Hello,

Here's the problem link: https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1159

I know and already got AC with other neater solutions, but I was trying various dp states/approaches for practice. I wanted to know what I am missing in this dp approach since I'm getting a bit lower value than the sample output (0.5012511 instead of 0.5002286)

Solution link: https://ideone.com/AjdoVF

approach:

- i is zero based

Dp definition:

- dp[i][rem] is probability to get a final even 'usedCandy' count in range [i, m) using 'rem' candies such that usedCandy = totalCandies — rem

base case:

- at i == m, return isEven(usedCandy)

transition:

at each [i][rem], if 'tk' is amount given to man 'i'. 'tk' is in [0, rem]

answer = Summation for all 'tk' in [0, rem] -> P(man 'i' getting exactly tk candies) * dp[i + 1][rem — tk]

P(a man getting exactly 'tk' candies) having 'rem' candies in total can be found through binomial theorom C[rem][tk] * p^tk q^(rem — tk) such that p is probability for

a person to get a single candy = 1/(m+w) and q = 1 — p

If something is not clear with my solution, please ask. Where am I going wrong with this dp?