codeforces314D 二分+滑窗

首先先将坐标轴旋转，之后二分答案，维护滑窗，前后缀优化判定连通性即可。

#include <bits/stdc++.h>using namespace std;const int maxn = 110000;const double eps = 1e-8;int n;double premax[maxn], premin[maxn];double sufmax[maxn], sufmin[maxn];struct Point {    double x, y;    void in() {        scanf("%lf%lf", &x, &y);        double tmp = x;        x -= y;        y = tmp + y;//        cout<<x<<" "<<y<<" denug "<<endl;    }    bool operator < (const Point & b) const {        if(x == b.x) return y < b.y;        return x < b.x;    }} p[maxn];bool check(double d) {    for(int i = 1, j = 1; i <= n; i++) {        while(p[i].x - p[j].x > d) j++;        double ymax = max(sufmax[i+1], premax[j-1]);        double ymin = min(sufmin[i+1], premin[j-1]);        if(ymax - ymin <= d || ymax == -1e18 || ymin == 1e18)            return 1;    }    return 0;}int main() {    scanf("%d", &n);    for(int i = 1; i <= n; i++)        p[i].in();    sort(p+1, p+1+n);    premax[0] = sufmax[n+1] = -1e18;    premin[0] = sufmin[n+1] = 1e18;    for(int i = 1; i <= n; i++) {        premax[i] = max(premax[i-1], p[i].y);        premin[i] = min(premin[i-1], p[i].y);    }    for(int i = n; i >= 1; i--) {        sufmax[i] = max(sufmax[i+1], p[i].y);        sufmin[i] = min(sufmin[i+1], p[i].y);    }    double L = 0, R = 1e18, M;    for(int i = 0; i < 100; i++) {        M = (L + R) / 2;        if(check(M)) R = M;        else L = M;    }    printf("%.10f\n", L/2);    return 0;}