Write initial version of the library.

spec/advent_spec.cr

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+require "./spec_helper"

spec/graph_spec.cr

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+require "./spec_helper"
+
+describe Graph do
+  describe "#find_path" do
+    it "reports no paths in a graph with no edges" do
+      gr = Graph(String).new
+      elems = ["a", "b", "c", "d"]
+      elems.each &->gr.add_node(String)
+      elems.each do |elem|
+        elems.each do |other|
+          next if elem == other
+          gr.find_path(elem, other).should be_nil
+        end
+      end
+    end
+
+    it "computes the shortest path" do
+      gr = Graph(String).new
+      [{"a", "b", 1}, {"a", "c", 1}, {"c", "b", 1}, {"b", "d", 1}].each do |t|
+        from, to, cost = t
+        gr.add_edge(from, to, cost)
+      end
+      gr.find_path("a", "d").should eq({["a", "b", "d"], 2})
+    end
+  end
+end

spec/heap_spec.cr

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+require "./spec_helper"
+
+describe Array do
+  describe "#heapify" do
+    it "preserves the elements in the array" do
+      a = Array(Int32).new(20) { rand(10) }
+      a.sort.should eq(a.clone.heapify!.sort)
+    end
+
+    it "creates an array with proper ordering" do
+      a = Array(Int32).new(20) { rand(10) }
+      a.heapify!
+      a.is_heap?.should be_true
+    end
+
+    it "maintains heap property while popping" do
+      a = Array(Int32).new(20) { rand(10) }
+      a.heapify!
+      20.times do |i|
+        a.heap_pop
+        a.is_heap?.should be_true
+      end
+    end
+
+    it "maintains heap property while pushing" do
+      a = [] of Int32
+      20.times do 
+        a.heap_push(rand 10)
+        a.is_heap?.should be_true
+      end
+    end
+
+    it "pops numbers in descending order" do
+      a = Array(Int32).new(20) { rand(10) }
+      a.heapify!
+      last = Int32::MAX
+      20.times do
+        popped = a.heap_pop
+        popped.should be <= last
+        last = popped
+      end
+    end
+  end
+end

spec/knapsack_spec.cr

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+describe Array do
+  describe "#knapsack" do
+    it "works with costs of one" do
+      ans = [1,2,3,4,5,6].shuffle.knapsack(3) do |i|
+        {1, i}
+      end
+      ans[1].sort!
+      ans.should eq({15, [4,5,6]})
+    end
+
+    it "works in the non-greedy case" do
+      ans = [{2, 2}, {2, 2}, {3, 3}].shuffle.knapsack(4) do |i|
+        i
+      end
+      ans.should eq({4, [{2,2},{2,2}]})
+    end
+  end
+end

spec/spec_helper.cr

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+require "spec"
+require "../src/advent"