RockPaperScissorsMagicEasy | Topcoder Archive

Problem Statement

Alice and Bob are going to play a variant of the traditional rock-paper-scissors game. Their game is played using cards. Each card shows one of the three pictures: a rock, a paper, or scissors. There is a sufficient supply of cards of each type. Bob has already chosen a sequence of cards and he has arranged them into a row, face down. It is now Alice's turn to do the same. Once she does that, they will use the two sequences of cards to play the game: For each i, Alice's i-th card and Bob's i-th card will be revealed and compared using the standard rules of rock-paper-scissors. Whenever Alice's card wins, Alice gets a point. Alice gets no points for a loss or a tie.

Alice has marked Bob's cards, so now she can tell which card has which symbol on it. You are given this information as a int[] card. Each element of card is between 0 and 2, inclusive: 0 is a rock, 1 is a paper, and 2 are scissors.

You are also given an int score. Alice has just announced that she will get a total of score points.

Let X be the number of sequences in which Alice can play her cards if she wants to achieve exactly score points. Return the value (X modulo 1,000,000,007).

Definition

Class:: RockPaperScissorsMagicEasy
Method:: count
Parameters:: int[], int
Returns:: int
Method signature:: int count(int[] card, int score)
(be sure your method is public)

Constraints

The number of elements in card will be between 1 and 2,000, inclusive.
All elements of card will be between 0 and 2, inclusive.
score will be between 0 and 2,000, inclusive.

Examples

```
{0,1,2}
```
```
2
```
```
Returns: 6
```
Bob has played his cards in the order rock-paper-scissors. Alice wants to score 2 points. Hence, she must win twice, and lose to Bob or tie him once. One possible way in which she can play her cards is paper-scissors-scissors: her paper beats Bob's rock (1 point), scissors beat paper (1 point), and scissors tie with scissors (0 points). There are five other ways how Alice can score 2 points: paper-scissors-paper, paper-paper-rock, paper-rock-rock, rock-scissors-rock, and scissors-scissors-rock.
```
{1,2}
```
```
0
```
```
Returns: 4
```
```
{2,2,1,0,0}
```
```
10
```
```
Returns: 0
```

{0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}

Returns: 286226628

```
{0,1,2,0,1,2,2,1,0}
```
```
8
```
```
Returns: 18
```

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