Problemele 4-6 pentru pregatirea LOT-ului

4.Cow Yahtzee

In their usual clumsy way, the cows are play a version of Yahtzee,
the dice-rolling game. They roll N (1 <= N <= 20) dice, each having
S (1 <= S <= 8) sides. They are curious as to the number of ways
a dice roll can meet a particular criterion (like "contains three
2's" or "contains one 2 and two 3's").

Help them learn about probability. Write a program that reads not
only N and S but also some expressions that describe their criteria.
Count the number ways the expression can be satisfied over the
entire set of all possible dice rolls (the entire set of rolls for
three two-sided dice is: {1,1,1; 1,1,2; 1,2,1; 1,2,2; 2,1,1; 2,1,2;
2,2,1; 2,2,2};

Expressions comprise combinations of a basic form that expresses
the thought "want at least W copies of result R". It looks like this:

WxR

where (0 <= W <= N and 1 <= R <= S). Each test run will supply E
expressions (1 <= E <= 20), each of which contains a number 1..10
of the basic forms separated by a '+', which means 'and' (see below).
The set of lines expresses the thought that is the 'inclusive or'
of each of the lines individually. Thus the pair of expressions
shown below means "at least three rolls of five OR both at least
one roll of 3 and also at least two rolls of 4":

3×5
1×3+2×4

Here are some of the combinations of four five-sided dice that
satisfy the above expression: 5,5,5,1; 4,5,5,5; 3,4,4,2; 3,4,4,3;
3,4,4,5; 4,4,5,3.

Programming note: Be sure to verify that you can read in two integers
from one line and a string from the next line. In some languages'
I/O schema, this is harder than it looks!

Also note that the total number of dice combinations will never
exceed 1,512,768 in the supplied test data.

PROBLEM NAME: cowyotz

INPUT FORMAT:

• Line 1: Three space-separated integers: N, S, and E

• Lines 2..E+1: Line i+1 describes expression i as above.

SAMPLE INPUT (file cowyotz.in):

4 5 2
3×5
1×3+2×4

INPUT DETAILS:

This is the encoding of the expression used as an example in the task text.

OUTPUT FORMAT:

• Line 1: A single integer that is the number of ways the
    expression(s) can be satisfied by rolling the dice in all
    combinations.

SAMPLE OUTPUT (file cowyotz.out):

63

OUTPUT DETAILS:

63 rolls satisfy the expression.