problem11.go

package projecteuler

var arr [][]int = [][]int{
	{8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8},
	{49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0},
	{81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65},
	{52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91},
	{22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80},
	{24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50},
	{32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70},
	{67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21},
	{24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72},
	{21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95},
	{78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92},
	{16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57},
	{86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58},
	{19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40},
	{4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66},
	{88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69},
	{4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36},
	{20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16},
	{20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54},
	{1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48}}

// first explore neighbours, from a given index with in GRID
//
// there'll be at most 8 possible neighbor sequence, i.e.
// 1 > left
// 2 > right
// 3 > top
// 4 > down
// 5 > top-left
// 6 > top-right
// 7 > bottom-left
// 8 > bottom-right
//
// now along these directions, we'll pick up specified number of elements from
// GRID, given that there does exist some element in certain index
// ( otherwise program will panic, due to out of index error )
//
// A 2D array of those neighbors to be returned
func exploreNeighbors(i int, j int, count int, sizeR int, sizeC int) [][]int {
	neighbors := [][]int{}
	// along top
	if i-count+1 >= 0 {
		tmp := []int{}
		for x := i; x > i-count; x-- {
			tmp = append(tmp, arr[x][j])
		}
		neighbors = append(neighbors, tmp)
	}
	// along down
	if i+count-1 < sizeR {
		tmp := []int{}
		for x := i; x < i+count; x++ {
			tmp = append(tmp, arr[x][j])
		}
		neighbors = append(neighbors, tmp)
	}
	// along left
	if j-count+1 >= 0 {
		tmp := []int{}
		for x := j; x > j-count; x-- {
			tmp = append(tmp, arr[i][x])
		}
		neighbors = append(neighbors, tmp)
	}
	// along right
	if j+count-1 < sizeC {
		tmp := []int{}
		for x := j; x < j+count; x++ {
			tmp = append(tmp, arr[i][x])
		}
		neighbors = append(neighbors, tmp)
	}
	// along bottom-right
	if i+count-1 < sizeR && j+count-1 < sizeC {
		tmp := []int{}
		for x, y := i, j; x < i+count && y < j+count; {
			tmp = append(tmp, arr[x][y])
			x++
			y++
		}
		neighbors = append(neighbors, tmp)
	}
	// along top-left
	if i-count+1 >= 0 && j-count+1 >= 0 {
		tmp := []int{}
		for x, y := i, j; x > i-count && y > j-count; {
			tmp = append(tmp, arr[x][y])
			x--
			y--
		}
		neighbors = append(neighbors, tmp)
	}
	// along bottom-left
	if i+count-1 < sizeR && j-count+1 >= 0 {
		tmp := []int{}
		for x, y := i, j; x < i+count && y > j-count; {
			tmp = append(tmp, arr[x][y])
			x++
			y--
		}
		neighbors = append(neighbors, tmp)
	}
	// along top-right
	if i-count+1 >= 0 && j+count-1 < sizeC {
		tmp := []int{}
		for x, y := i, j; x > i-count && y < j+count; {
			tmp = append(tmp, arr[x][y])
			x--
			y++
		}
		neighbors = append(neighbors, tmp)
	}
	return neighbors
}

// given that, we've already retrieved all neighbors for a certain
// index in GRID, we need to now calculate max product ( of elements ) from these sequences
// i.e. which inner array produces max product, among all arrays present in outer array
func getMaxProdFromNeighbors(neighbors [][]int) int {
	maxProd := 0
	for i := 0; i < len(neighbors); i++ {
		prod := 1
		for _, j := range neighbors[i] {
			prod *= j
		}
		if prod > maxProd {
			maxProd = prod
		}
	}
	return maxProd
}

// LargestProductInGrid - Finds largest product, found by multiplying
// element sequences, along any of these directions left, right, up, down or diagonally
// i.e. possible 8 directions ( at max from any index in GRID )
func LargestProductInGrid() int {
	maxProd := 0
	for i := 0; i < len(arr); i++ {
		for j := 0; j < len(arr[i]); j++ {
			if tmp := getMaxProdFromNeighbors(exploreNeighbors(i, j, 4, 20, 20)); tmp > maxProd {
				maxProd = tmp
			}
		}
	}
	return maxProd
}