#include "plants.h"
#include <vector>
#include <iostream>
using namespace std;
int N;
int K;
const long long INF = 1e9;
const int logN = 19;
vector< vector<int> > edge;
vector<int> ht;
int dist(int x, int y) //clockwise distance from x to y
{
x = x % N;
y = y % N;
if(y < x) y += N;
return y-x;
}
struct segtree
{
int l;
int r;
pair<long long, int> mn; //min first, index second
pair<long long, int> mx; //max first, index second
int lp = 0;
segtree* left = NULL;
segtree* right = NULL;
segtree()
{
;
}
segtree(int L, int R)
{
l = L;
r = R;
mn = make_pair(0, l);
mx = make_pair(0, l);
if(l == r) return;
int m = (l+r)/2;
left = new segtree(l, m);
right = new segtree(m+1, r);
}
void add(int L, int R, long long V)
{
L = (L + 10*N) % N;
R = (R + 10*N) % N;
if(R < L)
{
add(L, N-1, V);
add(0, R, V);
return;
}
if(R < l || r < L) return;
else if(L <= l && r <= R)
{
lp += V;
mn.first += V;
mx.first += V;
}
else
{
left->add(L, R, V);
right->add(L, R, V);
mn = min(left->mn, right->mn);
mn.first += lp;
mx = max(left->mx, right->mx);
mx.first += lp;
}
}
pair<long long, int> rangemin(int L, int R)
{
L = (L + 10*N) % N;
R = (R + 10*N) % N;
if(R < L)
{
return min(rangemin(L, N-1), rangemin(0, R));
}
if(R < l || r < L) return make_pair(+2*INF, -1);
else if(L <= l && r <= R)
{
return mn;
}
else
{
pair<long long, int> A = min(left->rangemin(L, R), right->rangemin(L, R));
A.first += lp;
return A;
}
}
pair<long long, int> rangemax(int L, int R)
{
L = (L + 10*N) % N;
R = (R + 10*N) % N;
if(R < L)
{
return max(rangemax(L, N-1), rangemax(0, R));
}
if(R < l || r < L) return make_pair(-2*INF, -1);
else if(L <= l && r <= R)
{
return mx;
}
else
{
pair<long long, int> A = max(left->rangemax(L, R), right->rangemax(L, R));
A.first += lp;
// cerr << "returning " << A.first << ' ' << A.second << " for rangemax " << L << ' ' << R << '\n';
return A;
}
}
};
segtree R;
vector<int> pos;
vector< vector<int> > right_suc;
vector< vector<int> > left_suc;
void init(int k, vector<int> r)
{
N = r.size();
K = k;
segtree R(0, N-1); //R stores the array r, if an index is dead its value is INF
segtree S(0, N-1); //S[i] is equal to the number of indices j in [i-K, i-1] that have R[j] >= 1
// including dead
//If the index i is dead, S[i] is equal to -1.
/*
R: if index i is alive, R[i] = r[i]
if index i is dead, R[i] = >=INF
S: if index i is alive:
if R[i] == 0:
S[i] = #(j in [i-K, i-1], R[j] >= 1) (including dead stuff)
else:
S[i] = -INF + #(j in [i-K, i-1], R[j] >= 1)
if index i is dead: S[i] = -INF + ?
*/
vector<int> h_greedy;
for(int i = 0; i < N; i++)
{
R.add(i, i, +r[i]);
if(r[i] >= 1)
S.add(i+1, i+K-1, +1);
if(r[i] != 0)
S.add(i, i, -INF);
}
// cerr << "check\n";
// for(int i = 0; i < N; i++) cerr << R.rangemin(i, i).first << ' ' << R.rangemin(i, i).second << '\n';
// cerr << '\n';
for(int t = 0; t < N; t++)
{
// cerr << "\n\n";
// for(int i = 0; i < N; i++) cerr << S.rangemax(i, i).first << ' ' << S.rangemax(i, i).second << " | ";
// cerr << '\n';
// for(int i = 0; i < N; i++) cerr << R.rangemax(i, i).first << ' ' << R.rangemax(i, i).second << " | ";
// cerr << '\n';
// cerr << "t = " << t << ", ";
// cerr << "IMPORTANT CALL!\n";
// cerr << S.mx.first << ' ' << S.mx.second << '\n';
pair<long long, int> p = S.rangemax(0, N-1);
int I = p.second;
h_greedy.push_back(I);
// cerr << "I = " << I << '\n';
R.add(I, I, +INF);
S.add(I, I, -INF);
S.add(I+1, I+K-1, +1);
vector<int> newzeros;
// R.add(I+1, I+K-1, -1);
R.add(I-K+1, I-1, -1);
while(1)
{
// for(int i = 0; i < N; i++) cerr << R.rangemin(i, i).second << ' ';
// cerr << '\n';
pair<long long, int> q = R.rangemin(I-K+1, I-1);
if(q.first > 0) break;
// cerr << "q = " << q.second << '\n';
newzeros.push_back(q.second);
R.add(q.second, q.second, +1);
}
for(int z: newzeros)
{
R.add(z, z, -1);
S.add(z, z, +INF);
}
for(int z: newzeros)
S.add(z+1, z+K-1, -1);
}
// for(int h: h_greedy) cerr << h << ' ';
// cerr << '\n';
pos = vector<int>(N); //height position, 0 = highest height
for(int i = 0; i < N; i++)
pos[ h_greedy[i] ] = i;
ht = vector<int>(N);
for(int i = 0; i < N; i++)
ht[i] = N-1 - pos[i];
for(int i = 0; i < N; i++)
pos[ ht[i] ] = i;
for(int i = 0; i < N; i++)
{
right_suc[i] = vector<int>(1+logN);
left_suc[i] = vector<int>(1+logN);
}
segtree ST(0, N-1);
for(int i = 0; i < N; i++) S.add(i, i, +1'000'000);
for(int h = N-1; h >= 0; h--)
{
pair<long long, int> lft = S.rangemin(pos[h] - K + 1, pos[h] - 1);
if(lft.first >= 1'000'000)
left_suc[pos[h]][0] = pos[h];
else
left_suc[pos[h]][0] = lft.second;
pair<long long, int> rgt = S.rangemin(pos[h] + 1, pos[h] + K - 1);
if(rgt.first >= 1'000'000)
right_suc[pos[h]][0] = pos[h];
else
right_suc[pos[h]][0] = rgt.second;
S.add(pos[h], pos[h], -1'000'000 + h);
}
for(int e = 1; e <= logN; e++)
for(int i = 0; i < N; i++)
{
left_suc[i][e] = left_suc[ left_suc[i][e-1] ][e-1];
right_suc[i][e] = right_suc[ right_suc[i][e-1] ][e-1];
}
}
bool query_left(int x, int y) //check if there is increasing path from x to y
{
for(int e = logN; e >= 0; e--)
{
if(ht[ left_suc[x][e] ] > ht[y]) continue;
if(dist(y, x) > dist(left_suc[x][e], x) + dist(y, left_suc[x][e])) continue;
x = left_suc[x][e];
}
return (min(dist(x, y), dist(y, x)) < K && ht[x] <= ht[y]);
}
bool query_right(int x, int y) //check if there is increasing path from x to y
{
for(int e = logN; e >= 0; e--)
{
if(ht[ right_suc[x][e] ] > ht[y]) continue;
if(dist(x, y) > dist(x, right_suc[x][e]) + dist(right_suc[x][e], y)) continue;
x = right_suc[x][e];
}
return (min(dist(x, y), dist(y, x)) < K && ht[x] <= ht[y]);
}
int compare_plants(int x, int y)
{
if(query_left(x, y)) return -1;
else if(query_right(x, y)) return -1;
else if(query_left(y, x)) return 1;
else if(query_right(y, x)) return 1;
else return 0;
}
