m=1
n = 4 * (1+2)
m=2
n = 4 * (3+2+3+4)
m=3
n = 4 * (5+4+3+4+5+6)
m=m
n = 4 * (m + 2(m+1) + 2(m+2) + 2(m+3) + ... + 2(m+m-1) + m+m)
= 4 * [(m + 2*m + 2*m + 2*m + ... (m times)) + 2 * (1+2+3+...+(m-1))]
= 4 * [m + 2*m*m + 2 * m*(m-1)/2]
= 4 * [m + 2*m*m + m*m - m]
= 4 * [3*m*m]
= 12*m*m
N(m) = n(1) + n(2) + n(3) + ... + n(m)
= 12*1 + 12*4 + 12*9 + ... + 12*m*m
= 12 * (1 + 4 + 9 + ... + m*m) //Σn2 = [n(n+1)(2n+1)]/6
= 12 * (m)*(m+1)*(2*m+1)/6
= 2 * m*(m+1)*(2*m+1)
Algorithm
class Solution {
public long minimumPerimeter(long neededApples) {
int c=0,s=0;
while(s<neededApples)
{
c++;
s=s+12*c*c;
}
return(8*c);
}
public static void main(String args[])
{
Scanner sc=new Scanner(System.in);
long n=sc.nextLong();
Solution S=new Solution();
System.out.println(S.minimumPerimeter(n));
}
}