Count the divisors or multiples present in the Array for each element
Last Updated :
01 Dec, 2022
Given an array A[] with N integers, for each integer A[i] in the array, the task is to find the number of integers A[j] (j != i) in the array such that A[i] % A[j] = 0 or A[j] % A[i] = 0.
Examples:
Input: A = {2, 3, 4, 5, 6}
Output: 2 1 1 0 2
Explanation:
For i=0, the valid indices are 2 and 4 as 4%2 = 0 and 6%2 = 0.
For i=1, the only valid index is 4 as 6%3 = 0.
For i=2, the only valid index is 0 as 4%2 = 0.
For i=3, there are no valid indices.
For i=0, the valid indices are 0 and 1 as 6%2 = 0 and 6%3 = 0.
Input: A = {6, 6, 6, 6, 6}
Output: 4 4 4 4 4
Approach: The given problem can be solved by using the observation that the number of integers that satisfies the given condition can be categorized into two cases. Suppose the current integer is P and Q is an integer that satisfies the given conditions.
- Case 1 where Q is a multiple of P. Therefore, the count of integers in the given array that are divisible by P is the required answer. This case can be handled using a simple modification of Sieve of Eratosthenes which is discussed here.
- Case 2 where P is a multiple of Q. Therefore, the count of integers in the given array that Q divides P is the required answer. This case can be handled similarly using sieve as that of 1st Case.
So, the required answer for any integer is the sum of resulting integers of Case 1 and Case 2. In cases where P = Q, both Case 1 and Case 2 represents the same value and should be considered only once.
Below is the implementation of the above approach:
C++
// C++ Program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find the count of integers
// such that A[i]%A[j] = 0 or A[j]%A[i] = 0
// for each index of the array A[]
void countIndex(int A[], int N)
{
// Stores the maximum integer in A[]
int MAX = *max_element(A, A + N);
// Stores the frequency of each
// element in the array A[]
vector<int> freq(MAX + 1, 0);
for (int i = 0; i < N; i++)
freq[A[i]]++;
// Stores the valid integers in A[]
// for all integers from 1 to MAX
vector<int> res(MAX + 1, 0);
for (int i = 1; i <= MAX; ++i) {
for (int j = i; j <= MAX; j += i) {
// Case where P = Q
if (i == j) {
// Subtract 1 because P & Q
// cannot have same index
res[i] += (freq[j] - 1);
}
else {
// Case 1
res[i] += freq[j];
// Case 2
res[j] += freq[i];
}
}
}
// Loop to print answer for
// each index of array A[]
for (int i = 0; i < N; i++) {
cout << res[A[i]] << " ";
}
}
// Driver Code
int main()
{
int A[] = { 2, 3, 4, 5, 6 };
int N = sizeof(A) / sizeof(int);
// Function Call
countIndex(A, N);
return 0;
}
// Java Program for the above approach
import java.util.*;
class GFG{
// Function to find the count of integers
// such that A[i]%A[j] = 0 or A[j]%A[i] = 0
// for each index of the array []A
static void countIndex(int []A, int N)
{
// Stores the maximum integer in []A
int MAX = Arrays.stream(A).max().getAsInt();
// Stores the frequency of each
// element in the array []A
int []freq = new int[MAX + 1];
for (int i = 0; i < N; i++)
freq[A[i]]++;
// Stores the valid integers in []A
// for all integers from 1 to MAX
int []res = new int[MAX + 1];
for (int i = 1; i <= MAX; ++i) {
for (int j = i; j <= MAX; j += i) {
// Case where P = Q
if (i == j) {
// Subtract 1 because P & Q
// cannot have same index
res[i] += (freq[j] - 1);
}
else {
// Case 1
res[i] += freq[j];
// Case 2
res[j] += freq[i];
}
}
}
// Loop to print answer for
// each index of array []A
for (int i = 0; i < N; i++) {
System.out.print(res[A[i]]+ " ");
}
}
// Driver Code
public static void main(String[] args)
{
int []A = { 2, 3, 4, 5, 6 };
int N = A.length;
// Function Call
countIndex(A, N);
}
}
// This code is contributed by Princi Singh
# Python 3 Program for the above approach
# Function to find the count of integers
# such that A[i]%A[j] = 0 or A[j]%A[i] = 0
# for each index of the array A[]
def countIndex(A, N):
# Stores the maximum integer in A[]
MAX = max(A)
# Stores the frequency of each
# element in the array A[]
freq = [0 for i in range(MAX+1)]
for i in range(N):
if freq[A[i]] > 0:
freq[A[i]] += 1
else:
freq[A[i]] = 1
# Stores the valid integers in A[]
# for all integers from 1 to MAX
res = [0 for i in range(MAX+1)]
for i in range(1, MAX + 1, 1):
for j in range(i, MAX + 1, i):
# Case where P = Q
if (i == j):
# Subtract 1 because P & Q
# cannot have same index
res[i] += (freq[j] - 1)
else:
# Case 1
res[i] += freq[j]
# Case 2
res[j] += freq[i]
# Loop to print answer for
# each index of array A[]
for i in range(N):
print(res[A[i]],end = " ")
# Driver Code
if __name__ == '__main__':
A = [2, 3, 4, 5, 6]
N = len(A)
# Function Call
countIndex(A, N)
# This code is contributed by SURENDRA_GANGWAR.
// C# program of above approach
using System;
public class GFG {
static void countIndex(int[] A, int N)
{
// Stores the maximum integer in []A
int MAX = A[0];
for (int i = 1; i < N; i++) {
if (A[i] > MAX) {
MAX = A[i];
}
}
// Stores the frequency of each
// element in the array []A
int[] freq = new int[MAX + 1];
for (int i = 0; i < N; i++)
freq[A[i]]++;
// Stores the valid integers in []A
// for all integers from 1 to MAX
int[] res = new int[MAX + 1];
for (int i = 1; i <= MAX; ++i) {
for (int j = i; j <= MAX; j += i) {
// Case where P = Q
if (i == j) {
// Subtract 1 because P & Q
// cannot have same index
res[i] += (freq[j] - 1);
}
else {
// Case 1
res[i] += freq[j];
// Case 2
res[j] += freq[i];
}
}
}
// Loop to print answer for
// each index of array []A
for (int i = 0; i < N; i++) {
Console.Write(res[A[i]] + " ");
}
}
// Driver Code
static public void Main()
{
int[] A = { 2, 3, 4, 5, 6 };
int N = A.Length;
// Function Call
countIndex(A, N);
}
}
// This code is contributed by maddler.
<script>
// JavaScript program for the above approach;
// Function to find the count of integers
// such that A[i]%A[j] = 0 or A[j]%A[i] = 0
// for each index of the array A[]
function max_element(A, N) {
let MAX = Number.MIN_VALUE;
for (let i = 0; i < A.length; i++) {
if (A[i] > MAX) {
MAX = A[i];
}
}
return MAX;
}
function countIndex(A, N) {
// Stores the maximum integer in A[]
let MAX = max_element(A, A + N);
// Stores the frequency of each
// element in the array A[]
let freq = new Array(MAX + 1).fill(0);
for (let i = 0; i < N; i++)
freq[A[i]]++;
// Stores the valid integers in A[]
// for all integers from 1 to MAX
let res = new Array(MAX + 1).fill(0);
for (let i = 1; i <= MAX; ++i) {
for (let j = i; j <= MAX; j += i) {
// Case where P = Q
if (i == j) {
// Subtract 1 because P & Q
// cannot have same index
res[i] += (freq[j] - 1);
}
else {
// Case 1
res[i] += freq[j];
// Case 2
res[j] += freq[i];
}
}
}
// Loop to print answer for
// each index of array A[]
for (let i = 0; i < N; i++) {
document.write(res[A[i]] + " ");
}
}
// Driver Code
let A = [2, 3, 4, 5, 6];
let N = A.length;
// Function Call
countIndex(A, N);
// This code is contributed by Potta Lokesh
</script>
Time Complexity: O(N*log N)
Auxiliary Space: O(MAX) where MAX represents the maximum integer in the given array.
Similar Reads
Count of N size Arrays with each element as multiple or divisor of its neighbours Given two numbers N and K, the task is to count the number of all possible arrays of size N such that each element is a positive integer less than or equal to K and is either a multiple or a divisor of its neighbours. Since the answer can be large, print it modulo 109 + 7. Examples: Input: N = 2, K
15 min read
Count of integers that divide all the elements of the given array Given an array arr[] of N elements. The task is to find the count of positive integers that divide all the array elements. Examples: Input: arr[] = {2, 8, 10, 6} Output: 2 1 and 2 are the only integers that divide all the elements of the given array. Input: arr[] = {6, 12, 18, 12, 6} Output: 4 Appro
5 min read
Count array elements whose count of divisors is a prime number Given an array arr[] consisting of N positive integers, the task is to find the number of array elements whose count of divisors is a prime number. Examples: Input: arr[] = {3, 6, 4}Output: 2Explanation:The count of divisors for each element are: arr[0]( = 3): 3 has 2 divisors i.e., 1 and 3.arr[1](
9 min read
Count number of pairs not divisible by any element in the array Given an array arr[] of size N, the task is to count the number of pairs of integers (i, j) for which there does not exist an integer k such that arr[i] is divisible by arr[k] and arr[j] is divisible by arr[k], such that k can be any index between [0, N - 1]. Examples: Input: N = 4, arr[] = {2, 4, 5
5 min read
Count numbers from a given range that are not divisible by any of the array elements Given an array arr[] consisting of N positive integers and integers L and R, the task is to find the count of numbers in the range [L, R] which are not divisible by any of the array elements. Examples: Input: arr[] = {2, 3, 4, 5, 6}, L = 1, R = 20Output: 6Explanation:The 6 numbers in the range [1, 2
7 min read
Count distinct prime factors for each element of an array Given an array arr[] of size N, the task is to find the count of distinct prime factors of each element of the given array. Examples: Input: arr[] = {6, 9, 12}Output: 2 1 2Explanation: 6 = 2 × 3. Therefore, count = 29 = 3 × 3. Therefore, count = 112 = 2 × 2 × 3. Therefore, count = 2The count of dist
15+ min read