http://61.187.179.132/JudgeOnline/problem.php?id=1038

const double EPS = 1e-10 ;
const int Max_N =  305 ;
const double inf = 1e10 ; // 这个 开小了 1e9 都WA了好几次
double add(double a, double b){
return (fabs(a + b) < EPS * (fabs(a) + fabs(b)) ) ?  0 : (a + b );
}
struct Point {
double x, y;
Point(){}
Point(double x, double y):x(x) , y(y){}
Point operator - (Point a){
return Point(add(x , -a.x) , add(y , -a.y)) ;
}
Point operator + (Point a){
return Point(add(x , a.x) , add(y , a.y)) ;
}
double operator ^(Point a){
return add(x * a.y ,  - y * a.x) ;
}
Point operator * (double d){
return Point(x * d , y * d) ;
}
void write(){
printf("%lf %lf\n" , x , y) ;
}
};
struct Line{  //有向直线
Point st, ed;
Line(){}
Line(Point s, Point e){
st = s ;
ed = e ;
}
bool onRight(Point a){ //点a在直线向量的右边
return ((ed - st)^(a - st)) < 0 ;
}
bool parallel(Line l){
return ((ed -st)^(l.ed - l.st)) == 0 ;
}
Point Crossnode(Line l){ //两直线的交点
double t = (l.ed - l.st) ^(l.st - st) ;
double t1 = (l.ed - l.st)^(ed - st) ;
return st + (ed - st)*(t / t1) ;
}
bool onseg(Point a){
return ((a.x - st.x)*(a.x - ed.x) <EPS) && ((a.y - st.y)*(a.y - ed.y) <EPS) ;
}
double jijiao(){
return atan2(ed.y - st.y , ed.x - st.x) ;
}
void write(){
printf("%lf %lf %lf %lf\n" , st.x ,st.y ,ed.x ,ed.y) ;
}
};
//排序函数 [优先顺序：1极角  2. 前面的直线在后面的左边 ]
bool operator < (Line l, Line r){
double lp = l.jijiao() ;
double rp = r.jijiao() ;
if( fabs(lp - rp) > EPS)
return lp < rp ;
return ((l.st - r.st)^(r.ed - r.st)) < -EPS ;
}
//用于计算的双端队列
Line dequeue[Max_N] ;
Point pt[Max_N] ;
int halfPanelCross(Line line[] , int ln){
int i, tn;
sort(line, line  + ln ) ;
// 平面在向量左边 的筛选
for(i = tn = 1 ; i < ln ; i++){// 处理极角相同的，选择向量方向最左边的
if(fabs(line[i].jijiao() - line[i -1].jijiao())  > EPS)
line[tn++] = line[i] ;
}
ln = tn ;
int bot = 0 , top = 1 ;
dequeue[0] = line[0] ;
dequeue[1] = line[1] ;
for(i = 2 ; i < ln ; i++){
if(dequeue[top].parallel(dequeue[top - 1])|| dequeue[bot].parallel(dequeue[bot + 1]))
return 0 ;
while(bot < top &&
line[i].onRight(dequeue[top].Crossnode(dequeue[top - 1])))
top -- ;
while(bot < top &&
line[i].onRight(dequeue[bot].Crossnode(dequeue[bot + 1])))
bot ++ ;
dequeue[++ top] = line[i] ;
}
while(bot < top &&
dequeue[bot].onRight(dequeue[top].Crossnode(dequeue[top -1])))
top -- ;
while(bot < top &&
dequeue[top].onRight(dequeue[bot].Crossnode(dequeue[bot + 1])))
bot ++ ;
if(top <= bot + 1) return 0 ;  // 若队列为空， 则空集
int n = 0 ;
//计算交点（注意不同直线形成的交点可能重合） 半平面交是凸多边形
for(i = bot ; i < top ; i++)
pt[n ++] = dequeue[i].Crossnode(dequeue[i + 1]) ;
if(bot < top +1)
pt[n ++] = dequeue[bot].Crossnode(dequeue[top]) ;
return n ;
}
Line List[Max_N] ;
Point p[Max_N] ;
int n;
void go(){
int i , j;
Point s, t ;
Line tmp ;
double ans = inf;
i = n  -1 ;
List[i ++] = Line(Point(-inf ,-inf) , Point(inf , -inf)) ;
List[i ++] = Line(Point(inf ,-inf) , Point(inf , inf)) ;
List[i ++] = Line(Point(inf ,inf) , Point(-inf , inf)) ;
List[i ++] = Line(Point(-inf ,inf) , Point(-inf , -inf)) ;
int ttn = i ;
int tn = halfPanelCross(List , ttn) ;
for(i = 0 ; i < n ; i++){
s = p[i] ;
t.x = s.x  , t.y = 1000 ;
for( j = 0 ; j < tn ; j++){
tmp = Line(pt[j] , pt[(j + 1) % tn]) ;
Point cross = Line(s ,t).Crossnode(tmp) ;
if(tmp.onseg(cross))
ans = min(ans , cross.y - s.y) ;
}
}
for(i = 0 ; i < tn ; i++){
s = pt[i] ;
t.x = s.x , t.y = 1000 ;
for(j = 0 ; j < n - 1 ; j++){
tmp = Line(p[j] , p[j + 1]) ;
Point cross = Line(s,t).Crossnode(tmp) ;
if(tmp.onseg(cross))
ans = min(ans , s.y - cross.y) ;
}
}
printf("%.3lf\n" , ans + EPS) ;
}
int main(){
int i ;
while(scanf("%d" , &n) != EOF){
for(i = 0 ; i < n ; i++)
scanf("%lf" , &p[i].x) ;
for(i = 0 ; i < n ; i++)
scanf("%lf" , &p[i].y) ;
for(i = 0 ; i < n-1 ; i++){
List[i] = Line(p[i] , p[i + 1]) ;
}
go() ;
}
}