Given arrays A[] and B[] each of length N and A[i] has all the elements from 1 to N, the task is to check if it is possible to convert A[] to B[] by replacing any pair of A[] with their GCD.
Examples:
Input: N = 2, A[] = {1, 2}, B[] = {1, 1}
Output: YES
Explanation:
First Operation – For A[], choose i = 0 and j = 1. GCD(A[0], A[1]) = GCD(1, 2) = 1. Replace both the elements with GCD = 1. So A[] = {1, 1}.Input: N = 3, A[] = {1, 2, 3}, B[] = {1, 2, 2}
Output: NO
Explanation: It can be verify that it’s not possible to convert A[] to B[] by using given operation.
Approach: Implement the idea below to solve the problem
The problem is observation based and can be solved by calculating GCD of A[i] and B[i] for each index. It should be noted that if B[i]>A[i] at any index, then it is impossible to change A[i] as B[i].
So, This idea gives us approach if GCD(A[i], B[i]) = B[i], Then it is possible to convert A[i] to B[i] at that index, else not possible.
Follow the steps mentioned below to implement the idea:
- Make a boolean variable flag and initialize it to true.
- Run a loop from i = 0 to N-1:
- If GCD(A[i], B[i])=B[i] then continue the loop.
- Else mark the flag as false and break the loop.
- If the flag is true then output YES else NO.
Below is the implementation of the above approach.
C++
// C++ code#include <bits/stdc++.h>using namespace std;// Euclidean algorithm to find GCD(a, b),// where a and b are two input argumentsint GCD(int a, int b){ return b == 0 ? a : GCD(b, a % b);}// Function to check conversionbool conversionChecker(int N, int B[]){ // Flag which will be false if B[i]>A[i] // at any index i bool flag = true; // Loop for traversing on B[] for (int i = 0; i < N; i++) { if (GCD((i + 1), B[i]) == B[i]) { continue; } else { flag = false; break; } } // Returning true/false stored in flag return flag;}int main() { // Testcase 1 int N = 4; // Input array B[], We don't need array A[] // Because it can be achieved by traversing on loop // from 1 to N As A[] is an array of {1, 2, . . ., // N} int B1[] = { 1, 2, 3, 2 }; // Function call for checking if conversion is // possible or not cout<<(conversionChecker(N, B1) ? "YES" : "NO")<<endl; // Testcase 2 N = 5; int B2[] = { 2, 4, 5, 6, 7 }; cout<<(conversionChecker(N, B2) ? "YES" : "NO")<<endl; return 0;}// This code is contributed by ksam24000 |
Java
// Java code to implement the approachimport java.io.*;import java.lang.*;import java.util.*;class GFG { // Driver code public static void main(String[] args) { // Testcase 1 int N = 4; // Input array B[], We don't need array A[] // Because it can be achieved by traversing on loop // from 1 to N As A[] is an array of {1, 2, . . ., // N} int B1[] = { 1, 2, 3, 2 }; // Function call for checking if conversion is // possible or not System.out.println(conversionChecker(N, B1) ? "YES" : "NO"); // Testcase 2 N = 5; int B2[] = { 2, 4, 5, 6, 7 }; System.out.println(conversionChecker(N, B2) ? "YES" : "NO"); ; } // Function to check conversion static boolean conversionChecker(int N, int B[]) { // Flag which will be false if B[i]>A[i] // at any index i boolean flag = true; // Loop for traversing on B[] for (int i = 0; i < N; i++) { if (GCD((i + 1), B[i]) == B[i]) { continue; } else { flag = false; break; } } // Returning true/false stored in flag return flag; } // Euclidean algorithm to find GCD(a, b), // where a and b are two input arguments static int GCD(int a, int b) { return b == 0 ? a : GCD(b, a % b); }} |
Python3
# Python code to implement the approach# Euclidean algorithm to find GCD(a, b),# where a and b are two input argumentsdef GCD(a, b): return a if b == 0 else GCD(b, a % b)# Function to check conversiondef conversionChecker(N, B): # Flag which will be false if B[i]>A[i] # at any index i flag = True # loop for traversing on B[] for i in range(N): if(GCD((i + 1), B[i]) == B[i]): continue else: flag = False break # Returning true/false stored in flag return flag# Testcase 1N = 4# Input array B[], We don't need array A[]# Because it can be achieved by traversing on loop# from 1 to N As A[] is an array of {1, 2, . . .,# N}B1 = [1, 2, 3, 2]# Function call for checking if conversion is# possible or notprint("YES" if conversionChecker(N, B1) else "NO")# Testcase 2N = 5B2 = [2, 4, 5, 6, 7]print("YES" if conversionChecker(N, B2) else "NO")# This code is contributed by lokeshmvs21. |
C#
// C# code to implement the approachusing System;public class GFG { static public void Main() { // Testcase 1 int N = 4; // Input array B[], We don't need array A[] // Because it can be achieved by traversing on loop // from 1 to N As A[] is an array of {1, 2, . . ., // N} int[] B1 = { 1, 2, 3, 2 }; // Function call for checking if conversion is // possible or not Console.WriteLine(conversionChecker(N, B1) ? "YES" : "NO"); // Testcase 2 N = 5; int[] B2 = { 2, 4, 5, 6, 7 }; Console.WriteLine(conversionChecker(N, B2) ? "YES" : "NO"); } // Function to check conversion static bool conversionChecker(int N, int[] B) { // Flag which will be false if B[i]>A[i] // at any index i bool flag = true; // Loop for traversing on B[] for (int i = 0; i < N; i++) { if (GCD((i + 1), B[i]) == B[i]) { continue; } else { flag = false; break; } } // Returning true/false stored in flag return flag; } // Euclidean algorithm to find GCD(a, b), // where a and b are two input arguments static int GCD(int a, int b) { return b == 0 ? a : GCD(b, a % b); }}// This code is contributed by lokesh |
Javascript
// Javascript code// Euclidean algorithm to find GCD(a, b),// where a and b are two input argumentsfunction GCD(a, b){ return b == 0 ? a : GCD(b, a % b);}// Function to check conversionfunction conversionChecker(N, B){ // Flag which will be false if B[i]>A[i] // at any index i let flag = true; // Loop for traversing on B[] for (let i = 0; i < N; i++) { if (GCD((i + 1), B[i]) == B[i]) { continue; } else { flag = false; break; } } // Returning true/false stored in flag return flag;} let N = 4; // Input array B[], We don't need array A[] // Because it can be achieved by traversing on loop // from 1 to N As A[] is an array of {1, 2, . . ., // N} let B1 = [1, 2, 3, 2 ]; // Function call for checking if conversion is // possible or not console.log(conversionChecker(N, B1) ? "YES" : "NO"); // Testcase 2 N = 5; let B2 = [2, 4, 5, 6, 7 ]; console.log(conversionChecker(N, B2) ? "YES" : "NO");// This code is contributed by poojaagarwal2 |
Output
YES NO
Time Complexity: O(N * logM), Where M is the max element of B[].
Auxiliary Space: O(1)
Efficient Approach:
In this approach, We don’t need to calculate GCD at each index, Which will save a little bit of time. For A[i] and B[i], There are 3 possible cases. Which are discussed below:
- If B[i] = A[i]: In such indices, We don’t need to perform the operation, Because A[i] is already equal to B[i].
- If B[i] < A[i]: In this case, A[i] can be converted to B[i] only and only if A[i] % B[i] = 0. Formally B[i] is a perfect divisor of A[i].
- If B[i] > A[i]: In this case, it is impossible to convert A[i] as B[i].
Follow the steps mentioned below to implement the idea:
- Make a boolean variable flag and initialize it to true.
- Run a loop from i = 0 to N-1:
- If A[i] and B[i] are equal, then continue the loop.
- Else if B[i] < A[i], then continue only if B[i] perfectly divides A[i].
- Else mark flag as false and break the loop.
- 3. If flag is true output YES else NO.
Code to implement the approach:
C++
#include <cstring>#include <iostream>using namespace std;// Function to check conversionbool conversionChecker(int N, int B[]){ // Flag which will be false if B[i]>A[i] at any // index i bool flag = true; // Loop for traversing on B[] for (int i = 0; i < N; i++) { // Condition when A[i] is already equal to B[i] if (B[i] == (i + 1)) { continue; } // Condition when B[i] is smaller than A[i] and // A[i] can be converted to B[i] only and only // if A[i]%B[i]==0 else if (B[i] < (i + 1) && (i + 1) % B[i] == 0) { continue; } // Else it will not possible to convert // A[i] to B[i] else { // Marking flag as false flag = false; // Breaking loop break; } } // Returning true/false stored in flag return flag;}// Euclidean algorithm to find GCD(a, b),// where a and b are two input argumentsint GCD(int a, int b) { return b == 0 ? a : GCD(b, a % b); }int main(){ // Testcase 1 int N = 4; // Input array B[], We don't need array A[] // Because it can be achieved by traversing on loop // from 1 to N As A[] is an array of {1, 2 . . . N} int B1[] = { 1, 2, 3, 2 }; // Function call for checking if conversion is // possible or not cout << (conversionChecker(N, B1) ? "YES" : "NO") << endl; // Testcase2 N = 6; int B2[] = { 4, 6, 9, 1, 0, 5 }; // Function call for checking if conversion is // possible or not cout << (conversionChecker(N, B2) ? "YES" : "NO") << endl; return 0;}// This code is contributed by akashish__ |
Java
// Java code to implement the approachimport java.io.*;import java.lang.*;import java.util.*;class GFG { // Driver Function public static void main(String[] args) { // Testcase 1 int N = 4; // Input array B[], We don't need array A[] // Because it can be achieved by traversing on loop // from 1 to N As A[] is an array of {1, 2 . . . N} int B1[] = { 1, 2, 3, 2 }; // Function call for checking if conversion is // possible or not System.out.println(conversionChecker(N, B1) ? "YES" : "NO"); // Testcase2 N = 6; int B2[] = { 4, 6, 9, 1, 0, 5 }; // Function call for checking if conversion is // possible or not System.out.println(conversionChecker(N, B2) ? "YES" : "NO"); } // Function to check conversion static boolean conversionChecker(int N, int B[]) { // Flag which will be false if B[i]>A[i] at any // index i boolean flag = true; // Loop for traversing on B[] for (int i = 0; i < N; i++) { // Condition when A[i] is already equal to B[i] if (B[i] == (i + 1)) { continue; } // Condition when B[i] is smaller than A[i] and // A[i] can be converted to B[i] only and only // if A[i]%B[i]==0 else if (B[i] < (i + 1) && (i + 1) % B[i] == 0) { continue; } // Else it will not possible to convert // A[i] to B[i] else { // Marking flag as false flag = false; // Breaking loop break; } } // Returning true/false stored in flag return flag; } // Euclidean algorithm to find GCD(a, b), // where a and b are two input arguments static int GCD(int a, int b) { return b == 0 ? a : GCD(b, a % b); }} |
Python3
# Python code for the above approach# Function to check conversiondef conversionChecker(N, B): # Flag which will be false if B[i]>A[i] at any # index i flag = True # Loop for traversing on B[] for i in range(N): # Condition when A[i] is already equal to B[i] if B[i] == (i + 1): continue # Condition when B[i] is smaller than A[i] and # A[i] can be converted to B[i] only and only # if A[i]%B[i]==0 elif (B[i] < (i + 1) and (i + 1) % B[i] == 0): continue # Else it will not possible to convert # A[i] to B[i] else: # Marking flag as false flag = False # Breaking loop break # Returning true/false stored in flag return flag# Euclidean algorithm to find GCD(a, b),# where a and b are two input argumentsdef GCD(a, b): return a if b == 0 else GCD(b, a % b)# Testcase 1N = 4# Input array B[], We don't need array A[]# Because it can be achieved by traversing on loop# from 1 to N As A[] is an array of {1, 2 . . . N}B1 = [1, 2, 3, 2]# Function call for checking if conversion is# possible or notif (conversionChecker(N, B1) is True): print("YES")else: print("NO")# Testcase2N = 6;B2 = [4, 6, 9, 1, 0, 5];# Function call for checking if conversion is# possible or notif (conversionChecker(N, B2) is True): print("YES")else: print("NO")# This code is contributed by akashish__ |
C#
// C# code to implement the approachusing System;class GFG { // Driver Function public static void Main(string[] args) { // Testcase 1 int N = 4; // Input array B[], We don't need array A[] // Because it can be achieved by traversing on loop // from 1 to N As A[] is an array of {1, 2 . . . N} int[] B1 = { 1, 2, 3, 2 }; // Function call for checking if conversion is // possible or not Console.WriteLine(conversionChecker(N, B1) ? "YES" : "NO"); // Testcase2 N = 6; int[] B2 = { 4, 6, 9, 1, 0, 5 }; // Function call for checking if conversion is // possible or not Console.WriteLine(conversionChecker(N, B2) ? "YES" : "NO"); } // Function to check conversion static bool conversionChecker(int N, int[] B) { // Flag which will be false if B[i]>A[i] at any // index i bool flag = true; // Loop for traversing on B[] for (int i = 0; i < N; i++) { // Condition when A[i] is already equal to B[i] if (B[i] == (i + 1)) { continue; } // Condition when B[i] is smaller than A[i] and // A[i] can be converted to B[i] only and only // if A[i]%B[i]==0 else if (B[i] < (i + 1) && (i + 1) % B[i] == 0) { continue; } // Else it will not possible to convert // A[i] to B[i] else { // Marking flag as false flag = false; // Breaking loop break; } } // Returning true/false stored in flag return flag; } // Euclidean algorithm to find GCD(a, b), // where a and b are two input arguments static int GCD(int a, int b) { return b == 0 ? a : GCD(b, a % b); }}// This code is contributed by karandeep1234 |
Javascript
// JavaScript code for the above approach // Function to check conversion function conversionChecker(N, B) { // Flag which will be false if B[i]>A[i] at any // index i let flag = true; // Loop for traversing on B[] for (let i = 0; i < N; i++) { // Condition when A[i] is already equal to B[i] if (B[i] == (i + 1)) { continue; } // Condition when B[i] is smaller than A[i] and // A[i] can be converted to B[i] only and only // if A[i]%B[i]==0 else if (B[i] < (i + 1) && (i + 1) % B[i] == 0) { continue; } // Else it will not possible to convert // A[i] to B[i] else { // Marking flag as false flag = false; // Breaking loop break; } } // Returning true/false stored in flag return flag; } // Euclidean algorithm to find GCD(a, b), // where a and b are two input arguments function GCD(a, b) { return b == 0 ? a : GCD(b, a % b); } // Driver Function // Testcase 1 let N = 4; // Input array B[], We don't need array A[] // Because it can be achieved by traversing on loop // from 1 to N As A[] is an array of {1, 2 . . . N} let B1 = [1, 2, 3, 2]; // Function call for checking if conversion is // possible or not console.log(conversionChecker(N, B1) ? "YES" : "NO"); console.log('<br>') // Testcase2 N = 6; let B2 = [4, 6, 9, 1, 0, 5]; // Function call for checking if conversion is // possible or not console.log(conversionChecker(N, B2) ? "YES" : "NO");// This code is contributed by Potta Lokesh |
Output
YES NO
Time Complexity: O(N)
Auxiliary Space: O(1)
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