二次元でギフト包装アルゴリズムを実装するためのC++プログラム

ギフト包装アルゴリズムを2次元で実装するC++プログラムを開発します。ギフト包装アルゴリズムは、特定の点のセットの凸包を計算するためのアルゴリズムです。

アルゴリズム

Begin
   function convexHull() to find convex hull of a set of n points:
   There must be at least three points.
   Initialize the result.
   Find the leftmost point.
   Starting from leftmost point, keep moving counterclockwise
   until reach the start point again.
   Print the result.
End

サンプルコード

#include <iostream>
using namespace std;
#define INF 10000
struct P {
   int x;
   int y;
};
int orient(P a, P b, P c) {
   int v = (b.y - a.y) * (c.x - b.x) - (b.x - a.x) * (c.y - b.y);
   if (v == 0)
      return 0; // colinear
      return (v >0) ? 1 : 2; // clock or counterclock wise
}
void convexHull(P points[], int m) {
   if (m < 3)//at least three points required
      return;
   int n[m];
   for (int i = 0; i < m; i++)
      n[i] = -1;
      int l = 0;//initialize result.
   for (int i = 1; i < m; i++)
      if (points[i].x < points[l].x)
         l = i; //find left most point
         int p = l, q;
   do {
      q = (p + 1) % m;
      for (int i = 0; i < m; i++)
         if (orient(points[p], points[i], points[q]) == 2)
            q = i;
            n[p] = q;
            p = q;
   } while (p != l);
   for (int i = 0; i < m; i++) {
      if (n[i] != -1)
         cout << "(" << points[i].x << ", " << points[i].y << ")\n";
   }
}
int main() {
   P points[] = {{0, 4}, {2, 1}, {2, 3}, {4, 1}, {3, 0}, {1, 1}, {7, 6}};
   cout << "The points in the convex hull are: ";
   int n = sizeof(points) / sizeof(points[0]);
   convexHull(points, n);
   return 0;
}

出力

The points in the convex hull are: (0, 4)
(4, 1)
(3, 0)
(1, 1)
(7, 6)