add the graham scan in go (#402)

* add the graham scan in go

* change the name golang to go

* remove merge marker

Author: Julian

contents/graham_scan/code/golang/graham.go

@@ -0,0 +1,54 @@
+package main
+
+import (
+	"fmt"
+	"math"
+	"sort"
+)
+
+type point struct {
+	x, y int
+}
+
+func counterClockwise(p1, p2, p3 point) bool {
+	return (p3.y-p1.y)*(p2.x-p1.x) >= (p2.y-p1.y)*(p3.x-p1.x)
+}
+
+func polarAngle(ref, point point) float64 {
+	return math.Atan2(float64(point.y-ref.y), float64(point.x-ref.x))
+}
+
+func grahamScan(points []point) []point {
+	sort.Slice(points, func(a, b int) bool {
+		return points[a].y < points[b].y || (points[a].y == points[b].y && points[a].x < points[b].x)
+	})
+
+	start := points[0]
+	points = points[1:]
+
+	sort.Slice(points, func(a, b int) bool {
+		return polarAngle(start, points[a]) < polarAngle(start, points[b])
+	})
+
+	hull := []point{start, points[0], points[1]}
+	for _, p := range points[2:] {
+		for !counterClockwise(hull[len(hull)-2], hull[len(hull)-1], p) {
+			hull = hull[:len(hull)-1]
+		}
+		hull = append(hull, p)
+	}
+
+	return hull
+}
+
+func main() {
+	points := []point{{-5, 2}, {5, 7}, {-6, -12}, {-14, -14}, {9, 9},
+		{-1, -1}, {-10, 11}, {-6, 15}, {-6, -8}, {15, -9},
+		{7, -7}, {-2, -9}, {6, -5}, {0, 14}, {2, 8}}
+
+	fmt.Println("The points in the hull are:")
+	hull := grahamScan(points)
+	for _, p := range hull {
+		fmt.Println(p)
+	}
+}

contents/graham_scan/graham_scan.md

@@ -22,6 +22,8 @@ We can find whether a rotation is counter-clockwise with trigonometric functions
 [import:36-38, lang:"javascript"](code/javascript/graham-scan.js)
 {% sample lang="py" %}
 [import:4-6, lang:"python"](code/python/grahamScan.py)
+{% sample lang="go" %}
+[import:13-15, lang:"go"](code/golang/graham.go)
 {% sample lang="java" %}
 [import:27-29, lang:"java"](code/java/GrahamScan.java)
 {% endmethod %}
@@ -48,6 +50,8 @@ In the end, the code should look something like this:
 [import:1-30, lang:"javascript"](code/javascript/graham-scan.js)
 {% sample lang="py" %}
 [import:14-27, lang:"python"](code/python/grahamScan.py)
+{% sample lang="go" %}
+[import:21-42, lang:"go"](code/golang/graham.go)
 {% sample lang="java" %}
 [import:35-70, lang:"java"](code/java/GrahamScan.java)
 {% endmethod %}
@@ -69,6 +73,8 @@ In the end, the code should look something like this:
 [import, lang:"javascript"](code/javascript/graham-scan.js)
 {% sample lang="py" %}
 [import, lang:"python"](code/python/grahamScan.py)
+{% sample lang="go" %}
+[import, lang:"go"](code/golang/graham.go)
 {% sample lang="java" %}
 [import, lang:"java"](code/java/GrahamScan.java)
 {% endmethod %}