In this post, we will solve **Dice Path HackerRank Solution**. This problem **(Dice Path)** is a part of **HackerRank Functional Programming** series.

**Task**

You are given an *MxN* grid and a 6 sided dice starting at the point (1, 1). You can only move dice toward right or down by rotating it in the respective direction. The value of the dice is the number of pips on the top face of it.

If at *i ^{th}* step dice is rotated to right, then new configuration will be

*Top[i]*=*Left[i-1]**Bottom[i]*=*Right[i-1]**Left[i]*=*Bottom[i-1]**Right[i]*=*Top[i-1]**Front[i]*=*Front[i-1]**Back[i]*=*Back[i-1]*

Similarly, if at *i ^{th}* step dice is rotated down, then new configuration will be

*Top[i]*=*Back[i-1]**Bottom[i]*=*Front[i-1]**Left[i]*=*Left[i-1]**Right[i]*=*Right[i-1]**Front[i]*=*Top[i-1]**Back[i]*=*Bottom[i-1]*

Initially dice is at point (1, 1), and its top face has 1 pip, front face has 2 pips, and left face has 3 pips.

A path sum to a point is the sum of value of dice when it is rolled to that point from (1, 1). As already stated, value at the current location is the number of pips on the top face of the dice. Find the maximum path sum to (*M*, *N*).

**Note**

The sum of pips at each pair of opposing sides is always 7.

**Input**

The first line contains an integer, *T*, which denotes the number of test cases. *T* lines follow.

Each of these lines contains two space separated integers, *M N*, which represent the final point in the grid.

**Output**

For each test case, print the sum of maximal path to (*M*, *N*).

**Constraints**

- 1 ≤
*T*≤ 3600 - 1 ≤
*M, N*≤ 60

**Sample Input #00**

```
4
2 2
1 2
2 1
3 3
```

**Sample Output #00**

```
9
4
6
19
```

**Explanation**

* Case #00:* There are two ways to reach (2, 2). Both’s sum will be 9.

```
Position : (1, 1) -> (1, 2) -> (2, 2)
Direction: Right Down
Value : 1 + 3 + 5 = 9
```

* Case #01:* Dice has to roll toward right only one time.

```
Position : (1, 1) -> (1, 2)
Direction: Right
Value : 1 + 3 = 4
```

* Case #02:* Dice has to roll down only one time.

```
Position : (1, 1) -> (2, 1)
Direction: Down
Value : 1 + 5 = 6
```

* Case #03:* There are six ways in which dice can be rotated to (3, 3)

```
Position : (1, 1) -> (1, 2) -> (1, 3) -> (2, 3) -> (3, 3)
Direction: Right Right Down Down
Value : 1 + 3 + 6 + 5 + 1 = 16
Position : (1, 1) -> (1, 2) -> (2, 2) -> (2, 3) -> (3, 3)
Direction: Right Down Right Down
Value : 1 + 3 + 5 + 6 + 4 = 19
Position : (1, 1) -> (1, 2) -> (2, 2) -> (3, 2) -> (3, 4)
Direction: Right Down Down Right
Value : 1 + 3 + 5 + 4 + 6 = 19
Position : (1, 1) -> (2, 1) -> (2, 2) -> (2, 3) -> (3, 3)
Direction: Down Right Right Down
Value : 1 + 5 + 3 + 2 + 6 = 17
Position : (1, 1) -> (2, 1) -> (2, 2) -> (3, 2) -> (3, 3)
Direction: Down Right Down Right
Value : 1 + 5 + 3 + 6 + 2 = 17
Position : (1, 1) -> (2, 1) -> (3, 1) -> (3, 2) -> (3, 3)
Direction: Down Down Right Right
Value : 1 + 5 + 6 + 3 + 1 = 16
```

So (Right, Down, Right, Down) or (Right, Down, Down, Right) will be best rotations for this case.

**Solution – Dice Path – HackerRank Solution**

**Scala**

import java.util.Scanner import scala.collection.mutable object Solution { private val data = mutable.Map[(Int, Int, Dice), Int]() def main(args: Array[String]): Unit = { val sc = new Scanner(System.in) val t = sc.nextInt println((0 until t).map(_ => solve(sc.nextInt, sc.nextInt)).mkString("\n")) } def solve(m: Int, n: Int): Int = { def inner(m: Int, n: Int, dice: Dice, acc: Int): Int = data.getOrElseUpdate((m, n, dice), if (m < 0 || n < 0) 0 else math.max(inner(m - 1, n, dice.turnFront, dice.top), inner(m, n - 1, dice.turnRight, dice.top)) ) + acc inner(m - 1, n - 1, Dice(1, 2, 3), 0) } case class Dice(top: Int, front: Int, left: Int) { private val pairwiseSum = 7 def right: Int = pairwiseSum - left def turnRight: Dice = Dice(left, front, bottom) def bottom: Int = pairwiseSum - top def turnFront: Dice = Dice(back, top, left) def back: Int = pairwiseSum - front } }

**Note:** This problem **(Dice Path)** is generated by **HackerRank** but the solution is provided by **CodingBroz**. This tutorial is only for **Educational** and **Learning** purpose.