# Count of largest sized groups while grouping according to product of digits

Given an integer N, the task is to find the number of groups having the largest size. Each number from 1 to N is grouped according to the product of its digits.
Examples:

Input: N = 13
Output:
Explanation:
There are 9 groups in total, they are grouped according to the product of its digits
of numbers from 1 to 13: [1, 11] [2, 12] [3, 13]      .
Out of these, 3 groups have the largest size that is 2.

Input: N = 2
Output:
Explanation:
There are 2 groups in total, they are grouped according to the product of its digits
of numbers from 1 to 2:  .
Out of these, 2 groups have the largest size that is 1.

Approach:
To solve the problem mentioned above we have to store the product of digit of every element from 1 to N using hash map and increment its frequency if it repeats. Then we have to find the maximum frequency within the hash map, which would be the largest size of the group. Finally, count all the groups who have the same frequency count as the largest group and return the count.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to Count the ` `// groups having largest size while ` `// grouping is according to ` `// the product of its digits ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find out product of digit ` `int` `digit_prod(``int` `x) ` `{ ` `    ``int` `prod = 1; ` ` `  `    ``// calculate product ` `    ``while` `(x) { ` `        ``prod *= x % 10; ` `        ``x = x / 10; ` `    ``} ` ` `  `    ``// return the product of digits ` `    ``return` `prod; ` `} ` ` `  `// Function to find the count ` `int` `find_count(``int` `n) ` `{ ` ` `  `    ``// hash map for ` `    ``// counting frequency ` `    ``map<``int``, ``int``> mpp; ` ` `  `    ``for` `(``int` `i = 1; i <= n; i++) { ` `        ``// counting freq of each element ` `        ``mpp[digit_prod(i)] += 1; ` `    ``} ` ` `  `    ``int` `ans = 1; ` `    ``int` `maxm = 0; ` `    ``for` `(``auto` `x : mpp) { ` ` `  `        ``// find the maximum ` `        ``if` `(x.second > maxm) { ` `            ``maxm = x.second; ` `            ``ans = 1; ` `        ``} ` ` `  `        ``else` `if` `(x.second == maxm) { ` `            ``// count the number of groups having ` `            ``// size of equal to largest group. ` `            ``ans++; ` `        ``} ` `    ``} ` ` `  `    ``return` `ans; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``// initialise N ` `    ``int` `N = 13; ` ` `  `    ``cout << find_count(N); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation to Count the  ` `// groups having largest size while  ` `// grouping is according to  ` `// the product of its digits  ` `import` `java.io.*; ` `import` `java.util.*;  ` ` `  `class` `GFG{ ` ` `  `// Function to find out product of digit  ` `static` `int` `digit_prod(``int` `x)  ` `{  ` `    ``int` `prod = ``1``;  ` ` `  `    ``// Calculate product  ` `    ``while` `(x != ``0``)  ` `    ``{  ` `        ``prod *= x % ``10``;  ` `        ``x = x / ``10``;  ` `    ``}  ` ` `  `    ``// Return the product of digits  ` `    ``return` `prod;  ` `}  ` ` `  `// Function to find the count  ` `static` `int` `find_count(``int` `n)  ` `{  ` `     `  `    ``// Hash map for counting frequency  ` `    ``Map mpp = ``new` `HashMap<>();  ` ` `  `    ``for``(``int` `i = ``1``; i <= n; i++) ` `    ``{  ` `         `  `        ``// Counting freq of each element  ` `        ``int` `t = digit_prod(i); ` `        ``mpp.put(t, mpp.getOrDefault(t, ``0``) + ``1``); ` `    ``}  ` ` `  `    ``int` `ans = ``1``;  ` `    ``int` `maxm = ``0``;  ` `     `  `    ``for``(Integer x : mpp.values()) ` `    ``{  ` `         `  `        ``// Find the maximum  ` `        ``if` `(x > maxm)  ` `        ``{  ` `            ``maxm = x;  ` `            ``ans = ``1``;  ` `        ``}  ` ` `  `        ``else` `if` `(x == maxm)  ` `        ``{ ` `             `  `            ``// Count the number of groups having  ` `            ``// size of equal to largest group.  ` `            ``ans++;  ` `        ``}  ` `    ``}  ` `    ``return` `ans;  ` `}  ` ` `  `// Driver Code  ` `public` `static` `void` `main(String args[])  ` `{  ` `     `  `    ``// Initialise N  ` `    ``int` `N = ``13``;  ` ` `  `    ``System.out.print(find_count(N));  ` `} ` `}  ` ` `  `// This code is contributed by offbeat`

## Python3

 `# Python3 implementation to Count the  ` `# groups having largest size while  ` `# grouping is according to  ` `# the product of its digits  ` ` `  `# Function to find out product of digit  ` `def` `digit_prod(x) : ` `    ``prod ``=` `1` ` `  `    ``# calculate product  ` `    ``while``(x) :  ` `        ``prod ``=` `prod ``*` `(x ``%` `10``)  ` `        ``x ``=` `x ``/``/` `10` `     `  `    ``# return the product of digits  ` `    ``return` `prod  ` ` `  `# Function to find the count  ` `def` `find_count(n) : ` `     `  `    ``# hash map for  ` `    ``# counting frequency  ` `    ``mpp ``=` `{}  ` ` `  `    ``for` `i ``in` `range``(``1``, n ``+` `1``):  ` `         `  `        ``# counting freq of each element  ` `        ``x ``=` `digit_prod(i) ` ` `  `        ``if` `x ``in` `mpp : ` `            ``mpp[x] ``+``=` `1` `        ``else` `: ` `            ``mpp[x] ``=` `1` ` `  `    ``ans ``=` `1` `    ``maxm ``=` `0` ` `  `    ``for` `value ``in` `mpp.values() :  ` ` `  `        ``# find the maximum  ` `        ``if` `(value > maxm) : ` `            ``maxm ``=` `value  ` `            ``ans ``=` `1` `        ``elif` `(value ``=``=` `maxm) : ` `             `  `            ``# count the number of groups having  ` `            ``# size of equal to largest group.  ` `            ``ans ``=` `ans ``+` `1` ` `  `    ``return` `ans  ` ` `  `# Driver code  ` ` `  `# initialise N  ` `N ``=` `13` ` `  `print``(find_count(N)) ` ` `  `# This code is contributed by Sanjit_Prasad `

## C#

 `// C# implementation to count the  ` `// groups having largest size while  ` `// grouping is according to  ` `// the product of its digits  ` `using` `System;  ` `using` `System.Collections;  ` `using` `System.Collections.Generic;  ` `using` `System.Text;  ` ` `  `class` `GFG{ ` `     `  `// Function to find out product of digit  ` `static` `int` `digit_prod(``int` `x)  ` `{  ` `    ``int` `prod = 1;  ` ` `  `    ``// Calculate product  ` `    ``while` `(x != 0)  ` `    ``{  ` `        ``prod *= x % 10;  ` `        ``x = x / 10;  ` `    ``}  ` ` `  `    ``// Return the product of digits  ` `    ``return` `prod;  ` `}  ` ` `  `// Function to find the count  ` `static` `int` `find_count(``int` `n)  ` `{  ` `     `  `    ``// Hash map for counting frequency  ` `    ``Dictionary<``int``, ` `               ``int``> mpp = ``new` `Dictionary<``int``, ` `                                         ``int``>();  ` ` `  `    ``for``(``int` `i = 1; i <= n; i++) ` `    ``{  ` `         `  `        ``// Counting freq of each element  ` `        ``int` `t = digit_prod(i); ` `        ``if` `(mpp.ContainsKey(t)) ` `        ``{ ` `            ``mpp[t]++; ` `        ``} ` `        ``else` `        ``{ ` `            ``mpp[i] = 1; ` `        ``} ` `    ``}  ` ` `  `    ``int` `ans = 1;  ` `    ``int` `maxm = 0;  ` `     `  `    ``foreach``(KeyValuePair<``int``, ``int``> x ``in` `mpp) ` `    ``{  ` `         `  `        ``// Find the maximum  ` `        ``if` `(x.Value > maxm)  ` `        ``{  ` `            ``maxm = x.Value;  ` `            ``ans = 1;  ` `        ``}  ` `        ``else` `if` `(x.Value == maxm)  ` `        ``{ ` `             `  `            ``// Count the number of groups having  ` `            ``// size of equal to largest group.  ` `            ``ans++;  ` `        ``}  ` `    ``}  ` `    ``return` `ans;  ` `} ` `     `  `// Driver Code ` `public` `static` `void` `Main(``string``[] args) ` `{ ` `     `  `    ``// Initialise N  ` `    ``int` `N = 13;  ` ` `  `    ``Console.Write(find_count(N)); ` `} ` `} ` ` `  `// This code is contributed by rutvik_56 `

Output:

```3
```

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