POJ1228 (stability convex packet problem)

 

Question: enter a vertex on a convex bag (the vertex inside the convex bag is not, either a convex bag vertex or a dot on the convex bag side) to check whether the convex bag is stable. Stability

It is determined whether the convex hull can be added to the original convex hull to obtain a larger convex hull. The convex hull contains all vertices on the original convex hull.

 

Analysis: it is easy to know that when a convex packet is stable, each side of the convex packet must have at least three points. If there are only two points, you can add one point to get a larger convex.

Package. In this way, we can find the convex hull and add the collocated points to the convex hull. In this way, we can determine whether three consecutive three-point colons exist. For details, see the code.

 

# Include <iostream> # include <algorithm> # include <stdio. h> # include <math. h> using namespace std; const int N = 40005; typedef double DIY; struct Point {DIY x, y ;}; Point p [N]; Point stack [N]; point MinA; int top; DIY dist (Point A, Point B) {return sqrt (. x-B.x) * (. x-B.x) +. y-B.y) * (. y-B.y);} DIY cross (Point A, Point B, Point C) {return (B. x-A.x) * (C. y-A.y)-(B. y-A.y) * (C. x-A.x);} bool cmp (Point a, Point B) {DIY k = c Ross (MinA, a, B); if (k> 0) return 1; if (k <0) return 0; return dist (MinA, a) <dist (MinA, b); // The collocated points are sorted by distance from small to large} void Graham (int n) {int I; for (I = 1; I <n; I ++) if (p [I]. y <p [0]. y | (p [I]. y = p [0]. y & p [I]. x <p [0]. x) swap (p [I], p [0]); MinA = p [0]; sort (p + 1, p + n, cmp ); stack [0] = p [0]; stack [1] = p [1]; top = 1; for (I = 2; I <n; I ++) {// Note: here we also press the collocated points into the convex hull while (cross (stack [top-1], stack [top], p [I]) <0 & top> = 1) -- top; stack [++ top] = p [I] ;}} bool Judge () {for (int I = 1; I <top; I ++) {// determine whether a side of a convex hull has at least 3 points if (cross (stack [I-1], stack [I + 1], stack [I])! = 0 & (cross (stack [I], stack [I + 2], stack [I + 1])! = 0) return false;} return true;} int main () {int t, n, I; scanf ("% d", & t); while (t --) {scanf ("% d", & n); for (I = 0; I <n; I ++) scanf ("% lf ", & p [I]. x, & p [I]. y); if (n <6) {puts ("NO"); continue;} Graham (n); cout <endl; for (I = 0; I <n; I ++) cout <p [I]. x <"" <p [I]. y <endl; cout <endl; for (I = 0; I <= top; I ++) cout <stack [I]. x <"" <stack [I]. y <endl; if (Judge () puts ("YES"); else puts ("NO");} return 0 ;}