Graham扫描法求凸包（附CodeVS - 1298 凸包周长代码）

Graham-Scan.cpp

@@ -0,0 +1,149 @@
+#include <cstdio>
+#include <cmath>
+
+#define POINT_COUNT 100000
+
+using namespace std;
+
+struct point
+{
+	int x, y;
+}P[POINT_COUNT];
+
+struct segment
+{
+	point begin, end;
+}D[POINT_COUNT];
+
+int S[POINT_COUNT], sp = 0;
+
+int n;
+
+void push(int x)
+{
+	S[sp++] = x;
+}
+
+int pop()
+{
+	return S[--sp];
+}
+
+int top()
+{
+	return S[sp - 1];
+}
+
+int subtop()
+{
+	return S[sp - 2];
+}
+
+int direction(segment &base, segment &s)
+{
+	return (s.end.x - s.begin.x) * (base.end.y - base.begin.y) - (base.end.x - base.begin.x) * (s.end.y - s.begin.y);
+}
+
+double distance(point &x, point &y)
+{
+	return sqrt(pow(x.x - y.x, 2) + pow(x.y - y.y, 2));
+}
+
+void qsort(int l, int r)
+{
+	if (l < r)
+	{
+		segment x = D[r];
+		int j = l - 1;
+		for (int i = l; i <= r; i++)
+		{
+			if (direction(x, D[i]) >= 0)
+			{
+				j++;
+				segment temps = D[i];
+				D[i] = D[j];
+				D[j] = temps;
+				point tempp = P[i];
+				P[i] = P[j];
+				P[j] = tempp;
+			}
+		}
+		qsort(l, j - 1);
+		qsort(j + 1, r);
+	}
+}
+
+int main()
+{
+	scanf("%d", &n);
+	for (int i = 0; i < n; i++)
+	{
+		scanf("%d%d", &P[i].x, &P[i].y);
+	}
+	int p0 = 0;
+	for (int i = 1; i < n; i++)
+	{
+		if (P[i].x < P[p0].x)
+		{
+			p0 = i;
+		}
+		else if (P[i].x == P[p0].x)
+		{
+			if (P[i].y < P[p0].y)
+			{
+				p0 = i;
+			}
+		}
+	}
+	point temp = P[p0];
+	P[p0] = P[0];
+	P[0] = temp;
+	for (int i = 1; i < n; i++)
+	{
+		D[i].begin = P[0];
+		D[i].end = P[i];
+	}
+	qsort(1, n - 1);
+	push(0);
+	for (int i = 1; i < n; i++)
+	{
+		if (sp >= 2)
+		{
+			if (direction(D[i], D[top()]) == 0)
+			{
+				if (P[i].x > P[top()].x)
+				{
+					pop();
+				}
+				else
+				{
+					continue;
+				}
+			}
+			int dir;
+			do
+			{
+				segment base, toward;
+				base.begin = P[subtop()];
+				base.end = P[top()];
+				toward.begin = P[top()];
+				toward.end = P[i];
+				dir = direction(base, toward);
+				if (dir > 0)
+				{
+					pop();
+				}
+			} while (dir > 0);
+		}
+		push(i);
+	}
+	double res = 0;
+	for (int i = 1; i < sp; i++)
+	{
+		res += distance(P[S[i]], P[S[i - 1]]);
+	}
+	res += distance(P[S[sp - 1]], P[0]);
+	printf("%.1lf", res);
+
+	return 0;
+}