Create Closest Pair of Points O(nlogn).cpp

Templates/Closest Pair of Points O(nlogn).cpp

@@ -0,0 +1,91 @@
+// Source: https://www.tutorialspoint.com/Closest-Pair-of-Points-Problem
+// Divide & Conquer. O(nlogn)
+struct point {
+   float x, y;
+};
+
+int cmpX(point p1, point p2) {    //to sort according to x value
+   return (p1.x < p2.x);
+}
+
+int cmpY(point p1, point p2) {    //to sort according to y value
+   return (p1.y < p2.y);
+}
+
+float dist(point p1, point p2) {    //find distance between p1 and p2
+   return sqrt((p1.x - p2.x)*(p1.x - p2.x) + (p1.y - p2.y)*(p1.y - p2.y));
+}
+
+float findMinDist(point pts[], int n) {    //find minimum distance between two points in a set
+   float min = 9999; // inf val
+   for (int i = 0; i < n; ++i)
+      for (int j = i+1; j < n; ++j)
+         if (dist(pts[i], pts[j]) < min)
+            min = dist(pts[i], pts[j]);
+   return min;
+}
+
+float min(float a, float b) {
+   return (a < b)? a : b;
+}
+
+float stripClose(point strip[], int size, float d) {    //find closest distance of two points in a strip
+   float min = d;
+   for (int i = 0; i < size; ++i)
+      for (int j = i+1; j < size && (strip[j].y - strip[i].y) < min; ++j)
+         if (dist(strip[i],strip[j]) < min)
+            min = dist(strip[i], strip[j]);
+   return min;
+}
+
+float findClosest(point xSorted[], point ySorted[], int n){
+   if (n <= 3)
+      return findMinDist(xSorted, n);
+   int mid = n/2;
+
+   point midPoint = xSorted[mid];
+   point ySortedLeft[mid+1];     // y sorted points in the left side
+   point ySortedRight[n-mid-1];  // y sorted points in the right side
+   intleftIndex = 0, rightIndex = 0;
+
+   for (int i = 0; i < n; i++) {       //separate y sorted points to left and right
+      if (ySorted[i].x <= midPoint.x)
+         ySortedLeft[leftIndex++] = ySorted[i];
+      else
+         ySortedRight[rightIndex++] = ySorted[i];
+   }
+
+   float leftDist = findClosest(xSorted, ySortedLeft, mid);
+   float rightDist = findClosest(ySorted + mid, ySortedRight, n-mid);
+   float dist = min(leftDist, rightDist);
+
+   point strip[n];      //hold points closer to the vertical line
+   int j = 0;
+
+   for (int i = 0; i < n; i++)
+      if (abs(ySorted[i].x - midPoint.x) <dist) {
+         strip[j] = ySorted[i];
+         j++;
+      }
+   return min(dist, stripClose(strip, j, dist));    //find minimum using dist and closest pair in strip
+}
+
+float closestPair(point pts[], int n) {    //find distance of closest pair in a set of points
+   point xSorted[n];
+   point ySorted[n];
+
+   for (int i = 0; i < n; i++) {
+      xSorted[i] = pts[i];
+      ySorted[i] = pts[i];
+   }
+
+   sort(xSorted, xSorted+n, cmpX);
+   sort(ySorted, ySorted+n, cmpY);
+   return findClosest(xSorted, ySorted, n);
+}
+
+int main() {
+   point P[] ={{2, 3}, {12, 30}, {40, 50}, {5, 1}, {12, 10}, {3, 4}};
+   int n = 6;
+   cout<< "The minimum distance is " <<closestPair(P, n);
+}