n probability of each count and occurrence of dice--dynamic planning

Title: The n Dice on the floor. All points of the dice on the upward side and one s. Enter n, the probability of printing s all possible values.

Statement ideas are not original! Just because the use of dynamic planning ideas is very good, write down.

Analysis: Dynamic planning is a phased consideration of issues. Give the variable. Find the relationship between adjacent phases. A detailed definition to forget.

1. Now the variables are: Dice number, points and.

When there is a K-dice. Points and is n. The number of occurrences is recorded as F (k,n). What is the relationship between that and the k-1 dice phase?

2. When I have k-1 a dice. Add another dice, the dice can only be 1, 2, 3, 4, 5 or 6. The case that K dice get points and for N is:

(k-1,n-1): K Dice Cast points 1

(k-1,n-2): K Dice Cast points 2

(k-1,n-3): K Dice Cast points 3

....

(k-1,n-6): K Dice Cast points 6

On the basis of k-1 dice, adding a dice to the number of points and the result of n is only 6 cases.

So:f (k,n) =f (k-1,n-1) +f (k-1,n-2) +f (k-1,n-3) +f (k-1,n-4) +f (k-1,n-5) +f (k-1,n-6)

3. There are 1 dice, f (=f) =f (1,3) =f (1,4) =f (1,5) =f (1,6) = 1.

The code is easy to write, recursive functions, returns, and the number of occurrences of N. Total sum of occurrences is 6^n.

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n probability of each count and occurrence of dice--dynamic planning