Count Colors to Paint Elements in Valid Way Using C++

Suppose we have an array A with n elements. We need to paint elements in colors such that −

• If we consider any color, all elements of this color must be divisible by the minimal element of the same color.

• The number of used colors should be minimized.

We have to find the minimum number of colors to paint all the given numbers in a valid way.

So, if the input is like A = [10, 2, 3, 5, 4, 2], then the output will be 3, because paint the first color to the elements A[0] and A[3], paint second color to the elements A[2] and paint the third color to the remaining three elements.

Steps

To solve this, we will follow these steps −

n := size of A
ans := 0
sort the array A
for initialize i := 0, when i < n, update (increase i by 1), do:
   ok := 1
   for initialize j := 0, when j < i, update (increase j by 1),
do:
      ok := ok AND (1 if A[i] mod A[j] is not 0, otherwise 0)
   ans := ans + ok
return ans

Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;
int solve(vector<int> A){
   int n = A.size();
   int ans = 0;
   sort(A.begin(), A.end());
   for (int i = 0; i < n; i++){
      int ok = 1;
      for (int j = 0; j < i; j++)
         ok &= (A[i] % A[j] != 0);
      ans += ok;
   }
   return ans;
}
int main(){
   vector<int> A = { 10, 2, 3, 5, 4, 2 };
   cout << solve(A) << endl;
}

Input

{ 10, 2, 3, 5, 4, 2 }

Output

3