#include "teams.h"
#pragma GCC optimize("Ofast,unroll-loops")
#include <bits/stdc++.h>
#define pii pair<int, int>
#define F first
#define S second
using namespace std;
int N, root[500005];
vector<int> v[500005];
struct node
{
int t = 0, l = -1, r = -1, val = 0;
};
vector<node> pSeg(1);
int copy_node(int i, int t)
{
int j = pSeg.size();
pSeg.emplace_back(pSeg[i]);
pSeg[j].t = t;
return j;
}
void build(int i, int L = 1, int R = N)
{
if (L != R)
{
int mid = (L + R) / 2;
pSeg[i].l = pSeg.size();
pSeg.emplace_back(node{});
build(pSeg[i].l, L, mid);
pSeg[i].r = pSeg.size();
pSeg.emplace_back(node{});
build(pSeg[i].r, mid + 1, R);
}
}
void modify(int pos, int i, int L = 1, int R = N)
{
if (L != R)
{
int mid = (L + R) / 2;
if (pos <= mid)
{
if (pSeg[pSeg[i].l].t < pSeg[i].t)
pSeg[i].l = copy_node(pSeg[i].l, pSeg[i].t);
modify(pos, pSeg[i].l, L, mid);
}
else
{
if (pSeg[pSeg[i].r].t < pSeg[i].t)
pSeg[i].r = copy_node(pSeg[i].r, pSeg[i].t);
modify(pos, pSeg[i].r, mid + 1, R);
}
pSeg[i].val = pSeg[pSeg[i].l].val + pSeg[pSeg[i].r].val;
}
else
pSeg[i].val++;
}
int query(int qL, int qR, int i, int L = 1, int R = N)
{
if (qL <= L && R <= qR)
return pSeg[i].val;
else if (R < qL || qR < L)
return 0;
else
{
int mid = (L + R) / 2;
return query(qL, qR, pSeg[i].l, L, mid) + query(qL, qR, pSeg[i].r, mid + 1, R);
}
}
int search(int dpi, int dpj, int minL, int pi, int pj, int L = 1, int R = N)
{
int mid = (L + R) / 2;
if(L == R)
return L;
if(mid < minL || dpi - pSeg[pSeg[pi].r].val < dpj - pSeg[pSeg[pj].r].val)
return search(dpi, dpj, minL, pSeg[pi].r, pSeg[pj].r, mid + 1, R);
else
return search(dpi - pSeg[pSeg[pi].r].val, dpj - pSeg[pSeg[pj].r].val, minL, pSeg[pi].l, pSeg[pj].l, L, mid);
// dp[i] - query(mid + 1, N, root[K[i]]) < dp[j] - query(mid + 1, N, root[K[j]]) => [mid + 1, R];
// else => [L, mid] ;
}
void init(int n, int A[], int B[])
{
N = n;
for (int i = 0; i < N; i++)
v[A[i]].emplace_back(B[i]);
root[0] = 0;
build(0);
for (int i = 1; i <= N; i++)
{
root[i] = copy_node(root[i - 1], i);
for (int j : v[i])
modify(j, root[i]);
}
}
// L R
// dp[i] = min dp[j] + n([K[j] + 1, K[i]] x [K[i], N]) - cnt
// Segment tree should maintain R, and binary search cost through two version of L (K[i] and K[j])
int can(int M, int k[])
{
sort(k, k + M);
vector<int> K(1, 0), cnt(1, 0);
for (int i = 0; i < M; i++)
if (k[i] == K.back())
cnt.back() += k[i];
else
{
K.emplace_back(k[i]);
cnt.emplace_back(k[i]);
}
M = (int)K.size() - 1;
vector<int> dp(K.size(), 0);
vector<pii> mono;
mono.emplace_back(pii(0, N + 1));
for (int i = 1; i <= M; i++)
{
while(mono.back().S < K[i])
mono.pop_back();
int j = mono.back().F;
dp[i] = dp[j] + query(K[i], N, root[K[i]]) - query(K[i], N, root[K[j]]) - cnt[i];
while(!mono.empty() && search(dp[i], dp[j], K[i], root[K[i]], root[K[j]]) >= mono.back().S)
{
mono.pop_back();
j = mono.back().F;
}
mono.emplace_back(pii(i, search(dp[i], dp[j], K[i], root[K[i]], root[K[j]])));
}
for (int i = 1; i <= M; i++)
if (dp[i] < 0)
return 0;
return 1;
}
