go: add «689. Maximum Sum of 3 Non-Overlapping Subarrays»

URL:	https://leetcode.com/problems/maximum-sum-of-3-non-overlapping-subarrays/
Signed-off-by: Matej Focko <me@mfocko.xyz>

go/maximum-sum-of-3-non-overlapping-subarrays.go

@@ -0,0 +1,47 @@
+package main
+
+type Solution struct {
+	Sum   int
+	Index int
+}
+
+func (s *Solution) Update(previous *Solution, sum, index int) {
+	if sum > previous.Sum {
+		s.Sum = sum
+		s.Index = index
+		return
+	}
+
+	s.Sum = previous.Sum
+	s.Index = previous.Index
+}
+
+func maxSumOfThreeSubarrays(nums []int, k int) []int {
+	n := len(nums)
+
+	prefix := make([]int, n+1)
+	for i := 1; i <= n; i++ {
+		prefix[i] = prefix[i-1] + nums[i-1]
+	}
+
+	best := make([][]Solution, 4)
+	for i, _ := range best {
+		best[i] = make([]Solution, n+1)
+	}
+
+	for subarrays := 1; subarrays <= 3; subarrays++ {
+		for end := k * subarrays; end <= n; end++ {
+			current := prefix[end] - prefix[end-k] + best[subarrays-1][end-k].Sum
+			best[subarrays][end].Update(&best[subarrays][end-1], current, end-k)
+		}
+	}
+
+	result := make([]int, 3)
+	end := n
+	for index := 3; index >= 1; index-- {
+		result[index-1] = best[index][end].Index
+		end = result[index-1]
+	}
+
+	return result
+}