From 8d0ff58f90a9af22e6e468de1b27650063cc9c1c Mon Sep 17 00:00:00 2001
From: Rootul Patel <rootulp@gmail.com>
Date: Mon, 12 Aug 2024 22:15:00 -0400
Subject: [PATCH] solve knapsack

---
 go/knapsack/knapsack.go | 45 +++++++++++++++++++++--------------------
 1 file changed, 23 insertions(+), 22 deletions(-)

diff --git a/go/knapsack/knapsack.go b/go/knapsack/knapsack.go
index 992e160e..d7e0d5b0 100644
--- a/go/knapsack/knapsack.go
+++ b/go/knapsack/knapsack.go
@@ -1,10 +1,5 @@
 package knapsack
 
-import (
-	"fmt"
-	"sort"
-)
-
 type Item struct {
 	Weight, Value int
 }
@@ -12,24 +7,30 @@ type Item struct {
 // Knapsack takes in a maximum carrying capacity and a collection of items
 // and returns the maximum value that can be carried by the knapsack
 // given that the knapsack can only carry a maximum weight given by maximumWeight
-func Knapsack(maximumWeight int, items []Item) (maxValue int) {
-	sorted := sortItemsByValuePerWeight(items)
-	fmt.Printf("sorted: %v\n", sorted)
-	currentWeight := maximumWeight
-	for _, item := range sorted {
-		if item.Weight <= currentWeight {
-			currentWeight -= item.Weight
-			maxValue += item.Value
-		}
+func Knapsack(maximumWeight int, items []Item) (total int) {
+	currentValue := 0
+	currentWeight := 0
+	return knapsack(items, currentValue, currentWeight, maximumWeight)
+}
+
+func knapsack(items []Item, value int, weight int, maxWeight int) (total int) {
+	if len(items) == 0 {
+		return value
 	}
-	return maxValue
+	item := items[0]
+	totalWithItem := knapsack(items[1:], value+item.Value, weight+item.Weight, maxWeight)
+	totalWithoutItem := knapsack(items[1:], value, weight, maxWeight)
+
+	// If the current item is too heavy, return the total without the current item
+	if weight+item.Weight > maxWeight {
+		return totalWithoutItem
+	}
+	return max(totalWithItem, totalWithoutItem)
 }
 
-func sortItemsByValuePerWeight(items []Item) []Item {
-	sort.Slice(items, func(i, j int) bool {
-		iValuePerWeight := float64(items[i].Value) / float64(items[i].Weight)
-		jValuePerWeight := float64(items[j].Value) / float64(items[j].Weight)
-		return iValuePerWeight > jValuePerWeight
-	})
-	return items
+func max(a int, b int) int {
+	if a > b {
+		return a
+	}
+	return b
 }