#include <bits/stdc++.h>
#include "circus.h"
#define mp make_pair
using namespace std;
const int INF = 1e9 + 1;
typedef pair<int, int> pi;
struct State {
int node;
bool forward;
int minlen;
};
bool operator > (const State& a, const State& b)
{
return a.minlen > b.minlen;
}
int N, M;
vector<int> p;
// nxt[i]: Next rope in the path from p[i] to M
vector<vector<int>> nxt;
/* minlen[i][fw]:
* The minimum length of rope needed in position p[i] to reach M.
* fw is a boolean variable denoting if the first step is forwards or backwards
*/
vector<vector<int>> minlen;
vector<int> tot;
/* change[i][fw]:
* The maximum/minimum position at which i becomes a better choice than i - 1
*/
vector<vector<int>> change;
priority_queue<State, vector<State>, greater<State>> q;
// Test if j can become the optimal next rope in the path from p[i] to M
void test(int i, int j)
{
if (i < 0 || i >= N) {
return;
}
bool fw = (i < j);
if (abs(p[i] - p[j]) >= tot[j] && abs(p[i] - p[j]) < minlen[i][fw]) {
minlen[i][fw] = abs(p[i] - p[j]);
nxt[i][fw] = j;
q.push({i, fw, minlen[i][fw]});
}
// If test fails then j cannot be used as a first step anymore(in the given direction)
}
void init(int n, int m, int P[]){
N = n;
M = m;
p.resize(N + 1);
minlen.assign(N + 1, vector<int>(2, INF));
nxt.resize(N + 1, vector<int>(2));
tot.assign(N + 1, INF);
change.resize(2, vector<int>(N + 1));
for (int i = 0; i < N; i++) {
p[i] = P[i];
}
p[N] = M;
minlen[N][1] = 0;
nxt[N][1] = N;
sort(p.begin(), p.end());
q.push({N, true, 0});
while (!q.empty()) {
int i, d;
bool fw;
auto res = q.top();
q.pop();
i = res.node;
d = res.minlen;
fw = res.forward;
if (minlen[i][fw] < d) {
continue;
}
tot[i] = min(tot[i], minlen[i][fw]);
// Advance nxt[i][fw]
int j;
if (fw) {
// Move more back
j = i - 1;
}
else {
// Move more front
j = i + 1;
}
test(j, nxt[i][fw]);
if (minlen[i][fw] != tot[i]) {
continue;
}
// Advance i
int p_l = upper_bound(p.begin(), p.end(), p[i] - tot[i]) - p.begin() - 1;
int p_r = lower_bound(p.begin(), p.end(), p[i] + tot[i]) - p.begin();
test(p_l, i);
test(p_r, i);
}
// Calculate the optimal first step forwards and backwards for each possile position
for (int i = 0; i <= N; i++) {
change[false][i] = p[i] + tot[i];
change[true][i] = p[i] - tot[i];
}
for (int i = 1; i <= N; i++) {
// If a rope further back allows a later forward step, propagate it
change[true][i] = max(change[true][i], change[true][i - 1]);
}
for (int i = N - 1; i >= 0; i--) {
// If a rope further font allows an earlier backward step, propagate it
change[false][i] = min(change[false][i], change[false][i + 1]);
}
}
int minLength(int D) {
// Find the positions that allow the best possible forward and backward steps
int f_pos = lower_bound(change[true].begin(), change[true].end(), D) - change[true].begin();
int b_pos = upper_bound(change[false].begin(), change[false].end(), D) - change[false].begin() - 1;
int ans = p[f_pos] - D;
if (b_pos >= 0) {
ans = min(ans, D - p[b_pos]);
}
return ans;
}
