in c++ how to compute the value of Pn by this formula

so can anyone tell me how to proceed on writing a function that uses bottom-up dynamic programming approach to compute the value of Pn defined by the recurrence:
P_n= floor(n/2) + P floor(n/2) + P ceil(n/2) for n>=1 with P_1=1

floor() is the function that rounds a number down.
ceil() is the function that rounds a number up.

sample manual calculation of the sequence would be:

P_2=floor(2/2) + P floor(2/2) + P ceil(2/2)= 1 + P1 + P1= (1+1+1) = 3

I really don't know how to proceed writing this function. Thanks in advance.

re: in c++ how to compute the value of Pn by this formula

Look up recursion/recursive functions. have an attempt at the problem yourself, the maths library has ceiling and floor functions look up math.h.

re: in c++ how to compute the value of Pn by this formula

Also note than if n is even then floor(n/2) == ceil(n/2); otherwise ceil(n/2) == floor(n/2)+1. This allows for a simple interval definition of P:

P(n) == if n even then n/2+P(n/2)+P(n/2)
else n/2+P(n/2)+P(n/2+1)

where '/' denotes integer division, i.e.

P(1) == 1
P(2) == 1+P(1)+P(1)
P(3) == 1+P(1)+P(2)
P(4) == 2+P(2)+P(2)
P(5) == 2+P(2)+P(3)
P(6) == 3+P(3)+P(3)
P(7) == 3+P(3)+P(4)
P(8) == 4+P(4)+P(4)
etc.

kind regards,

Jos

re: in c++ how to compute the value of Pn by this formula

#include<cmath>
#include<iostream>
using namespace std;
int main()
{
int p[100];
p[0]=0;
p[1]=1;

int n=0;
for(int i=2; i<=n;i++)
{
if(n % 2 == 0)
{
return n + floor(n/2) + ceil(n/2);
}
else
{
return n + (floor(n/2) + 1) + ceil(n/2);
}
}

return 0;
}
could anyone tell me is this the right logic? thanks for the help. I am getting an error that says floor anbiguos call to overloaded function.

re: in c++ how to compute the value of Pn by this formula

Did you read my previous reply? You don't need the floor() and ceil() functions. The integer division operator will do.

kind regards,

Jos

re: in c++ how to compute the value of Pn by this formula

The logic is wrong, because it immediately returns from main and stops calculation on the first iteration. Let alone it doesn't compile.

re: in c++ how to compute the value of Pn by this formula

so using integer division operator. what am I missing? any suggestions. Thank
for the help

re: in c++ how to compute the value of Pn by this formula

Look closely at your 'for' loop. How many times will the body of the loop be executed? How many times do you want it to execute?

Do you care whether you end up with an iterative or a recursive function? A 'for' loop suggests that you're aiming for an iterative function.

By the way, it would be helpful if you enclosed your source code in CODE tags.