Generate an N-length array A[] from an array arr[] such that arr[i] is the last index consisting of a multiple of A[i]
Last Updated :
25 Mar, 2022
Given an array arr[] of length N, with values less than N, the task is to construct another array A[] of same length such that for every ith element in the array A[], arr[i] is the last index (1-based indexing) consisting of a multiple of A[i].
Examples:
Input: arr[] = {4, 1, 2, 3, 4}
Output: 2 3 5 7 2
Explanation:
A[0]: Last index which can contain a multiple of A[0] has to be A[arr[0]] = A[4].
A[1]: Last index which can contain a multiple of A[1] has to be A[arr[1]] = A[1].
A[2]: Last index which can contain a multiple of A[2] has to be A[arr[2]] = A[2].
A[3]: Last index which can contain a multiple of A[3] has to be A[arr[3]] = A[3].
A[4]: Last index which can contain a multiple of A[4] has to be A[arr[4]] = A[4].
Hence, in the final array, A[4] must be divisible by A[0] and A[1], A[2] and A[3] must not be divisible by any other array elements.
Hence, the array A[] = {2, 3, 5, 7, 2} satisfies the condition.
Input: arr[] = {0, 1, 2, 3, 4}
Output: 2 3 5 7 11
Approach: The idea is to place prime numbers as array elements in required indices satisfying the conditions. Follow the steps below to solve the problem:
- Generate all Prime Numbers using Sieve Of Eratosthenes and store it in another array.
- Initialize array A[] with {0}, to store the required array.
- Traverse the array arr[] and perform the following steps:
- Check if A[arr[i]] is non-zero but A[i] is 0. If found to be true, then assign A[i] = A[arr[i]].
- Check if A[arr[i]] and A[i] are both 0 or not. If found to be true, then assign a prime number different to already assigned array elements, to both indices arr[i] and i.
- After completing the above steps, print the elements of array A[].
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int sieve[1000000];
void sieveOfPrimes()
{
memset (sieve, 1, sizeof (sieve));
int N = 1000000;
for ( int i = 2; i * i <= N; i++) {
if (sieve[i] == 0)
continue ;
for ( int j = i * i; j <= N; j += i)
sieve[j] = 0;
}
}
void getArray( int * arr, int N)
{
int A[N] = { 0 };
vector< int > v;
sieveOfPrimes();
for ( int i = 2; i <= 1e5; i++)
if (sieve[i])
v.push_back(i);
int j = 0;
for ( int i = 0; i < N; i++) {
int ind = arr[i];
if (A[i] != 0)
continue ;
else if (A[ind] != 0)
A[i] = A[ind];
else {
int prime = v[j++];
A[i] = prime;
A[ind] = A[i];
}
}
for ( int i = 0; i < N; i++) {
cout << A[i] << " " ;
}
}
int main()
{
int arr[] = { 4, 1, 2, 3, 4 };
int N = sizeof (arr) / sizeof (arr[0]);
getArray(arr, N);
return 0;
}
|
Java
import java.util.*;
class GFG
{
static int [] sieve = new int [ 10000000 ];
static void sieveOfPrimes()
{
Arrays.fill(sieve, 1 );
int N = 1000000 ;
for ( int i = 2 ; i * i <= N; i++)
{
if (sieve[i] == 0 )
continue ;
for ( int j = i * i; j <= N; j += i)
sieve[j] = 0 ;
}
}
static void getArray( int [] arr, int N)
{
int A[] = new int [N];
Arrays.fill(A, 0 );
ArrayList<Integer> v
= new ArrayList<Integer>();
sieveOfPrimes();
for ( int i = 2 ; i <= 1000000 ; i++)
if (sieve[i] != 0 )
v.add(i);
int j = 0 ;
for ( int i = 0 ; i < N; i++)
{
int ind = arr[i];
if (A[i] != 0 )
continue ;
else if (A[ind] != 0 )
A[i] = A[ind];
else {
int prime = v.get(j++);
A[i] = prime;
A[ind] = A[i];
}
}
for ( int i = 0 ; i < N; i++) {
System.out.print( A[i] + " " );
}
}
public static void main(String[] args)
{
int arr[] = { 4 , 1 , 2 , 3 , 4 };
int N = arr.length;
getArray(arr, N);
}
}
|
Python3
sieve = [ 1 ] * ( 1000000 + 1 )
def sieveOfPrimes():
global sieve
N = 1000000
for i in range ( 2 , N + 1 ):
if i * i > N:
break
if (sieve[i] = = 0 ):
continue
for j in range (i * i, N + 1 , i):
sieve[j] = 0
def getArray(arr, N):
global sieve
A = [ 0 ] * N
v = []
sieveOfPrimes()
for i in range ( 2 , int ( 1e5 ) + 1 ):
if (sieve[i]):
v.append(i)
j = 0
for i in range (N):
ind = arr[i]
if (A[i] ! = 0 ):
continue
elif (A[ind] ! = 0 ):
A[i] = A[ind]
else :
prime = v[j]
A[i] = prime
A[ind] = A[i]
j + = 1
for i in range (N):
print (A[i], end = " " )
if __name__ = = '__main__' :
arr = [ 4 , 1 , 2 , 3 , 4 ]
N = len (arr)
getArray(arr, N)
|
C#
using System;
using System.Collections.Generic;
class GFG
{
static int [] sieve = new int [10000000];
static void sieveOfPrimes()
{
for ( int i = 0; i < 10000000; i++)
{
sieve[i] = 1;
}
int N = 1000000;
for ( int i = 2; i * i <= N; i++)
{
if (sieve[i] == 0)
continue ;
for ( int j = i * i; j <= N; j += i)
sieve[j] = 0;
}
}
static void getArray( int [] arr, int N)
{
int [] A = new int [N];
for ( int i = 0; i < N; i++)
{
A[i] = 0;
}
List< int > v
= new List< int >();
sieveOfPrimes();
for ( int i = 2; i <= 1000000; i++)
if (sieve[i] != 0)
v.Add(i);
int j = 0;
for ( int i = 0; i < N; i++)
{
int ind = arr[i];
if (A[i] != 0)
continue ;
else if (A[ind] != 0)
A[i] = A[ind];
else {
int prime = v[j++];
A[i] = prime;
A[ind] = A[i];
}
}
for ( int i = 0; i < N; i++)
{
Console.Write( A[i] + " " );
}
}
public static void Main(String[] args)
{
int [] arr = { 4, 1, 2, 3, 4 };
int N = arr.Length;
getArray(arr, N);
}
}
|
Javascript
<script>
var sieve = Array(1000000);
function sieveOfPrimes()
{
sieve = Array(1000000).fill(1);
var N = 1000000;
for ( var i = 2; i * i <= N; i++) {
if (sieve[i] == 0)
continue ;
for ( var j = i * i; j <= N; j += i)
sieve[j] = 0;
}
}
function getArray(arr, N)
{
var A = Array(N).fill(0);
var v = [];
sieveOfPrimes();
for ( var i = 2; i <= 1e5; i++)
if (sieve[i])
v.push(i);
var j = 0;
for ( var i = 0; i < N; i++) {
var ind = arr[i];
if (A[i] != 0)
continue ;
else if (A[ind] != 0)
A[i] = A[ind];
else {
var prime = v[j++];
A[i] = prime;
A[ind] = A[i];
}
}
for ( var i = 0; i < N; i++) {
document.write( A[i] + " " );
}
}
var arr = [4, 1, 2, 3, 4];
var N = arr.length;
getArray(arr, N);
</script>
|
Time Complexity: O(N*log(log(N)))
Auxiliary Space: O(N)
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