Recuento de múltiplos en un Array antes de cada elemento

Dada una array arr de tamaño N , la tarea es contar el número de índices j (j<i) tales que a[i] divide a[j] , para todos los índices válidos i . 
Ejemplos: 
 

Entrada: arr[] = {8, 1, 28, 4, 2, 6, 7} 
Salida: 0, 1, 0, 2, 3, 0, 1 
Número de múltiplos para cada elemento antes de sí mismo – 
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)
Entrada: arr[] = {1, 1, 1, 1} 
Salida: 0, 1, 2, 3 
 

Enfoque ingenuo: atravesar todos los índices válidos j, en el rango [0, i-1], para cada índice i ; y cuente los divisores para cada índice.
Complejidad de tiempo: O(N ² ) 
Complejidad de espacio: O(1)
Enfoque eficiente: Este enfoque consiste en utilizar map . Incremente el conteo de factores en el mapa mientras recorre la array y busque ese conteo en el mapa para encontrar todos los j (<i) válidos sin regresar.
A continuación se muestra la implementación del enfoque anterior.
 

// 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;
}

// 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

# 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

// 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

<script>
 
// Javascript program to count of multiples
// in an Array before every element
 
// Function to find all factors of N
// and keep their count in map
function add_factors(n, mp)
{
 
    // Traverse from 1 to sqrt(N)
    // if i divides N,
    // increment i and N/i in map
    for (var i = 1; i <= parseInt(Math.sqrt(n)); i++) {
        if (n % i == 0) {
            if (parseInt(n / i) == i)
            {
                if(mp.has(i))
                    mp.set(i, mp.get(i)+1)
                else
                    mp.set(i, 1)
            }
            else {
 
                if(mp.has(i))
                    mp.set(i, mp.get(i)+1)
                else
                    mp.set(i, 1)
                 
                if(mp.has(parseInt(n/i)))
                    mp.set(parseInt(n/i), mp.get(parseInt(n/i))+1)
                else
                    mp.set(parseInt(n/i), 1)
                     
            }
        }
    }
    return mp;
}
 
// Function to count of multiples
// in an Array before every element
function count_divisors(a, n)
{
 
    // To store factors all of all numbers
    var mp = new Map();
 
    // Traverse for all possible i's
    for (var i = 0; i < n; i++)
    {
     
        // Printing value of a[i] in map
        document.write( (mp.has(a[i])?mp.get(a[i]):0) + " ");
 
        // Now updating the factors
        // of a[i] in the map
        mp = add_factors(a[i], mp);
 
    }
}
 
// Driver code
var arr = [8, 1, 28, 4, 2, 6, 7];
var n = arr.length;
 
// Function call
count_divisors(arr, n);
 
// This code is contributed by famously.
</script>

0 1 0 2 3 0 1

Complejidad de tiempo: O(N * sqrt(val)), donde N es el tamaño de la array y val es el valor máximo de los elementos presentes en la array.

Espacio auxiliar: O(N), ya que estamos usando espacio extra para map mp.