#include "walk.h"
#include <algorithm>
#include <iostream>
#include <numeric>
#include <cassert>
#include <vector>
#include <queue>
#include <stack>
#include <map>
typedef long long llong;
const int MAXN = 100000 + 10;
const int INTERSECTIONS = 10 + 5;
const llong INF = 1e18;
const int INTINF = 1e9;
const int MAXLOG = 17;
namespace
{
int cnt;
int n, m;
int s, t;
int h[MAXN];
int x[MAXN];
int left[MAXN];
int right[MAXN];
int y[MAXN];
std::map <int,int> map[MAXN];
bool vis[MAXN * INTERSECTIONS];
llong dist[MAXN * INTERSECTIONS];
std::vector <std::pair <int,int>> g[MAXN * INTERSECTIONS];
int cntNodes;
}
struct Sparse
{
int sparse[MAXLOG][MAXN];
int getLOG[MAXN];
void build(int a[])
{
for (int i = 1 ; i <= n ; ++i)
{
sparse[0][i] = a[i];
}
for (int lg = 1 ; (1 << lg) <= n ; ++lg)
{
for (int i = 1 ; i + (1 << lg) - 1 <= n ; ++i)
{
sparse[lg][i] = std::max(sparse[lg - 1][i], sparse[lg - 1][i + (1 << lg - 1)]);
}
}
for (int i = 1 ; i <= n ; ++i)
{
getLOG[i] = getLOG[i - 1];
if ((1 << getLOG[i] + 1) < i) getLOG[i]++;
}
}
int findMAX(int l, int r)
{
int lg = getLOG[r - l + 1];
return std::max(sparse[lg][l], sparse[lg][r - (1 << lg) + 1]);
}
};
Sparse sparse;
llong solve()
{
for (int i = 1 ; i <= n ; ++i)
{
map[i][0] = ++cnt;
}
sparse.build(h);
for (int i = 1 ; i <= m ; ++i)
{
int prev = left[i];
if (map[left[i]][y[i]] == 0)
{
map[left[i]][y[i]] = ++cnt;
}
while (prev < right[i])
{
int l = prev, r = right[i] + 1, mid;
while (l < r - 1)
{
mid = l + r >> 1;
if (sparse.findMAX(prev + 1, mid) < y[i]) l = mid;
else r = mid;
}
if (map[r][y[i]] == 0)
{
map[r][y[i]] = ++cnt;
}
// std::cout << "here: " << prev << ' ' << r << ' ' << y[i] << '\n';
g[map[prev][y[i]]].push_back({map[r][y[i]], x[r] - x[prev]});
g[map[r][y[i]]].push_back({map[prev][y[i]], x[r] - x[prev]});
prev = r;
}
}
for (int i = 1 ; i <= n ; ++i)
{
auto prev = map[i].begin();
for (auto curr = std::next(map[i].begin()) ; curr != map[i].end() ; ++curr)
{
// std::cout << "edge ver: " << x[i] << ' ' << prev->first << ' ' << x[i] << ' ' << curr->first << '\n';
g[prev->second].push_back({curr->second, curr->first - prev->first});
g[curr->second].push_back({prev->second, curr->first - prev->first});
prev = curr;
}
}
std::priority_queue <std::pair <llong,int>> pq;
std::fill(dist + 1, dist + 1 + cnt, INF);
pq.push({0, map[s][0]});
dist[map[s][0]] = 0;
while (pq.size())
{
auto [d, node] = pq.top();
pq.pop();
if (vis[node])
{
continue;
}
vis[node] = true;
for (const auto &[u, ed] : g[node])
{
if (dist[u] > dist[node] + ed)
{
dist[u] = dist[node] + ed;
pq.push({-dist[u], u});
}
}
}
return (dist[map[t][0]] == INF ? -1 : dist[map[t][0]]);
}
long long min_distance(std::vector<int> x, std::vector<int> h, std::vector<int> l, std::vector<int> r, std::vector<int> y, int s, int t)
{
n = x.size();
m = l.size();
::s = s + 1; ::t = t + 1;
for (int i = 0 ; i < n ; ++i)
{
::h[i + 1] = h[i];
::x[i + 1] = x[i];
}
for (int i = 0 ; i < m ; ++i)
{
::left[i + 1] = l[i] + 1;
::right[i + 1] = r[i] + 1;
::y[i + 1] = y[i];
}
return solve();
}
