KnapSack Problem Recursion and Memoization

Author: gokivego

DynamicProgramming/KnapSack.go

@@ -0,0 +1,60 @@
+/*
+Knap Sack Problem. 
+*/
+
+package main
+
+import ("fmt"
+)
+
+// Returns the max value of the KnapSack
+func KnapSackRecursion(ItemWeight,ItemValue []int,n,c int) int {
+    if (n == 0 || c == 0) {
+        return 0
+    } else if (ItemWeight[n-1] > c) {
+        return KnapSackRecursion(ItemWeight,ItemValue,n-1,c)
+    } else {
+        tmp1 := KnapSackRecursion(ItemWeight,ItemValue,n-1,c)
+        tmp2 := ItemValue[n-1] + KnapSackRecursion(ItemWeight,ItemValue,n-1,c-ItemWeight[n-1])
+        if tmp1 >= tmp2 {
+            return tmp1
+        } else {
+            return tmp2
+        }
+    }
+}
+
+// Memoized  version of the problem, which minimizes recusrsion
+func KnapSackMemoization(MemoizedMap map[string]int,ItemWeight,ItemValue []int,n,c int) int { 
+    nc := fmt.Sprintf("%d:%d",n,c)
+    if val,ok := MemoizedMap[nc];ok {
+        return val
+    }
+    if (n == 0 || c == 0) {
+        return 0
+    } else if (ItemWeight[n-1] > c) {
+        return KnapSackMemoization(MemoizedMap,ItemWeight,ItemValue,n-1,c)
+    } else {
+        tmp1 := KnapSackMemoization(MemoizedMap,ItemWeight,ItemValue,n-1,c)
+        tmp2 := ItemValue[n-1] + KnapSackMemoization(MemoizedMap,ItemWeight,ItemValue,n-1,c-ItemWeight[n-1])
+        if tmp1 >= tmp2 {
+            MemoizedMap[nc] = tmp1
+        } else {
+            MemoizedMap[nc] = tmp2
+        }
+        return MemoizedMap[nc]
+    }
+}
+
+func main() {
+    capacity := 10
+    n := 5
+    ItemWeight := []int {1,2,4,2,5}
+    ItemValue := []int {5,3,5,3,2}
+    var MemoizedMap =  make(map[string]int)
+    valueRecursive := KnapSackRecursion(ItemWeight,ItemValue,n,capacity)
+    fmt.Println("The max value in the knapsack from Recursion is:",valueRecursive)
+    valueMemoized := KnapSackMemoization(MemoizedMap,ItemWeight,ItemValue,n,capacity)
+    fmt.Println("The max value in the knapsack from Memoization is:",valueMemoized)
+    
+}

DynamicProgramming/KnapSack_test.go

@@ -0,0 +1,33 @@
+/*
+KnapSack problem Unit Test
+*/
+
+package main
+
+import ("testing")
+
+func TestKnapSack(t *testing.T) {
+
+    ItemWeight := []int {1,2,4,2,5}
+    ItemValue := []int {5,3,5,3,2}
+    var MemoizedMap = make(map[string]int)
+    n := 5
+
+    tables := []struct {
+        capacity,maxValue int
+    } {
+        {1,5},
+        {2,5},
+        {4,8},
+        {5,11},
+        {6,11},
+    }
+
+    for _,table := range tables {
+        //total := KnapSackRecursion(ItemWeight,ItemValue,n,table.capacity)
+        total := KnapSackMemoization(MemoizedMap,ItemWeight,ItemValue,n,table.capacity)
+        if total != table.maxValue {
+            t.Errorf("KnapSack value of capacity %d is incorrect, got:%d, want: %d.",table.capacity,total,table.maxValue)
+        }
+    }
+}