Submission #1311123

#	Time	Username	Problem	Language	Result	Execution time	Memory
1311123		math_rabbit_1028	Shortcut (IOI16_shortcut)	C++20	100 / 100	782 ms	55228 KiB

shortcut

#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;

int n, c;
vector<int> l, d;
vector<long long> sum;
vector<int> ord, idx;
vector<pair<int, int>> spd, smd;

bool check(long long lim) {
    pair<long long, long long> xpy = {-1e18, 1e18}, xmy = {-1e18, 1e18};
    int q = 0;
    for (int p = 0; p < n; p++) {
        int i = ord[p];
        while (q < n && d[i] + d[idx[q]] + sum[idx[q]] - sum[i] <= lim) q++;
        if (q == n) break;
        int j1 = (spd[q].first == i ? spd[q].second : spd[q].first);
        int j2 = (smd[q].first == i ? smd[q].second : smd[q].first);
        // xpy.first <- sum[i] + sum[j] - lim + c + d[i] + d[j] (max)
        // xpy.second <- sum[i] + sum[j] + lim - c - d[i] - d[j] (min)
        // xmy.first <- sum[i] - sum[j] - lim + c + d[i] + d[j] (max)
        // xmy.second <- sum[i] - sum[j] + lim - c - d[i] - d[j] (min)
        if (j1 > i) xpy.first = max(xpy.first, sum[i] - lim + c + d[i] + sum[j1] + d[j1]);
        if (j2 > i) xpy.second = min(xpy.second, sum[i] + lim - c - d[i] + sum[j2] - d[j2]);
        if (j2 > i) xmy.first = max(xmy.first, sum[i] - lim + c + d[i] - sum[j2] + d[j2]);
        if (j1 > i) xmy.second = min(xmy.second, sum[i] + lim - c - d[i] - sum[j1] - d[j1]);
    }
    q = 0;
    for (int p = 0; p < n; p++) {
        long long lb = max(xpy.first - sum[p], sum[p] - xmy.second);
        long long ub = min(xpy.second - sum[p], sum[p] - xmy.first);
        if (lb > ub) continue;
        q = max(q, p+1);
        while (q < n && sum[q] < lb) q++;
        while (q > p+1 && sum[q-1] >= lb) q--;
        if (q < n && sum[q] <= ub) return true;
    }
    return false;
}

long long get_lower_bound() {
    long long ret = 0;
    int j;
    for (int i = 0; i < n; i++) {
        if (ret < d[i]) {
            ret = d[i];
            j = i;
        }
    }
    ret = 0;
    for (int i = 0; i < n; i++) {
        if (i == j) continue;
        ret = max(ret, (long long)d[i]);
    }
    return ret + d[j];
}

long long find_shortcut(int _n, vector<int> _l, vector<int> _d, int _c) {
    n = _n;
    l = _l;
    d = _d;
    c = _c;
    sum.resize(n);
    sum[0] = 0;
    for (int i = 1; i < n; i++) {
        sum[i] = sum[i-1] + l[i-1];
    }
    idx.resize(n);
    for (int i = 0; i < n; i++) idx[i] = i;
    sort(idx.begin(), idx.end(), [](int a, int b) {
        return sum[a] + d[a] < sum[b] + d[b];
    });
    ord.resize(n);
    for (int i = 0; i < n; i++) ord[i] = i;
    sort(ord.begin(), ord.end(), [](int a, int b) {
        return sum[a] - d[a] < sum[b] - d[b];
    });
    spd.resize(n);
    for (int p = n - 1; p >= 0; p--) {
        int j = idx[p];
        if (p == n-1) spd[p] = {j, j};
        else if (p == n-2) spd[p] = sum[j] + d[j] > sum[idx[p+1]] + d[idx[p+1]] ? make_pair(j, idx[p+1]) : make_pair(idx[p+1], j);
        else {
            if (sum[j] + d[j] > sum[spd[p+1].first] + d[spd[p+1].first]) {
                spd[p] = {j, spd[p+1].first};
            }
            else if (sum[j] + d[j] > sum[spd[p+1].second] + d[spd[p+1].second]) {
                spd[p] = {spd[p+1].first, j};
            }
            else {
                spd[p] = spd[p+1];
            }
        }
    }
    smd.resize(n);
    for (int p = n - 1; p >= 0; p--) {
        int j = idx[p];
        if (p == n-1) smd[p] = {j, j};
        else if (p == n-2) smd[p] = sum[j] - d[j] < sum[idx[p+1]] - d[idx[p+1]] ? make_pair(j, idx[p+1]) : make_pair(idx[p+1], j);
        else {
            if (sum[j] - d[j] < sum[smd[p+1].first] - d[smd[p+1].first]) {
                smd[p] = {j, smd[p+1].first};
            }
            else if (sum[j] - d[j] < sum[smd[p+1].second] - d[smd[p+1].second]) {
                smd[p] = {smd[p+1].first, j};
            }
            else {
                smd[p] = smd[p+1];
            }
        }
    }

    long long st = get_lower_bound(), ed = 1e18;
    while (st < ed) {
        long long mid = (st + ed) / 2;
        if (check(mid)) ed = mid;
        else st = mid + 1;
    }
    
    return st;
}

Compilation message (stderr)

shortcut.h:1:9: warning: #pragma once in main file
    1 | #pragma once
      |         ^~~~
shortcut_c.h:1:9: warning: #pragma once in main file
    1 | #pragma once
      |         ^~~~

• Subtask 1: 9 / 9
• Subtask 2: 14 / 14
• Subtask 3: 8 / 8
• Subtask 4: 7 / 7
• Subtask 5: 33 / 33
• Subtask 6: 22 / 22
• Subtask 7: 4 / 4
• Subtask 8: 3 / 3