96 lines
2.5 KiB
C++
96 lines
2.5 KiB
C++
#include <iostream>
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#include <cstdio>
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#include <string.h>
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#include <string>
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#include <algorithm>
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#include <queue>
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#include <map>
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#include <vector>
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#include <set>
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#include <stack>
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#include <cmath>
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using namespace std;
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#define N 20
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#define inf 0x3f3f3f3f
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#define eps 1e-16
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#define LL long long
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#define Pi acos(-1)
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struct Point{
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double x, y;
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};
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Point p[N], pnt[N];
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int res, t, n;
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bool mark[N];
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double dot(double x1, double y1, double x2, double y2){
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return x1 * x2 + y1 * y2;
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}
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double cross(double x1, double y1, double x2, double y2){
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return x1 * y2 - x2 * y1;
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}
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int dblcmp(double n) {
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if (fabs(n) < eps) {
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return 0;
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} else {
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return n > 0 ? +1 : -1;
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}
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}
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bool segXseg(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4){
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double c1 = cross(x1 - x3, y1 - y3, x2 - x3, y2 - y3);
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double c2 = cross(x1 - x4, y1 - y4, x2 - x4, y2 - y4);
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double c3 = cross(x3 - x1, y3 - y1, x4 - x1, y4 - y1);
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double c4 = cross(x3 - x2, y3 - y2, x4 - x2, y4 - y2);
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if (c1 * c2 < -eps && c3 * c4 < -eps) return true;
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if ((dblcmp(c1) == 0 && dblcmp(dot(x1 - x3, y1 - y3, x2 - x3, y2 - y3)) <= 0) ||
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(dblcmp(c2) == 0 && dblcmp(dot(x1 - x4, y1 - y4, x2 - x4, y2 - y4)) <= 0) ||
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(dblcmp(c3) == 0 && dblcmp(dot(x3 - x1, y3 - y1, x4 - x1, y4 - y1)) <= 0) ||
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(dblcmp(c4) == 0 && dblcmp(dot(x3 - x2, y3 - y2, x4 - x2, y4 - y2)) <= 0)) {
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return true;
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}
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return false;
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}
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bool ok(int k){
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double c = cross(pnt[t].x - pnt[t - 1].x, pnt[t].y - pnt[t - 1].y, p[k].x - pnt[t].x, p[k].y - pnt[t].y);
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double d = dot(pnt[t].x - pnt[t - 1].x, pnt[t].y - pnt[t - 1].y, p[k].x - pnt[t].x, p[k].y - pnt[t].y);
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if (!((c > eps || (fabs(c) < eps && d > 0)))){
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return false;
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}
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Point tmp;
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for (int i = 0; i <= t - 2; ++i){
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tmp.x = pnt[t].x + (p[k].x - pnt[t].x) * 100000000.0;
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tmp.y = pnt[t].y + (p[k].y - pnt[t].y) * 100000000.0;
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if (segXseg(pnt[i].x, pnt[i].y, pnt[i + 1].x, pnt[i + 1].y, pnt[t].x, pnt[t].y, tmp.x, tmp.y)){
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return false;
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}
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}
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return true;
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}
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void DFS(){
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int i;
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for (i = 1; i <= n; ++i){
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if (res == n) return ;
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if (!mark[i] && (t < 1 || ok(i))){
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pnt[++t] = p[i];
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mark[i] = true;
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if (t > res) res = t;
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DFS();
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t--;
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mark[i] = false;
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}
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}
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}
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int main(){
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int i;
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while (scanf("%d", &n) != EOF){
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for (i = 1; i <= n; ++i){
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scanf("%lf%lf", &p[i].x, &p[i].y);
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}
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memset(mark, false, sizeof(mark));
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pnt[0].x = pnt[0].y = 0;
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t = 0;
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res = 0;
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DFS();
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printf("%d\n", res);
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}
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return 0;
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}
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