// A divide and conquer program in C/C++ to find the smallest distance from a// given set of points. #include <stdio.h>#include <float.h>#include <stdlib.h>#include <math.h> // A structure to represent a Point in 2D planestruct Point{ int x, y;}; /* Following two functions are needed for library function qsort(). Refer: http://www.cplusplus.com/reference/clibrary/cstdlib/qsort/ */ // Needed to sort array of points according to X coordinateint compareX(const void* a, const void* b){ Point *p1 = (Point *)a, *p2 = (Point *)b; return (p1->x - p2->x);}// Needed to sort array of points according to Y coordinateint compareY(const void* a, const void* b){ Point *p1 = (Point *)a, *p2 = (Point *)b; return (p1->y - p2->y);} // A utility function to find the distance between two pointsfloat dist(Point p1, Point p2){ return sqrt( (p1.x - p2.x)*(p1.x - p2.x) + (p1.y - p2.y)*(p1.y - p2.y) );} // A Brute Force method to return the smallest distance between two points// in P[] of size nfloat bruteForce(Point P[], int n){ float min = FLT_MAX; for (int i = 0; i < n; ++i) for (int j = i+1; j < n; ++j) if (dist(P[i], P[j]) < min) min = dist(P[i], P[j]); return min;} // A utility function to find minimum of two float valuesfloat min(float x, float y){ return (x < y)? x : y;} // A utility function to find the distance beween the closest points of// strip of given size. All points in strip[] are sorted accordint to// y coordinate. They all have an upper bound on minimum distance as d.// Note that this method seems to be a O(n^2) method, but it's a O(n)// method as the inner loop runs at most 6 timesfloat stripClosest(Point strip[], int size, float d){ float min = d; // Initialize the minimum distance as d qsort(strip, size, sizeof(Point), compareY); // Pick all points one by one and try the next points till the difference // between y coordinates is smaller than d. // This is a proven fact that this loop runs at most 6 times/* 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]); */for (int i = 0; i < size - 7; ++i)for (int j = i + 1; j < i + 8 && (strip[j].y - strip[i].y) < min; ++j)if(dist(strip[i], strip[j]) < min) min = dist(strip[i], strip[j]); return min;} // A recursive function to find the smallest distance. The array P contains// all points sorted according to x coordinatefloat closestUtil(Point P[], int n){ // If there are 2 or 3 points, then use brute force if (n <= 3) return bruteForce(P, n); // Find the middle point int mid = n/2; Point midPoint = P[mid]; // Consider the vertical line passing through the middle point // calculate the smallest distance dl on left of middle point and // dr on right side float dl = closestUtil(P, mid); float dr = closestUtil(P + mid, n-mid); // Find the smaller of two distances float d = min(dl, dr); // Build an array strip[] that contains points close (closer than d) // to the line passing through the middle point Point strip[n]; int j = 0; for (int i = 0; i < n; i++) if (abs(P[i].x - midPoint.x) < d) strip[j] = P[i], j++; // Find the closest points in strip. Return the minimum of d and closest // distance is strip[] return min(d, stripClosest(strip, j, d) );} // The main functin that finds the smallest distance// This method mainly uses closestUtil()float closest(Point P[], int n){ qsort(P, n, sizeof(Point), compareX); // Use recursive function closestUtil() to find the smallest distance return closestUtil(P, n);} 0 0
