Straights | Topcoder Archive

Problem Statement

You are playing a game of cards in which the number of straights, i.e., sets of consecutive-valued cards, determines the strength of your hand. You will be given a int[] hand, where the i-th element of hand is the number of cards of value i in your hand. You should return the number of straights of length k. For example, suppose you have the hand:

2 of spades
2 of diamonds
2 of clubs
3 of clubs
4 of hearts
4 of clubs

You would be given hand = { 0, 3, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 }. The number of two-card straights is 5:

2 of spades, 3 of clubs
2 of diamonds, 3 of clubs
2 of clubs, 3 of clubs
3 of clubs, 4 of hearts
3 of clubs, 4 of clubs

Definition

Class:: Straights
Method:: howMany
Parameters:: int[], int
Returns:: int
Method signature:: int howMany(int[] hand, int k)
(be sure your method is public)

Notes

Straights do not wrap around: if hand is {1,0,0,0,0,0,0,0,0,0,0,0,1}, you have no straights of length 2.

Constraints

hand will contain exactly 13 elements.
Each element of hand will be between 0 and 4 inclusive.
k will be between 1 and 13 inclusive.

Examples

```
{0,3,1,2,0,0,0,0,0,0,0,0,0}
```
```
2
```
```
Returns: 5
```
The example given.
```
{1,1,1,1,1,1,1,1,1,1,1,1,1}
```
```
5
```
```
Returns: 9
```
Say hand[0] references Aces. There are 9 ways to make a straight of length 5: Ace-Five up to Nine-King.

{4,4,4,4,4,4,4,4,4,4,4,4,4}

Returns: 67108864

```
{4,0,4,0,4,0,4,0,4,0,4,0,4}
```
```
2
```
```
Returns: 0
```
Straights do not wrap around; we have no straights here.
```
{1,2,3,4,1,2,3,4,1,2,3,4,1}
```
```
1
```
```
Returns: 31
```

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