Add knapsack implementation.

knapsack.cr

@@ -0,0 +1,40 @@
+class Array(T)
+  def knapsack(budget, &cv : T -> {Int32,Int32})
+    cost_values = map &cv
+
+    memo = {} of {Int32, Int32} => Int32
+    bt = {} of {Int32, Int32} => Bool
+    compute = uninitialized Int32, Int32 -> Int32
+    compute = ->(size : Int32, budget : Int32) {
+      if m = memo[{size, budget}]?
+        return m 
+      end
+      return memo[{size, budget}] = 0 if size == 0
+
+      cost, value = cost_values[size-1]
+      no_val = compute.call(size-1, budget)
+      yes_val = (budget < cost) ? 0 : compute.call(size-1, budget - cost) + value  
+
+      if yes_val > no_val
+        bt[{size, budget}] = true
+        return yes_val
+      else
+        bt[{size, budget}] = false
+        return no_val
+      end
+    }
+
+    value = compute.call(size, budget)
+    i = size
+    items = [] of T
+    puts bt
+    while i != 0
+      if bt[{i, budget}]
+        items << self[i-1]
+        budget -= cost_values[i-1][0]
+      end
+      i -= 1
+    end
+    {value, items}
+  end
+end