UVa 10088-trees on My Island (pick theorem)

Examples:

Input:
12
3 1
6 3
7 |
8 4
9 6
9 9
8 9
6 5
5 8
4 4
3 5
1 3
12
1000 1000
2000 1000
4000 2000
6000 1000
8000 3000
8000 8000
7000 8000
5000 4000
4000 5000
3000 4000
3000 5000
1000 3000
4
0 0
1000000 0
1000000 1000000
0 1000000
4
0 0
100 0
100 100
0 100

Output:

21st

25990001

999998000001

9801

Analysis: Pick theorem: A polygon area formula for calculating vertices on lattice points in a lattice: S=a+b/2.0-1, where a represents the number of points inside the polygon, B represents the number of points on the polygon boundary, and S represents the area of the polygon.

Firstly, the area S of polygon is obtained by cross product.

Then find B, the method is to enumerate each edge, and then to change the edge to form a right triangle, the right angle edge length is n,m, the number of integral points on the hypotenuse is gcd (n,m)-1 (excluding the two ends of the point) finally b=b+n;

Can

Finally a=s+1-b/2.0;

The point to note is: A can explode int

1#include"stdio.h"2#include"string.h"3#include"algorithm"4#include"stdlib.h"5#include"math.h"6#include"Map"7#include"Queue"8#include"iostream"9 #defineM 1009Ten #defineINF 0x3f3f3f3f One #defineEPS 1e-9 A using namespacestd; - structnode - { the     Doublex, y; - node () {} -NodeDoubleXDoubley) -     { +          This->x=x; -          This->y=y; +     } ANodeoperator-(Node A) at     { -         returnNode (x-a.x,y-a.y); -     } -Nodeoperator+(Node A) -     { -         returnNode (x+a.x,y+a.y); in     } -     Double operator*(Node A) to     { +         returnx*a.x+y*a.y; -     } the     Double operator^(Node A) *     { $         returnx*a.y-y*a.x;Panax Notoginseng     } - }p[m]; the DoubleLen (Node A) + { A     returnsqrt (A *a); the } + DoubleDis (node A,node b) - { $     returnLen (b-a); $ } - DoubleCross (node A,node b,node c) - { the     return(b-a) ^ (c-a); - }Wuyi intgcdintAintb) the { -     returnb==0? A:GCD (b,a%b); Wu } - intPoint (node A,node b) About { $     intM= (int) (Fabs (b.x-a.x) +0.5); -     intN= (int) (Fabs (B.Y-A.Y) +0.5); -     intR=gcd (m,n); -     returnR1; A } + intMain () the { -     intN; $      while(SCANF ("%d",&N), N) the     { the          for(intI=0; i<n;i++) thescanf"%LF%LF",&p[i].x,&p[i].y); the         Doublesum=0; -Node O (0,0); in         Doublenum=N; the          for(intI=0; i<n;i++) the         { AboutNum+=point (p[i],p[(i+1)%n]); theSum+=cross (o,p[i],p[(i+1)%n]); the         } theSum=fabs (SUM)/2.0; +         Doubleans=sum+1-0.5*num; -printf"%.0f\n", ans+0.001); the     }Bayi     return 0; the } the /* -  A - 3 1 the 6 3 the 9 2 the 8 4 the 9 6 - 9 9 the 8 9 the 6 5 the 5 894 4 4 the 3 5 the 1 3 the  A98  the About  the - 4000101 6000102 8000103 8000 8000104 7000 8000 the 4000106 4000107 4000108  About109  the the 4111 0 0 the 1000000 0113 1000000 1000000 the 0 1000000 the 4 the 0 0117 0118  the119 0 - */

UVa 10088-trees on My Island (pick theorem)