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:Â Â
Input: str = {10000, 20, 16}, X = 16Â
Output: YesÂ
Explanation:Â
Every number in array is equal to 16 when converted to Decimal base, if following bases are selected:Â
(10000)2 = (16)10Â
(20)8 = (16)10Â
(16)10 = (16)10Input: str = {10100, 5A, 1011010}, X = 90Â
Output: YesÂ
Every number in array is equal to 90 when converted to Decimal base, if following bases are selected:Â
(10100)3 = (90)10Â
(5A)16 = (90)10Â
(1011010)2 = (90)10Â
 Â
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.Â
The step-by-step algorithm for the above approach is described below – Â
- Initialize 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 –Â
- 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// whether array of strings// can correspond to a number XÂ
#include <bits/stdc++.h>using namespace std;Â
// Function to find the maximum // base possible for the number Nint val(char c){    if (c >= '0' && c <= '9')        return (int)c - '0';    else        return (int)c - 'A' + 10;}Â
// Function to find the decimal// equivalent of the numberint 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;}Â
// 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();Â
    // 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";}Â
// Driver Codeint main(){Â Â Â Â int x = 16;Â
    // The set of strings     // in base from [2, 36]    vector<string> str =         { "10000", "20", "16" };    checkCorrespond(str, x);    return 0;} |
Java
// Java implementation to check// whether array of Strings// can correspond to a number XÂ
class GFG{  // Function to find the maximum // base possible for the number Nstatic 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 numberstatic 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 Codepublic 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);}}Â
// This code contributed by PrinciRaj1992 |
Python3
# Python3 implementation to check# whether array of strings# can correspond to a number XÂ
# Function to find the maximum # base possible for the number Ndef val(c):    if (c >= '0' and c <= '9'):        return int(c)    else:        return c - 'A' + 10         # Function to find the decimal# equivalent of the numberdef 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 numÂ
Â
# 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 string            # 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")Â
# Driver Codex = 16Â
# The set of strings # in base from [2, 36]strr = ["10000", "20", "16"]checkCorrespond(strr, x)Â
# This code is contributed by shubhamsingh10 |
C#
// C# implementation to check// whether array of Strings// can correspond to a number Xusing System;Â
class GFG{   // Function to find the maximum // base possible for the number Nstatic 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 numberstatic 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 Codepublic 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);}}Â
// This code is contributed by Princi Singh |
Javascript
<script>// Javascript implementation to check// whether array of Strings// can correspond to a number XÂ
// Function to find the maximum // base possible for the number Nfunction val(c){    if (c >= '0' && c <= '9')        return c - '0';    else        return c - 'A' + 10;}  // Function to find the decimal// equivalent of the numberfunction toDeci(str, base){    let len = str.length;    let power = 1;    let num = 0;    let 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 function checkCorrespond(str, x){                                          // counter to count the numbers    // those are convertible to X    let counter = 0;    let n = str.length;      // Loop to iterate over the array    for (let i = 0; i < n; i++) {        for (let 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)        document.write("YES"           + "<br/>");    else        document.write("NO"           + "<br/>");}Â
// Driver Code         let x = 16;      // The set of Strings     // in base from [2, 36]    let str =         [ "10000", "20", "16" ];    checkCorrespond(str, x);         </script> |
Output:Â
YES
Â
Performance Analysis:Â
- Time Complexity: O(N).
- Auxiliary Space: O(1).
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