From b2b260de43cad7fbd91783e2699ab5a225998dfa Mon Sep 17 00:00:00 2001
From: Vasko Zdravevski <vaskoz@users.noreply.github.com>
Date: Wed, 19 Sep 2018 11:36:32 -0600
Subject: [PATCH] skyline problem

---
 skyline/README.md       |  1 +
 skyline/problem.go      | 87 +++++++++++++++++++++++++++++++++++++++++
 skyline/problem_test.go | 37 ++++++++++++++++++
 3 files changed, 125 insertions(+)
 create mode 100644 skyline/README.md
 create mode 100644 skyline/problem.go
 create mode 100644 skyline/problem_test.go

diff --git a/skyline/README.md b/skyline/README.md
new file mode 100644
index 0000000..11c0557
--- /dev/null
+++ b/skyline/README.md
@@ -0,0 +1 @@
+# Skyline problem
diff --git a/skyline/problem.go b/skyline/problem.go
new file mode 100644
index 0000000..9b4319e
--- /dev/null
+++ b/skyline/problem.go
@@ -0,0 +1,87 @@
+package skyline
+
+import (
+	"container/heap"
+	"sort"
+)
+
+// Point represents a 0-dimensional geometric point.
+type Point struct {
+	X, Y int
+}
+
+// Building represents a 2-dimensional representation of a building in a skyline.
+type Building struct {
+	LeftX, RightX, Height int
+}
+
+type edge struct {
+	X, Height int
+	Up        bool
+}
+
+// HeightHeap is a max-heap of building heights.
+type HeightHeap []int
+
+func (h HeightHeap) Len() int           { return len(h) }
+func (h HeightHeap) Less(i, j int) bool { return h[i] > h[j] }
+func (h HeightHeap) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }
+
+// Push adds a new height to the heap.
+func (h *HeightHeap) Push(x interface{}) {
+	*h = append(*h, x.(int))
+}
+
+// Pop removes and returns the max height from the heap.
+func (h *HeightHeap) Pop() interface{} {
+	old := *h
+	n := len(old)
+	x := old[n-1]
+	*h = old[0 : n-1]
+	return x
+}
+
+// Skyline returns all the points describing a skyline silhouette.
+// Runs in O(N log N) time with some extra space O(N)
+func Skyline(buildings []Building) []Point {
+	edges := make([]edge, 0, 2*len(buildings))
+	for _, building := range buildings {
+		edges = append(edges, edge{building.LeftX, building.Height, true})
+		edges = append(edges, edge{building.RightX, building.Height, false})
+	}
+	sort.Slice(edges, func(i, j int) bool {
+		return edges[i].X < edges[j].X
+	})
+	var points []Point
+	h := &HeightHeap{}
+	heap.Init(h)
+	for _, edge := range edges {
+		if edge.Up {
+			if h.Len() == 0 {
+				points = append(points, Point{edge.X, 0})
+				points = append(points, Point{edge.X, edge.Height})
+			} else if edge.Height > (*h)[0] {
+				points = append(points, Point{edge.X, (*h)[0]})
+				points = append(points, Point{edge.X, edge.Height})
+			}
+			heap.Push(h, edge.Height)
+		} else if !edge.Up {
+			var removeIndex int
+			for i, v := range *h {
+				if v == edge.Height {
+					removeIndex = i
+					break
+				}
+			}
+			heap.Remove(h, removeIndex)
+			if h.Len() == 0 {
+				points = append(points, Point{edge.X, edge.Height})
+				points = append(points, Point{edge.X, 0})
+			} else if edge.Height > (*h)[0] {
+				points = append(points, Point{edge.X, edge.Height})
+				points = append(points, Point{edge.X, (*h)[0]})
+			}
+		}
+	}
+	return points
+}
diff --git a/skyline/problem_test.go b/skyline/problem_test.go
new file mode 100644
index 0000000..c4af310
--- /dev/null
+++ b/skyline/problem_test.go
@@ -0,0 +1,37 @@
+package skyline
+
+import (
+	"reflect"
+	"testing"
+)
+
+var testcases = []struct {
+	buildings []Building
+	expected  []Point
+}{
+	{[]Building{
+		{5, 7, 10},
+		{8, 20, 5},
+		{9, 12, 7},
+		{10, 15, 12},
+		{18, 25, 6},
+	},
+		[]Point{{5, 0}, {5, 10}, {7, 10}, {7, 0}, {8, 0}, {8, 5}, {9, 5}, {9, 7}, {10, 7}, {10, 12},
+			{15, 12}, {15, 5}, {18, 5}, {18, 6}, {25, 6}, {25, 0}}},
+}
+
+func TestSkyline(t *testing.T) {
+	for _, tc := range testcases {
+		if skyline := Skyline(tc.buildings); !reflect.DeepEqual(skyline, tc.expected) {
+			t.Errorf("Expected %v got %v", tc.expected, skyline)
+		}
+	}
+}
+
+func BenchmarkSkyline(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		for _, tc := range testcases {
+			Skyline(tc.buildings)
+		}
+	}
+}