#include "obstacles.h"
#include <stdio.h>
#include <vector>
#include <queue>
#include <algorithm>
#include <iostream>
#include <string>
#include <bitset>
#include <map>
#include <set>
#include <tuple>
#include <string.h>
#include <math.h>
#include <random>
#include <functional>
#include <assert.h>
#include <math.h>
#define all(x) (x).begin(), (x).end()
#define xx first
#define yy second
using namespace std;
template<typename T, typename Pr = less<T>>
using pq = priority_queue<T, vector<T>, Pr>;
using i64 = long long int;
using ii = pair<int, int>;
using ii64 = pair<i64, i64>;
constexpr int clog2(int n) { return ((n < 2) ? 1 : 1 + clog2(n / 2)); }
class SegmentTree
{
public:
SegmentTree() = default;
void init(const vector<int>& raw_)
{
raw = raw_;
n = (int)raw.size();
int sz = (1 << (clog2(n) + 1));
data.resize(sz);
_init(raw, 1, 0, n - 1);
}
int update(int idx, const int& newVal) { raw[idx] = newVal; return _update(1, 0, n - 1, idx, newVal); }
int query(int left, int right) { return _query(1, 0, n - 1, left, right); }
private:
vector<int> raw;
vector<int> data;
int n;
int merge(int l, int r) { return max(l, r); }
int _init(const vector<int>& raw, int node, int start, int end)
{
int mid = (start + end) / 2;
if (start == end)
return data[node] = raw[start];
else
return data[node] = merge(_init(raw, node * 2, start, mid),
_init(raw, node * 2 + 1, mid + 1, end));
}
int _update(int node, int start, int end, int index, const int& newVal)
{
if (index < start || index > end)
return data[node];
if (start == end)
data[node] = newVal;
else
{
int mid = (start + end) / 2;
data[node] = merge(_update(node * 2, start, mid, index, newVal),
_update(node * 2 + 1, mid + 1, end, index, newVal));
}
return data[node];
}
int _query(int node, int start, int end, int left, int right)
{
if (left <= start && end <= right)
return data[node];
int mid = (start + end) / 2;
if (mid < left)
return _query(node * 2 + 1, mid + 1, end, left, right);
if (mid + 1 > right)
return _query(node * 2, start, mid, left, right);
return merge(_query(node * 2, start, mid, left, right),
_query(node * 2 + 1, mid + 1, end, left, right));
}
};
vector<int> t, h;
vector<int> tmin;
vector<int> tmax;
int lbig[200005];
int rbig[200005];
int li[200005];
int ri[200005];
int nxt[200005][20];
int lnxt[200005][20];
int rnxt[200005][20];
int nxtl[200005][20];
int nxtr[200005][20];
SegmentTree canMoveMax;
// 도달 가능 범위가 l..r을 안 벗어나는 범위에서 최대한 확장
int nxtmost(int st, int l, int r)
{
for (int i = 19; i >= 0; i--)
{
if (nxtl[st][i] < l || nxtr[st][i] > r)
continue;
st = nxt[st][i];
}
if (l <= li[st] && ri[st] <= r)
st = nxt[st][0];
return st;
}
int lmost(int st, int l)
{
for (int i = 19; i >= 0; i--)
{
int k = lnxt[st][i];
if (k < l)
continue;
st = k;
}
return st;
}
int rmost(int st, int r)
{
for (int i = 19; i >= 0; i--)
{
int k = rnxt[st][i];
if (k > r)
continue;
st = k;
}
return st;
}
bool can_reach(int l, int r, int s, int d)
{
s = nxtmost(s, l, r);
d = nxtmost(d, l, r);
s = lmost(s, l);
s = rmost(s, r);
d = lmost(d, l);
d = rmost(d, r);
int sl = li[s], sr = ri[s];
sl = max(sl, l);
sr = min(sr, r);
int dl = li[d], dr = ri[d];
dl = max(dl, l);
dr = min(dr, r);
return max(sl, dl) <= min(sr, dr) && h[s] == h[d];
}
void initialize(vector<int> T, vector<int> H)
{
t = T;
h = H;
tmin = T;
tmax = T;
for (int i = 1; i < t.size(); i++)
{
tmin[i] = min(tmin[i - 1], t[i]);
tmax[i] = max(tmax[i - 1], t[i]);
}
vector<int> lbs;
for (int i = 0; i < h.size(); i++)
{
while (!lbs.empty() && h[lbs.back()] >= h[i])
lbs.pop_back();
if (lbs.empty())
lbig[i] = -1;
else
lbig[i] = lbs.back();
lbs.push_back(i);
}
vector<int> rbs;
for (int i = h.size() - 1; i >= 0; i--)
{
while (!rbs.empty() && h[rbs.back()] >= h[i])
rbs.pop_back();
if (rbs.empty())
rbig[i] = h.size();
else
rbig[i] = rbs.back();
rbs.push_back(i);
}
vector<int> canLive(h.size());
vector<int> canMove(h.size());
for (int i = 0; i < h.size(); i++)
{
canLive[i] = -1;
int lo = 0, hi = t.size() - 1;
while (lo <= hi)
{
int mid = (lo + hi) / 2;
if (tmin[mid] > h[i])
{
canLive[i] = mid;
lo = mid + 1;
}
else
{
hi = mid - 1;
}
}
nxt[i][0] = i;
lnxt[i][0] = i;
rnxt[i][0] = i;
}
for (int i = 0; i < h.size(); i++)
{
canMove[i] = t.size();
int lo = 0, hi = t.size() - 1;
while (lo <= hi)
{
int mid = (lo + hi) / 2;
if (tmax[mid] > h[i])
{
canMove[i] = mid;
hi = mid - 1;
}
else
{
lo = mid + 1;
}
}
}
canMoveMax.init(canMove);
for (int i = 0; i < h.size(); i++)
{
int sl = i, sr = i;
int lo = 0, hi = i;
int target = canLive[i];
while (lo <= hi)
{
int mid = (lo + hi) / 2;
auto v = canMoveMax.query(mid, i);
if (v > target)
{
lo = mid + 1;
}
else
{
sl = mid;
hi = mid - 1;
}
}
lo = i; hi = h.size() - 1;
while (lo <= hi)
{
int mid = (lo + hi) / 2;
auto v = canMoveMax.query(i, mid);
if (v > target)
{
hi = mid - 1;
}
else
{
sr = mid;
lo = mid + 1;
}
}
li[i] = sl;
ri[i] = sr;
}
for (int i = 0; i < h.size(); i++)
{
vector<int> canNxt;
if (li[i] <= lbig[i])
{
canNxt.push_back(lbig[i]);
lnxt[i][0] = lbig[i];
}
if (ri[i] >= rbig[i])
{
canNxt.push_back(rbig[i]);
rnxt[i][0] = rbig[i];
}
if (canNxt.size() == 2)
{
if (h[canNxt[0]] > h[canNxt[1]])
nxt[i][0] = canNxt[0];
else
nxt[i][0] = canNxt[1];
}
if (canNxt.size() == 1)
nxt[i][0] = canNxt[0];
nxtl[i][0] = min(i, nxt[i][0]);
nxtr[i][0] = max(i, nxt[i][0]);
}
for (int l = 1; l < 20; l++)
{
for (int i = 0; i < h.size(); i++)
{
nxt[i][l] = nxt[nxt[i][l - 1]][l - 1];
nxtl[i][l] = min(nxtl[i][l - 1], nxtl[nxt[i][l - 1]][l - 1]);
nxtr[i][l] = max(nxtr[i][l - 1], nxtr[nxt[i][l - 1]][l - 1]);
lnxt[i][l] = lnxt[lnxt[i][l - 1]][l - 1];
rnxt[i][l] = rnxt[rnxt[i][l - 1]][l - 1];
}
}
}
