UVa 10910

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10910 - Marks Distribution[edit]

Summary[edit]

A Dynamic Programming counting problem. Solve the problem by counting it with its subproblems. This is an implicit solution. There is also another explicit solution which gives a direct formula.

Explanation[edit]

can be defined recursively
and which basically just states that the number of ways we can have N objects that sum up to T and up to minimum P is just the summation of the number of ways that having the number i as the current number, and the subproblem of N-1 objects that sums up to T-i, still with a minimum P.


Alternate Solution
First, for getting a pass mark in all the N subjects, put 'P' for all the subjects. Now, the number of ways for the rest of the marks to be distributed in 'N' subjects is the number of integrals solutions of . So, finally the answer reduces to

Optimizations[edit]

Memoization is fine, and this problem can be solved bottom-up.

Input[edit]

3
3 34 10
3 34 10
7 50 2

Output[edit]

15
15
5245786