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| 1 | +#include<bits/stdc++.h> |
| 2 | +using namespace std; |
| 3 | + |
| 4 | +#define iPair pair<int, int> |
| 5 | + |
| 6 | +// Stores the result (points of convex hull) |
| 7 | +set<iPair> hull; |
| 8 | + |
| 9 | +int findSide(iPair p1, iPair p2, iPair p) |
| 10 | +{ |
| 11 | + int val = (p.second - p1.second) * (p2.first - p1.first) - |
| 12 | + (p2.second - p1.second) * (p.first - p1.first); |
| 13 | + |
| 14 | + if (val > 0) |
| 15 | + return 1; |
| 16 | + if (val < 0) |
| 17 | + return -1; |
| 18 | + return 0; |
| 19 | +} |
| 20 | + |
| 21 | +int lineDist(iPair p1, iPair p2, iPair p) |
| 22 | +{ |
| 23 | + return abs ((p.second - p1.second) * (p2.first - p1.first) - |
| 24 | + (p2.second - p1.second) * (p.first - p1.first)); |
| 25 | +} |
| 26 | + |
| 27 | +void quickHull(iPair a[], int n, iPair p1, iPair p2, int side) |
| 28 | +{ |
| 29 | + int ind = -1; |
| 30 | + int max_dist = 0; |
| 31 | + |
| 32 | + for (int i=0; i<n; i++) |
| 33 | + { |
| 34 | + int temp = lineDist(p1, p2, a[i]); |
| 35 | + if (findSide(p1, p2, a[i]) == side && temp > max_dist) |
| 36 | + { |
| 37 | + ind = i; |
| 38 | + max_dist = temp; |
| 39 | + } |
| 40 | + } |
| 41 | + |
| 42 | + if (ind == -1) |
| 43 | + { |
| 44 | + hull.insert(p1); |
| 45 | + hull.insert(p2); |
| 46 | + return; |
| 47 | + } |
| 48 | + |
| 49 | + quickHull(a, n, a[ind], p1, -findSide(a[ind], p1, p2)); |
| 50 | + quickHull(a, n, a[ind], p2, -findSide(a[ind], p2, p1)); |
| 51 | +} |
| 52 | + |
| 53 | +void printHull(iPair a[], int n) |
| 54 | +{ |
| 55 | + if (n < 3) |
| 56 | + { |
| 57 | + cout << "Convex hull not possible\n"; |
| 58 | + return; |
| 59 | + } |
| 60 | + |
| 61 | + int min_x = 0, max_x = 0; |
| 62 | + for (int i=1; i<n; i++) |
| 63 | + { |
| 64 | + if (a[i].first < a[min_x].first) |
| 65 | + min_x = i; |
| 66 | + if (a[i].first > a[max_x].first) |
| 67 | + max_x = i; |
| 68 | + } |
| 69 | + |
| 70 | + quickHull(a, n, a[min_x], a[max_x], 1); |
| 71 | + |
| 72 | + quickHull(a, n, a[min_x], a[max_x], -1); |
| 73 | + |
| 74 | + cout << "The points in Convex Hull are:\n"; |
| 75 | + while (!hull.empty()) |
| 76 | + { |
| 77 | + cout << "(" <<( *hull.begin()).first << ", " |
| 78 | + << (*hull.begin()).second << ") "; |
| 79 | + hull.erase(hull.begin()); |
| 80 | + } |
| 81 | +} |
| 82 | + |
| 83 | +// Driver code example |
| 84 | +int main() |
| 85 | +{ |
| 86 | + iPair a[] = {{0, 3}, {1, 1}, {2, 2}, {4, 4}, |
| 87 | + {0, 0}, {1, 2}, {3, 1}, {3, 3}}; |
| 88 | + int n = sizeof(a)/sizeof(a[0]); |
| 89 | + printHull(a, n); |
| 90 | + return 0; |
| 91 | +} |
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