BearDartsDiv2 | Topcoder Archive

Problem Statement

Limak is an old brown bear who likes to play darts.

Limak just picked up an empty scorecard. He then threw a sequence of darts into a dartboard and for each dart he recorded the point value of the area it hit. You are given a int[] w containing the contents of Limak's scorecard: a sequence of point values.

Today there is a special jackpot. In order to win the jackpot, the player must present a scorecard with exactly four scores: (a, b, c, d). Additionally, these scores must be such that a*b*c = d. Note that order matters: the scores a, b, c, d must have been obtained in this particular order.

Limak wants to erase all but four scores from his scorecard in such a way that he will win the jackpot. Compute and return the number of different ways in which he can do that.

Definition

Class:: BearDartsDiv2
Method:: count
Parameters:: int[]
Returns:: long
Method signature:: long count(int[] w)
(be sure your method is public)

Notes

Pay attention to the unusual time limit.

Constraints

w will contain between 4 and 500 elements, inclusive.
Each element in w will be between 1 and 10^6, inclusive.

Examples

```
{10,2,2,7,40,160}
```
```
Returns: 2
```
Limak must erase two of the six scores on his scorecard. There are two ways to do that and win the jackpot: Erase the elements on 0-based indices 3 and 5. You are left with (a,b,c,d) = (10,2,2,40), and 10*2*2 = 40. Erase the elements on 0-based indices 0 and 3. You are left with (a,b,c,d) = (2,2,40,160), and 2*2*40 = 160.
```
{128,64,32,16,8,4,2,1}
```
```
Returns: 0
```
Regardless of which four scores Limak erases, the remaining four will always have a > b > c > d and therefore it cannot be the case that a*b*c = d.

{2,3,4,5,6,8,12,16,20,24,40,24,20,16,12,8,6,5,4,3,2}

Returns: 3

{100,100,100,1000000,1000000,1000000,1000000,1000000}

Returns: 5

{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

Returns: 2573031125

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