Divide and Conquer in O(nlogn)

Author: coderick14

closestPair.cpp

@@ -0,0 +1,95 @@
+#include <bits/stdc++.h>
+#define ll long long
+using namespace std;
+
+struct point {
+	ll x;
+	ll y;
+};
+
+bool compX(point a, point b) {
+	return a.x < b.x;
+}
+
+bool compY(point a, point b) {
+	if(a.y < b.y)
+		return true;
+	if(a.y > b.y)
+		return false;
+	return a.x < b.x;
+}
+
+point result1, result2;
+double minDist = DBL_MAX;
+
+double euclideanDistance(point a, point b) {
+	return sqrt(pow(a.x - b.x, 2) + pow(a.y - b.y, 2));
+}
+
+double bruteMin(vector<point> &pointsByX, ll low, ll high) {
+	ll i,j;
+	double dist,bestDistance = DBL_MAX;
+	for(i=low; i<=high; i++) {
+		for(j=i+1; j<=high; j++) {
+			dist = euclideanDistance(pointsByX[i], pointsByX[j]);
+			if(dist < bestDistance) {
+				bestDistance = dist;
+				if(bestDistance < minDist) {
+					minDist = bestDistance;
+					result1 = pointsByX[i];
+					result2 = pointsByX[j];
+				}
+			}
+		}
+	}
+	return bestDistance;
+}
+
+double closestPair(vector<point> &pointsByX, vector<point> &pointsByY, ll low, ll high) {
+	ll i,j,n = high - low + 1;
+	if (n <= 3)	{
+		return bruteMin(pointsByX, low, high);
+	}
+
+	ll mid = low + (high - low)/2;
+
+	double distLeft = closestPair(pointsByX, pointsByY, low, mid);
+	double distRight = closestPair(pointsByX, pointsByY, mid+1, high);
+
+	double bestDistance = min(distLeft, distRight);
+
+	vector<point> pointsInStrip;
+	for(i=0; i<n && abs(pointsByY[i].x - pointsByX[mid].x) < bestDistance; i++) {
+		pointsInStrip.push_back(pointsByY[i]);
+	}
+
+	for(i=0; i<pointsInStrip.size(); i++) {
+		for(j=i+1; j<pointsInStrip.size() && abs(pointsInStrip[i].y - pointsInStrip[j].y) < bestDistance; j++) {
+			double dist = euclideanDistance(pointsInStrip[i], pointsInStrip[j]);
+			if(dist < bestDistance) {
+				bestDistance = dist;
+				result1 = pointsInStrip[i];
+				result2 = pointsInStrip[j];
+			}
+		}
+	}
+
+	return bestDistance;
+}
+
+int main() {
+	ll i,n;
+	cin>>n;
+	vector<point> pointsByX(n), pointsByY(n);
+	for(i=0; i<n; i++) {
+		cin>>pointsByX[i].x>>pointsByX[i].y;
+		pointsByY[i].x = pointsByX[i].x;
+		pointsByY[i].y = pointsByX[i].y;
+	}
+	sort(pointsByX.begin(), pointsByX.end(), compX);
+	sort(pointsByY.begin(), pointsByY.end(), compY);
+
+	cout<<"Shortest distance = "<<closestPair(pointsByX, pointsByY, 0, n-1)<<endl;
+	cout<<"Points are ("<<result1.x<<","<<result1.y<<") and ("<<result2.x<<","<<result2.y<<")\n";
+	return 0;
+}