137 lines
3.1 KiB
C++
137 lines
3.1 KiB
C++
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/*
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* C++ Program to Find Closest Pair of Points in an Array
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*/
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#include <iostream>
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#include <cfloat>
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#include <cstdlib>
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#include <cmath>
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using namespace std;
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/*
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* Point Declaration
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*/
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struct Point
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{
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int x, y;
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};
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/*
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* sort array of points according to X coordinate
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*/
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int compareX(const void* a, const void* b)
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{
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Point *p1 = (Point *)a, *p2 = (Point *)b;
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return (p1->x - p2->x);
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}
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/*
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* sort array of points according to Y coordinate
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*/
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int compareY(const void* a, const void* b)
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{
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Point *p1 = (Point *)a, *p2 = (Point *)b;
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return (p1->y - p2->y);
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}
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/*
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* find the distance between two points
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*/
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float dist(Point p1, Point p2)
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{
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return sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));
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}
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/*
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* return the smallest distance between two points
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*/
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float small_dist(Point P[], int n)
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{
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float min = FLT_MAX;
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for (int i = 0; i < n; ++i)
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{
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for (int j = i + 1; j < n; ++j)
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{
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if (dist(P[i], P[j]) < min)
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min = dist(P[i], P[j]);
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}
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}
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return min;
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}
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/*
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* find the distance beween the closest points of strip of given size
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*/
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float stripClosest(Point strip[], int size, float d)
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{
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float min = d;
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for (int i = 0; i < size; ++i)
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{
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for (int j = i + 1; j < size && (strip[j].y - strip[i].y) < min; ++j)
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{
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if (dist(strip[i],strip[j]) < min)
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min = dist(strip[i], strip[j]);
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}
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}
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return min;
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}
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/*
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* find the smallest distance.
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*/
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float closestUtil(Point Px[], Point Py[], int n)
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{
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if (n <= 3)
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return small_dist(Px, n);
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int mid = n / 2;
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Point midPoint = Px[mid];
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Point Pyl[mid + 1];
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Point Pyr[n - mid - 1];
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int li = 0, ri = 0;
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for (int i = 0; i < n; i++)
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{
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if (Py[i].x <= midPoint.x)
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Pyl[li++] = Py[i];
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else
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Pyr[ri++] = Py[i];
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}
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float dl = closestUtil(Px, Pyl, mid);
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float dr = closestUtil(Px + mid, Pyr, n-mid);
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float d = min(dl, dr);
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Point strip[n];
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int j = 0;
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for (int i = 0; i < n; i++)
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{
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if (abs(Py[i].x - midPoint.x) < d)
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strip[j] = Py[i], j++;
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}
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return min(d, stripClosest(strip, j, d));
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}
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/*
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* finds the smallest distance
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*/
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float closest(Point P[], int n)
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{
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Point Px[n];
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Point Py[n];
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for (int i = 0; i < n; i++)
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{
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Px[i] = P[i];
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Py[i] = P[i];
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}
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qsort(Px, n, sizeof(Point), compareX);
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qsort(Py, n, sizeof(Point), compareY);
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return closestUtil(Px, Py, n);
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}
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/*
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* Main
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*/
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int main()
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{
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Point P[] = {{2, 3}, {12, 30}, {40, 50}, {5, 1}, {12, 10}, {3, 4}};
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int n = sizeof(P) / sizeof(P[0]);
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cout << "The smallest distance is " << closest(P, n);
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return 0;
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}
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/*
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The smallest distance is 1.41421
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------------------
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(program exited with code: 1)
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Press return to continue
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