Converting recursive formulate into pseudocode using memoization

Question

i've been trying to turn the recurrence formula underneath into a pseudocode that uses memoization, however currently all i know is my below attempt is incorrect, is anyone able to point me in the right direction?

My recurrence formula:

N(C,i) =
1 if C = 0
0 if i=0 or C<0}
N(C-p_i, i-1) + N(C, i-1) otherwise

My current attempt:

MEM-N(C, i, r)
    if r[i] >= 0 then
        return r[i]
    if i = 0 and r[i] >= 0 or C < 0 and r[i] >= 0 then
        return 0
    else if C = 0 and r[i] >= 0 then
        return 1
    else
        q = -$\infty$
        q = MEM-N(C - $p_i$, i-1) + MEM-N(C,i - x, r)
        r[i] = q
        return q

if r[i] <= 0 then -- shouldn't this be > 0, since all return values are bound to be positive? — meowgoesthedog
– meowgoesthedog, Commented Jun 2, 2018 at 17:07
And perhaps return 0 instead of q = 0, assuming the indentation is correct. — meowgoesthedog
– meowgoesthedog, Commented Jun 2, 2018 at 17:12
While that's also correct, for now all i know is there's something wrong with the recursion in the last else statement, but im not sure of what — danjo
– danjo, Commented Jun 2, 2018 at 18:05
How then do you know that it is wrong? Also you should pass r to the first recursive call. — meowgoesthedog
– meowgoesthedog, Commented Jun 2, 2018 at 18:44

meowgoesthedog · Accepted Answer · 2018-06-04 09:10:35Z

0

Following on from the comments:

MEM-N(C, i, r)
    if C = 0 then
        return 1
    else if i = 0 or C < 0 then
        return 0
    else if r[i] >= 0 then
        return r[i]                                        # move here
    else
        q = MEM-N(C - p_i, i - 1, r) + MEM-N(C, i - 1, r)  # fix
        r[i] = q
        return q

answered Jun 4, 2018 at 9:10

meowgoesthedog

15.1k4 gold badges30 silver badges43 bronze badges

Sign up to request clarification or add additional context in comments.

Collectives™ on Stack Overflow

Converting recursive formulate into pseudocode using memoization

1 Answer 1

Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

Comments

Your Answer

Sign up or log in

Post as a guest

Related