// model_solution/solution.cpp
#include "overtaking.h"
#include <vector>
#include <algorithm>
#include <iostream>
#include <set>
#define MAXNM 1001000
#define MAXTIME 1000000000000000000
using namespace std;
long long L, N, M, X, Y, id, station;
long long a;
long long T[MAXNM];
long long W[MAXNM];
long long S[MAXNM];
vector<long long> currT[MAXNM];
vector<int> cars[MAXNM];
// set<pair<int, int>> overtake[MAXNM];
pair<int, int> overtake[1000][1000];
// set<pair<long long, long long>> ans[MAXNM];
long long ans[1000][1000];
vector<pair<int, long long>> mem;
bool ahead(int x, int y)
{
return currT[id][x] < currT[id][y] || (currT[id][x] == currT[id][y] && W[x] < W[y]);
}
void init(int LL, int NN, std::vector<long long> TT, std::vector<int> WW, int XX, int MM, std::vector<int> SS)
{
L = LL;
N = NN;
M = MM;
X = XX;
id = 0;
for (long long i : TT)
T[id++] = i;
id = 0;
for (int i : WW)
W[id++] = i;
id = 0;
for (int i : SS)
S[id++] = i;
id = 0;
for (int i = 0; i < N; i++)
{
if (W[i] > X)
{
W[id] = W[i];
T[id] = T[i];
id++;
}
}
N = id;
for (int s = 0; s < M; s++)
{
currT[s] = vector<long long>(N);
cars[s] = vector<int>(N);
for (int i = 0; i < N; i++)
cars[s][i] = i;
}
for (int i = 0; i < N; i++)
{
currT[0][i] = T[i];
}
id = 0;
std::sort(cars[0].begin(), cars[0].end(), ahead);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M - 1; j++)
overtake[i][j] = {-1, -1};
overtake[i][M - 1] = {M, -1};
}
for (int s = 1; s < M; s++)
{
long long d = S[s] - S[s - 1];
long long maxTime = 0, maxCar = -1;
for (int i = 0; i < N; i++)
{
int car = cars[s - 1][i];
if (maxTime < currT[s - 1][car] + W[car] * d)
{
maxTime = currT[s - 1][car] + W[car] * d;
maxCar = car;
}
else
{
// overtake[car].insert({s, maxCar});
if (overtake[car][s].second == -1 || W[overtake[car][s].second] < W[maxCar])
overtake[car][s] = {s, maxCar};
}
currT[s][car] = maxTime;
}
id = s;
std::sort(cars[s].begin(), cars[s].end(), ahead);
}
// for (int i = 0; i < N; i++)
// overtake[i].insert({M, -1});
for (int i = 0; i < N; i++)
{
for (int j = M - 2; j >= 0; j--)
{
if (overtake[i][j].first == -1)
overtake[i][j] = overtake[i][j + 1];
}
}
}
int vertBin(int s, int x, int y)
{
if (Y <= currT[s][cars[s][0]])
return -1;
if (x == y)
return cars[s][x];
int half = (x + y + 1) / 2;
if (currT[s][cars[s][half]] < Y)
return vertBin(s, half, y);
return vertBin(s, x, half - 1);
}
int horBin(int carId, int x, int y)
{
if (x == y)
return x;
int half = (x + y) / 2;
if (Y + X * (S[half] - S[station]) > currT[half][carId])
return horBin(carId, half + 1, y);
return horBin(carId, x, half);
}
long long arrival_time(long long YY)
{
Y = YY;
if (N == 0)
return Y + L * X;
station = 0;
int below = vertBin(0, 0, N - 1);
mem.clear();
while (station != M - 1)
{
if (below == -1)
{
Y += X * (L - S[station]);
break;
}
//auto it = overtake[below].lower_bound({station + 1, -1});
//int pos = (*it).first;
int pos = overtake[below][station + 1].first;
int st = pos - 1;
if (Y + (S[st] - S[station]) * X > currT[st][below])
{
Y += (S[st] - S[station]) * X;
below = overtake[below][station + 1].second;
station = st;
}
else
{
int ost = horBin(below, station, st);
Y = currT[ost][below];
station = ost;
if (below != -1 && ans[station][below] != 0)
{
Y = ans[station][below];
break;
}
mem.push_back({station, below});
below = vertBin(station, 0, N - 1);
}
}
for (auto it : mem)
// ans[it.first].insert({it.second, Y});
ans[it.first][it.second] = Y;
return Y;
}
