``        ``while` `(i < size)``        ``{``            ``temp += (result[i]).ToString();``            ``i++;``        ``}``        ``return` `temp;``    ``}` `    ``// Removes Extra zeroes from front of a string.``    ``static` `String removeLeadingZeores(String s)``    ``{``        ``int` `n = s.Length;``        ``int` `i = 0;``        ``while` `(i < n && s[i] == ``'0'``)``            ``i++;``        ``if` `(i == n)``            ``return` `"0"``;``        ``String temp = ``""``;``        ``while` `(i < n)``        ``{``            ``temp += s[i];``            ``i++;``        ``}` `        ``return` `temp;``    ``}` `    ``static` `bool` `isPower(String s1, String s2)``    ``{` `        ``// Make sure there are no leading zeroes``        ``// in the string.``        ``s1 = removeLeadingZeores(s1);``        ``s2 = removeLeadingZeores(s2);``        ``if` `(s1 == ``"0"` `|| s2 == ``"0"``)``            ``return` `false``;``        ``if` `(s1 == ``"1"` `&& s2 == ``"1"``)``            ``return` `true``;``        ``if` `(s1 == ``"1"` `|| s2 == ``"1"``)``            ``return` `true``;` `        ``// Making sure that s1 is smaller.``        ``// If it is greater, we recur we``        ``// reversed parameters.``        ``if` `(s1.Length > s2.Length)``            ``return` `isPower(s2, s1);` `        ``String temp = s1;``        ``while` `(!isGreaterThanEqual(s1, s2))``            ``s1 = multiply(s1, temp);` `        ``if` `(s1.CompareTo(s2) == 0)``            ``return` `true``;``        ``return` `false``;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``String s1 = ``"374747"``, s2 = ``"52627712618930723"``;``        ``if` `(isPower(s1, s2))``            ``Console.WriteLine(``"Yes"``);``        ``else``            ``Console.WriteLine(``"No"``);` `        ``s1 = ``"4099"``;``        ``s2 = ``"2"``;` `        ``if` `(isPower(s1, s2))``            ``Console.WriteLine(``"Yes"``);``        ``else``            ``Console.WriteLine(``"No"``);``    ``}``}` `// This code is contributed by Rajput-Ji`

Javascript

 ``

Output

```YES
NO```

Complexity Analysis:

• Time complexity : O(n*m) where n and m are the sizes of the respective input strings.
• Auxiliary Space : O(n+m) where n and m are the sizes of the respective input strings.

My Personal Notes arrow_drop_up