Hard

We're having trouble loading the toys onto Santa's 🎅 sleigh 🛷! It seems like the toy distribution isn't quite right and the sleigh can't take off. Could you help us solve this problem?

To solve it we've decided to use a method similar to that of an image filter. At each position, we're going to distribute the load of the toys based on the number of toys in the neighboring positions.

A neighboring position is one that is above, below, to the left, or to the right of the current position. Therefore, positions diagonally are not considered neighbors.

Write a function distributeGifts that receives a matrix of numbers representing the toys in the sleigh and returns another matrix of the same size and number of elements but where each element is the average of its original value and the values of its neighbors.

Bear in mind that there are positions that are null and that won't count for the average as a neighbor but will indeed be replaced by the average value of its neighbors.

For example, let's look at a complete example:

const input = [
  [4, 5, 1],
  [6, null, 3],
  [8, null, 4]
]

distributeGifts(input)

// Step by step result of the first few calculations:

// At position [0][0] we have the value 4
// Its neighbors are the values 5 and 6
// (4 + 5 + 6) / 3 = 5

// At position [0][1] we have the value 5
// Its neighbors are the values 4 and 1
// (5 + 4 + 1) / 3 = 3.33
// Math.round(3.33) = 3

// At position [0][2] we have the value 1
// Its neighbors are the values 5 and 3
// (1 + 5 + 3) / 3 = 3

// At position [1][0] we have the value 6
// Its neighbors are the values 4, 8
// (6 + 4 + 8 ) / 3 = 6

// At position [1][1] we have the value null
// Its neighbors are the values 5, 6 and 3
// (5 + 6 + 3) / 3 = 4.66
// Math.round(4.66) = 5
// ... and so on with the rest of the positions
[
  [(4 + 5 + 6) / 3, (5 + 4 + 1) / 3, (1 + 5 + 3) / 3],
  [(6 + 4 + 8) / 3, (5 + 6 + 3) / 3, (3 + 1 + 4) / 3],
  [(8 + 6) / 2, (8 + 4) / 2, (4 + 3) / 2]
]

// Final result after rounding with Math.round()
[
  [5, 3, 3],
  [6, 5, 3],
  [7, 6, 4]
]

Please note:

  • Matrices are not always square, they can have more rows than columns or vice versa.
  • To round off the values, you should use the Math.round() function from JavaScript.
  • Null values are not counted for calculating the average but they are replaced by the average value of their neighbors.
  • The edges of the matrix have fewer possible neighbors than the rest of the positions.
  • They are always positive integers.