#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef basic_string<int> B;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937 mrand(random_device{}());
const ll mod=1000000007;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head
const int N=100100;
const int L=20;
const int S=sqrt(N);
int n,m,st[N][L],logs[N];
ll d[N];
mt19937 rng(time(0));
struct pt {
int x,y;
pt(int _x=0,int _y=0) : x(_x),y(_y) {}
}p[N];
vector<pt> ch[N];
int orient(pt a,pt b,pt c) {
ll v=(b.y-a.y)*1ll*(c.x-b.x)-(b.x-a.x)*1ll*(c.y-b.y);
return v==0?0:(v<0?-1:1);
}
bool const operator<(const pt& a,const pt& b) {
if (orient(pt(0,0),a,b)==0) {
return (a.x==b.x?a.y<b.y:a.x<b.x);
}
return orient(pt(0,0),a,b)>0;
}
ll dist(pt a,pt b,pt c) {
/* https://stackoverflow.com/questions/849211/shortest-distance-between-a-point-and-a-line-segment */
ll A = c.x - a.x;
ll B = c.y - a.y;
ll C = b.x - a.x;
ll D = b.y - a.y;
ll dot = A * C + B * D;
ll len_sq = C * C + D * D;
ll param = -1;
if (len_sq != 0) //in case of 0 length line
param = dot / len_sq;
ll xx, yy;
if (param < 0) {
xx = a.x;
yy = a.y;
}
else if (param > 1) {
xx = b.x;
yy = b.y;
}
else {
xx = a.x + param * C;
yy = a.y + param * D;
}
ll dx = c.x - xx;
ll dy = c.y - yy;
return dx*dx+dy*dy;
}
bool in_tri(pt a,pt b,pt c,pt p) {
return orient(a,b,p)!=-1&&orient(b,c,p)!=-1&&orient(c,a,p)!=-1;
}
int cmp(int i,int j) {
return d[i]<d[j]?i:j;
}
int query(int l,int r) {
int k=logs[r-l+1];
return cmp(st[l][k],st[r-(1<<k)+1][k]);
}
int main() {
scanf("%d%d",&n,&m);
rep(i,0,n) {
scanf("%d%d",&p[i].x,&p[i].y);
}
sort(p,p+n);
rep(i,0,n) {
st[i][0]=i;
d[i]=p[i].x*1ll*p[i].x+p[i].y*1ll*p[i].y;
}
rep(i,2,n+1) logs[i]=logs[i>>1]+1;
rep(j,1,L) {
rep(i,0,n-(1<<j)+1) {
st[i][j]=cmp(st[i][j-1],st[i+(1<<(j-1))][j-1]);
}
}
rep(i,0,n) {
ch[i/S].pb(p[i]);
}
rep(i,0,n+1) {
if (ch[i].empty()) continue;
vector<pt> hull;
sort(all(ch[i]),[&](pt a,pt b) { return a.x<b.x||(a.x==b.x&&a.y<b.y); });
for (auto& p:ch[i]) {
while (SZ(hull)>=2&&orient(hull[SZ(hull)-2],hull[SZ(hull)-1],p)>=0) {
hull.pop_back();
}
hull.pb(p);
}
ch[i]=hull;
}
while (m--) {
pt a,b;
scanf("%d%d%d%d",&a.x,&a.y,&b.x,&b.y);
if (orient(b,pt(0,0),a)<=0) swap(a,b);
int L,R;
{
L=n-1;
int low=0,high=n-1;
while (low<=high) {
int mid=low+high>>1;
if (orient(p[mid],pt(0,0),a)>=0) {
L=mid;
high=mid-1;
} else {
low=mid+1;
}
}
}
{
R=0;
int low=0,high=n-1;
while (low<=high) {
int mid=low+high>>1;
if (orient(p[mid],pt(0,0),b)<=0) {
R=mid;
low=mid+1;
} else {
high=mid-1;
}
}
}
if (L>R) {
printf("N\n");
continue;
}
if (R-L<=S) {
bool ok=false;
rep(i,L,R+1) if (in_tri(a,b,pt(0,0),p[i])) ok=true;
puts(ok?"Y":"N");
continue;
}
bool ok=false;
while (L%S!=0) {
if (in_tri(a,b,pt(0,0),p[L])) ok=true;
L++;
}
while (R>=L&&R%S!=S-1) {
if (in_tri(a,b,pt(0,0),p[R])) ok=true;
R--;
}
while (R>=L) {
if (in_tri(a,b,pt(0,0),p[R])) ok=true;
R--;
}
VI ord;
rep(i,L/S,R/S+1) ord.pb(i);
shuffle(ord.begin(),ord.end(),rng);
rep(i,L/S,R/S+1) {
int sz=SZ(ch[i]);
int low=0,high=sz-1;
while (low<=high) {
int mid=low+high>>1;
if (in_tri(a,b,pt(0,0),ch[i][mid])) {
ok=true;
break;
}
if (mid+1==sz||(!in_tri(a,b,pt(0,0),ch[i][mid+1])&&dist(a,b,p[mid+1])>dist(a,b,p[mid]))) {
high=mid-1;
} else {
low=mid+1;
}
}
if (ok) break;
}
puts(ok?"Y":"N");
}
}
Compilation message
tri.cpp: In function 'int main()':
tri.cpp:129:16: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
129 | int mid=low+high>>1;
| ~~~^~~~~
tri.cpp:142:16: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
142 | int mid=low+high>>1;
| ~~~^~~~~
tri.cpp:181:16: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
181 | int mid=low+high>>1;
| ~~~^~~~~
tri.cpp:90:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
90 | scanf("%d%d",&n,&m);
| ~~~~~^~~~~~~~~~~~~~
tri.cpp:92:8: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
92 | scanf("%d%d",&p[i].x,&p[i].y);
| ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
tri.cpp:122:8: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
122 | scanf("%d%d%d%d",&a.x,&a.y,&b.x,&b.y);
| ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5 ms |
6748 KB |
Output is correct |
| 2 |
Correct |
4 ms |
6772 KB |
Output is correct |
| 3 |
Execution timed out |
2039 ms |
9236 KB |
Time limit exceeded |
| 4 |
Execution timed out |
2025 ms |
9468 KB |
Time limit exceeded |
| 5 |
Execution timed out |
2047 ms |
13856 KB |
Time limit exceeded |
| 6 |
Execution timed out |
2040 ms |
12056 KB |
Time limit exceeded |
| 7 |
Execution timed out |
2035 ms |
13908 KB |
Time limit exceeded |
| 8 |
Correct |
1433 ms |
12608 KB |
Output is correct |
| 9 |
Correct |
1620 ms |
13352 KB |
Output is correct |
| 10 |
Correct |
1797 ms |
14096 KB |
Output is correct |
