How many ways I can put r1 (same) balls with color 1 , r2 balls with color 2 , ..., rp balls with color p in q different boxes with sizes s1,**s2**,..,**sq** ?

note : r1+r2...+rp=s1+s2+...+sq=N

note 2: N<=1000

I don't have a good algorithm to solve this problem .

There is 1 card with color c1 numbered 1 , 2 cards with color c2 numbered 1 and 2, ... and n cards with color cn numbered from 1 to n. find the number of permutation of these cards with a this restriction :

             any two cards with the same color and consecutive numbers cannot be adjacent.

I think it's an interesting problem :)

Let G be a graph with n vertices and Δ(G)≤10 . find an algorithm with O(n) compolexity to determine this graph has girth less than 20 or not ?

thanks for any hint :)

I solved this problem with dp bitmask but when I saw this I knew that it may has a better solution , maybe greedy.

a)I have n zeros and m ones and I want to counting the number of circular permutation of this m+n numbers .