adding knapsack (TheAlgorithms#19)

src/TheAlgorithms.jl

@@ -12,6 +12,10 @@ using Random
 ## Exports
 # Please keep the folders/functions sorted
 
+# Exports: knapsack
+export ZeroOnePack!
+export CompletePack!
+
 # Exports: math
 export collatz_sequence
 export euler_method
@@ -42,6 +46,9 @@ export is_palindrome
 ## Includes
 # Please keep the folders/files sorted (by dependencies then alphabetical order)
 
+# Includes: knapsack
+include("knapsack/knapsack.jl")
+
 # Includes: math
 include("math/area_under_curve.jl")
 include("math/collatz_sequence.jl")

src/knapsack/knapsack.jl

@@ -0,0 +1,47 @@
+"""
+This does 0-1 (each item can be chosen only once) knapsack :
+pack capacity = capacity
+weight of each item = weights
+value of each item = values
+dp array is what the function works on
+It returns the ans (dp[capacity])
+```
+julia> dp=zeros(Int,30)
+julia> ZeroOnePack!(20,[1,3,11],[2,5,30],dp)
+37
+```
+"""
+function ZeroOnePack!(capacity::N,weights::V,values::V,dp::V)where N<:Number where V<:AbstractVector
+    for i in 1:length(weights)
+        j=capacity
+        while j>weights[i] # reversed loop
+            dp[j]=max(dp[j],dp[j-weights[i]]+values[i])
+            j-=1
+        end
+        dp[weights[i]]=max(dp[weights[i]],values[i]) # dp[j]=max(dp[j],dp[0]+values[i])
+    end
+    return dp[capacity]
+end
+
+"""
+This does complete/infinite (each item can be chosen infinite times) knapsack :
+pack capacity = capacity
+weight of each item = weights
+value of each item = values
+dp array is what the function works on
+It returns the ans (dp[capacity])
+```
+julia> dp=zeros(Int,30)
+julia> CompletePack!(20,[1,2,9],[1,3,20],dp)
+43
+```
+"""
+function CompletePack!(capacity::N,weights::V,values::V,dp::V)where N<:Number where V<:AbstractVector
+    for i in 1:length(weights)
+        dp[weights[i]]=max(dp[weights[i]],values[i]) # dp[j]=max(dp[j],dp[0]+values[i])
+        for j in weights[i]+1:capacity
+            dp[j]=max(dp[j],dp[j-weights[i]]+values[i])
+        end
+    end
+    return dp[capacity]
+end

test/knapsack.jl

@@ -0,0 +1,17 @@
+@testset "Knapsack" begin
+
+@testset "Knapsack: ZeroOnePack!" begin
+    dp=zeros(Int,30)
+    @test ZeroOnePack!(20,[1,3,11],[2,5,30],dp) == 37
+    dp=zeros(Int,30)
+    @test ZeroOnePack!(10,[1,3,11],[20,5,80],dp) == 25
+end
+
+@testset "Knapsack: CompletePack!" begin
+    dp=zeros(Int,30)
+    @test CompletePack!(20,[1,2,9],[1,3,20],dp) == 43
+    dp=zeros(Int,30)
+    @test CompletePack!(10,[1,3,11],[20,5,80],dp) == 200
+end
+
+end

test/runtests.jl

@@ -10,6 +10,7 @@ using Random
 
 @testset "TheAlgorithms" begin
 
+include("knapsack.jl")
 include("math.jl")
 include("matrix.jl")
 include("project-rosalind.jl")