Count of multiples in an Array before every element

Given an array arr of size N, the task is to count the number of indices j (j<i) such that a[i] divides a[j], for all valid indexes i.

Examples:

Input: arr[] = {8, 1, 28, 4, 2, 6, 7}
Output: 0, 1, 0, 2, 3, 0, 1
No of multiples for each element before itself –
N(8) = 0 ()
N(1) = 1 (8)
N(28) = 0 ()
N(4) = 2 (28, 8)
N(2) = 3 (4, 28, 8)
N(6) = 0 ()
N(7) = 1 (28)



Input: arr[] = {1, 1, 1, 1}
Output: 0, 1, 2, 3

Naive Approach: Traverse through all valid indices j, in range [0, i-1], for each index i; and count the divisors for each indexes.

Time Complexity: O(N2)
Space Complexity: O(1)

Efficient Approach: This approach is to use map. Increment the count of factors in the map while traversing the array and lookup for that count in the map to find all valid j (< i) without traversing back.

Below is the implementation of the above approach.

C++

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// C++ program to count of multiples
// in an Array before every element
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to find all factors of N
// and keep their count in map
void add_factors(int n,
                 unordered_map<int, int>& mp)
{
    // Traverse from 1 to sqrt(N)
    // if i divides N,
    // increment i and N/i in map
    for (int i = 1; i <= int(sqrt(n)); i++) {
        if (n % i == 0) {
            if (n / i == i)
                mp[i]++;
            else {
                mp[i]++;
                mp[n / i]++;
            }
        }
    }
}
  
// Function to count of multiples
// in an Array before every element
void count_divisors(int a[], int n)
{
  
    // To store factors all of all numbers
    unordered_map<int, int> mp;
  
    // Traverse for all possible i's
    for (int i = 0; i < n; i++) {
        // Printing value of a[i] in map
        cout << mp[a[i]] << " ";
  
        // Now updating the factors
        // of a[i] in the map
        add_factors(a[i], mp);
    }
}
  
// Driver code
int main()
{
    int arr[] = { 8, 1, 28, 4, 2, 6, 7 };
    int n = sizeof(arr) / sizeof(arr[0]);
  
    // Function call
    count_divisors(arr, n);
  
    return 0;
}

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Java

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// Java program to count of multiples
// in an Array before every element
import java.util.*;
  
class GFG{
   
// Function to find all factors of N
// and keep their count in map
static void add_factors(int n,
                 HashMap<Integer,Integer> mp)
{
    // Traverse from 1 to Math.sqrt(N)
    // if i divides N,
    // increment i and N/i in map
    for (int i = 1; i <= (Math.sqrt(n)); i++) {
        if (n % i == 0) {
            if (n / i == i) {
                if(mp.containsKey(i))
                    mp.put(i, mp.get(i) + 1);
                else
                    mp.put(i, 1);
            }
            else {
                if(mp.containsKey(i))
                    mp.put(i, mp.get(i) + 1);
                else
                    mp.put(i, 1);
                if(mp.containsKey(n / i))
                    mp.put(n / i, mp.get(n / i) + 1);
                else
                    mp.put(n / i, 1);
            }
        }
    }
}
   
// Function to count of multiples
// in an Array before every element
static void count_divisors(int a[], int n)
{
   
    // To store factors all of all numbers
    HashMap<Integer,Integer> mp = new HashMap<Integer,Integer>();
   
    // Traverse for all possible i's
    for (int i = 0; i < n; i++) {
        // Printing value of a[i] in map
        System.out.print(mp.get(a[i]) == null ? 0 + " " : mp.get(a[i]) + " ");
   
        // Now updating the factors
        // of a[i] in the map
        add_factors(a[i], mp);
    }
}
   
// Driver code
public static void main(String[] args)
{
    int arr[] = { 8, 1, 28, 4, 2, 6, 7 };
    int n = arr.length;
   
    // Function call
    count_divisors(arr, n);
   
}
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python 3 program to count of multiples
# in an Array before every element
from collections import defaultdict
import math
   
# Function to find all factors of N
# and keep their count in map
def add_factors(n, mp):
  
    # Traverse from 1 to sqrt(N)
    # if i divides N,
    # increment i and N/i in map
    for i in range(1, int(math.sqrt(n)) + 1,):
        if (n % i == 0):
            if (n // i == i):
                mp[i] += 1 
            else :
                mp[i] += 1 
                mp[n // i] += 1 
   
# Function to count of multiples
# in an Array before every element
def count_divisors(a, n):
   
    # To store factors all of all numbers
    mp = defaultdict(int)
   
    # Traverse for all possible i's
    for i in range(n) :
        # Printing value of a[i] in map
        print(mp[a[i]], end=" ")
   
        # Now updating the factors
        # of a[i] in the map
        add_factors(a[i], mp)
   
# Driver code
if __name__ == "__main__":
      
    arr = [ 8, 1, 28, 4, 2, 6, 7 ]
    n = len(arr)
   
    # Function call
    count_divisors(arr, n)
   
# This code is contributed by chitranayal

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C#

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// C# program to count of multiples
// in an Array before every element
using System;
using System.Collections.Generic;
  
class GFG{
    
// Function to find all factors of N
// and keep their count in map
static void add_factors(int n,
                 Dictionary<int,int> mp)
{
    // Traverse from 1 to Math.Sqrt(N)
    // if i divides N,
    // increment i and N/i in map
    for (int i = 1; i <= (Math.Sqrt(n)); i++) {
        if (n % i == 0) {
            if (n / i == i) {
                if(mp.ContainsKey(i))
                    mp[i] = mp[i] + 1;
                else
                    mp.Add(i, 1);
            }
            else {
                if(mp.ContainsKey(i))
                    mp[i] = mp[i] + 1;
                else
                    mp.Add(i, 1);
                if(mp.ContainsKey(n / i))
                    mp[n / i] = mp[n / i] + 1;
                else
                    mp.Add(n / i, 1);
            }
        }
    }
}
    
// Function to count of multiples
// in an Array before every element
static void count_divisors(int []a, int n)
{
    
    // To store factors all of all numbers
    Dictionary<int,int> mp = new Dictionary<int,int>();
    
    // Traverse for all possible i's
    for (int i = 0; i < n; i++) {
        // Printing value of a[i] in map
        Console.Write(!mp.ContainsKey(a[i]) ? 0 + " " : mp[a[i]] + " ");
    
        // Now updating the factors
        // of a[i] in the map
        add_factors(a[i], mp);
    }
}
    
// Driver code
public static void Main(String[] args)
{
    int []arr = { 8, 1, 28, 4, 2, 6, 7 };
    int n = arr.Length;
    
    // Function call
    count_divisors(arr, n);
    
}
}
  
// This code is contributed by sapnasingh4991

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Output:

0 1 0 2 3 0 1

Time Complexity: O(N * sqrt(N))

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