POJ 2187 Beauty Contest(凸包、旋转卡壳、最远点对)

题意:

$N\le 5\times 10^4个点,求最远点的距离的平方$

分析:

$凸包,然后旋转卡壳辣$
$类似two pointers的做法,一图流$

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//
// Created by TaoSama on 2016-08-22
// Copyright (c) 2016 TaoSama. All rights reserved.
//
#pragma comment(linker, "/STACK:102400000,102400000")
#include <algorithm>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <string>
#include <set>
#include <vector>
using namespace std;
#define pr(x) cout << #x << " = " << x << " "
#define prln(x) cout << #x << " = " << x << endl
const int N = 1e5 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;
struct Point {
int x, y;
Point() {}
Point(int x, int y): x(x), y(y) {}
void read() {
scanf("%d%d", &x, &y);
}
Point operator-(const Point& p) const {
return Point(x - p.x, y - p.y);
}
int operator*(const Point& p) const {
return x * p.x + y * p.y;
}
int operator^(const Point& p) const {
return x * p.y - y * p.x;
}
bool operator<(const Point& p) const {
return x == p.x && y < p.y || x < p.x;
}
int length() {
return *this * *this;
}
} ps[N];
//输入不能有重点,函数执行完后输入顺序被破坏
Point ch[N];
int convexHull(Point* p, int n, Point* ch) {
sort(p, p + n);
int m = 0;
for(int i = 0; i < n; ++i) {
while(m > 1 && ((ch[m - 1] - ch[m - 2]) ^ (p[i] - ch[m - 2])) <= 0) --m;
ch[m++] = p[i];
}
for(int i = n - 2, t = m; ~i; --i) {
while(m > t && ((ch[m - 1] - ch[m - 2]) ^ (p[i] - ch[m - 2])) <= 0) --m;
ch[m++] = p[i];
}
if(n > 1) --m;
return m;
}
int rotatingCalipers(Point* ch, int n) {
if(n == 2) return (ch[1] - ch[0]).length();
int ret = 0;
ch[n] = ch[0];
for(int i = 0, j = 2; i < n; ++i) {
while(((ch[i + 1] - ch[i]) ^ (ch[j + 1] - ch[i]))
> ((ch[i + 1] - ch[i]) ^ (ch[j] - ch[i])))
j = (j + 1) % n;
ret = max(ret, max((ch[j] - ch[i + 1]).length(), (ch[j] - ch[i]).length()));
}
return ret;
}
int n;
int main() {
#ifdef LOCAL
freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);
// freopen("C:\\Users\\TaoSama\\Desktop\\out.txt","w",stdout);
#endif
ios_base::sync_with_stdio(0);
while(scanf("%d", &n) == 1) {
for(int i = 0; i < n; ++i) ps[i].read();
int chSz = convexHull(ps, n, ch);
int ans = rotatingCalipers(ch, chSz);
printf("%d\n", ans);
}
return 0;
}

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