This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("trapv")
#include<iostream>
#include<algorithm>
using namespace std;
using pii = pair<int, int>;
using ll = long long;
#define forn(i, n) for(int i=0; i<(int)n; ++i)
#define dforn(i, n) for(int i=n-1; i>=0; --i)
#define F first
#define S second
const int MAXN=1010, MOD=1000000007;
int n;
pii pt[MAXN], arr[MAXN];
ll ex(ll b, int e){
ll ret=1;
while(e){
if(e&1) ret = (ret*b)%MOD;
b = (b*b)%MOD;
e>>=1;
}
return ret;
}
bool up(pii a){
return (a.S==0? (a.F>0) : (a.S>0));
}
ll signed_area(pii a, pii b, pii c){
return (((ll)a.F)*b.S - ((ll)a.S)*b.F + ((ll)b.F)*c.S - ((ll)b.S)*c.F + ((ll)c.F)*a.S - ((ll)c.S)*a.F);
}
ll count(int ind){
ll ret=0;
copy(pt, pt+n, arr), swap(arr[ind], arr[n-1]);
sort(arr, arr+n-1, [](pii a, pii b){
pii A = {a.F - arr[n-1].F, a.S - arr[n-1].S};
pii B = {b.F - arr[n-1].F, b.S - arr[n-1].S};
return up(A)==up(B)? A.S*B.F < B.S*A.F : (up(A)>up(B));
});
forn(i, n-1){
int cur=i, off=0;
dforn(j, 10) if(off+(1<<j)<(n-1)){
int nxt = (cur+(1<<j))%(n-1);
if(signed_area(arr[n-1], arr[i], arr[nxt])>0){
cur = nxt, off+=(1<<j);
}
}
ret+=ex(2, off);
}
return ret+1;
}
int main(){
ll ans=0;
scanf("%d", &n);
forn(i, n) scanf("%d %d", &pt[i].F, &pt[i].S);
forn(i, n) ans+=count(i);
printf("%d\n", ((int)(n*(ex(2, n)) - (ans%MOD) + MOD)%MOD));
}
Compilation message (stderr)
Main.cpp: In function 'int main()':
Main.cpp:57:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
57 | scanf("%d", &n);
| ~~~~~^~~~~~~~~~
Main.cpp:58:21: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
58 | forn(i, n) scanf("%d %d", &pt[i].F, &pt[i].S);
| ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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