Given an integer X and an array of strings str which represents numbers in any base ranging from [2, 36], the task is to check whether all the strings can be converted into X by assigning each string the desired base from 2 to 36, such that decimal base equivalent of the string is X.
Examples:
Input: str = {10000, 20, 16}, X = 16
Output: Yes
Explanation:
Every number in array is equal to 16 when converted to Decimal base, if following bases are selected:
(10000)2 = (16)10
(20)8 = (16)10
(16)10 = (16)10Input: str = {10100, 5A, 1011010}, X = 90
Output: Yes
Every number in array is equal to 90 when converted to Decimal base, if following bases are selected:
(10100)3 = (90)10
(5A)16 = (90)10
(1011010)2 = (90)10
Approach: The idea is to convert every number of the array into decimal-base by assigning it to a base from 2 to 36 and then check for each of the converted numbers that it is equal to X or not.
The step-by-step algorithm for the above approach is described below –
- Intialize the count to 0 for checking the count of numbers those are equal to X when converted.
- Run a loop to iterate over the numbers of the array and then for each of the numbers –
- Run another loop from 2 to 36 to assign base to the number and find the decimal equivalent of the number.
- If the decimal equivalent of the number is equal to X, then increment the count by 1 and break the loop for not assigning any other base to the same number.
- If the count of the numbers that are convertible to X is equal to the length of the array, then the array can correspond to the number X.
Below is the implementation of the above approach:
C++
// C++ implementation to check // wheather array of strings // can correspond to a number X #include <bits/stdc++.h> using namespace std; // Function to find the maximum // base possible for the number N int val(char c) { if (c >= '0' && c <= '9') return (int)c - '0'; else return (int)c - 'A' + 10; } // Function to find the decimal // equivalent of the number int toDeci(string str, int base) { int len = str.size(); int power = 1; int num = 0; int i; for (i = len - 1; i >= 0; i--) { // Condition to check if the // number is convertible // to another base if (val(str[i]) >= base) { return -1; } num += val(str[i]) * power; power = power * base; } return num; } // Function to check that the // array can correspond to a number X void checkCorrespond(vector<string> str, int x){ // counter to count the numbers // those are convertible to X int counter = 0; int n = str.size(); // Loop to iterate over the array for (int i = 0; i < n; i++) { for (int j = 2; j <= 36; j++) { // Convert the current string // to every base for checking // whether it will correspond // to X from any base if (toDeci(str[i], j) == x) { counter++; break; } } } // Condition to check if every // number of the array can // be converted to X if (counter == n) cout << "YES" << "\n"; else cout << "NO" << "\n"; } // Driver Code int main() { int x = 16; // The set of strings // in base from [2, 36] vector<string> str = { "10000", "20", "16" }; checkCorrespond(str, x); return 0; } |
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Java
// Java implementation to check // wheather array of Strings // can correspond to a number X class GFG{ // Function to find the maximum // base possible for the number N static int val(char c) { if (c >= '0' && c <= '9') return (int)c - '0'; else return (int)c - 'A' + 10; } // Function to find the decimal // equivalent of the number static int toDeci(String str, int base) { int len = str.length(); int power = 1; int num = 0; int i; for (i = len - 1; i >= 0; i--) { // Condition to check if the // number is convertible // to another base if (val(str.charAt(i)) >= base) { return -1; } num += val(str.charAt(i)) * power; power = power * base; } return num; } // Function to check that the // array can correspond to a number X static void checkCorrespond(String[] str, int x){ // counter to count the numbers // those are convertible to X int counter = 0; int n = str.length; // Loop to iterate over the array for (int i = 0; i < n; i++) { for (int j = 2; j <= 36; j++) { // Convert the current String // to every base for checking // whether it will correspond // to X from any base if (toDeci(str[i], j) == x) { counter++; break; } } } // Condition to check if every // number of the array can // be converted to X if (counter == n) System.out.print("YES" + "\n"); else System.out.print("NO" + "\n"); } // Driver Code public static void main(String[] args) { int x = 16; // The set of Strings // in base from [2, 36] String[] str = { "10000", "20", "16" }; checkCorrespond(str, x); } } // This code contributed by PrinciRaj1992 |
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Python3
# Python3 implementation to check # wheather array of strrings # can correspond to a number X # Function to find the maximum # base possible for the number N def val(c): if (c >= '0' and c <= '9'): return int(c) else: return c - 'A' + 10 # Function to find the decimal # equivalennt of the number def toDeci(strr, base): lenn = len(strr) power = 1 num = 0 for i in range(lenn - 1, -1, -1): # Condition to check if the # number is convertible # to another base if (val(strr[i]) >= base): return -1 num += val(strr[i]) * power power = power * base return num # Function to check that the # array can correspond to a number X def checkCorrespond(strr, x): # counter to count the numbers # those are convertible to X counter = 0 n = len(strr) # Loop to iterate over the array for i in range(n): for j in range(2,37): # Convert the current strring # to every base for checking # whether it will correspond # to X from any base if (toDeci(strr[i], j) == x): counter += 1 break # Condition to check if every # number of the array can # be converted to X if (counter == n): print("YES") else: print("NO") # Driver Code x = 16 # The set of strrings # in base from [2, 36] strr = ["10000", "20", "16"] checkCorrespond(strr, x) # This code is contributed by shubhamsingh10 |
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C#
// C# implementation to check // wheather array of Strings // can correspond to a number X using System; class GFG{ // Function to find the maximum // base possible for the number N static int val(char c) { if (c >= '0' && c <= '9') return (int)c - '0'; else return (int)c - 'A' + 10; } // Function to find the decimal // equivalent of the number static int toDeci(String str, int Base) { int len = str.Length; int power = 1; int num = 0; int i; for (i = len - 1; i >= 0; i--) { // Condition to check if the // number is convertible // to another base if (val(str[i]) >= Base) { return -1; } num += val(str[i]) * power; power = power * Base; } return num; } // Function to check that the // array can correspond to a number X static void checkCorrespond(String[] str, int x){ // counter to count the numbers // those are convertible to X int counter = 0; int n = str.Length; // Loop to iterate over the array for (int i = 0; i < n; i++) { for (int j = 2; j <= 36; j++) { // Convert the current String // to every base for checking // whether it will correspond // to X from any base if (toDeci(str[i], j) == x) { counter++; break; } } } // Condition to check if every // number of the array can // be converted to X if (counter == n) Console.Write("YES" + "\n"); else Console.Write("NO" + "\n"); } // Driver Code public static void Main(String[] args) { int x = 16; // The set of Strings // in base from [2, 36] String[] str = { "10000", "20", "16" }; checkCorrespond(str, x); } } // This code is contributed by Princi Singh |
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Output:
YES
Performance Analysis:
- Time Complexity: O(N).
- Auxiliary Space: O(1).
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