Submission #915309

#	Time	Username	Problem	Language	Result	Execution time	Memory
915309		vjudge1	Shortcut (IOI16_shortcut)	C++17	71 / 100	2049 ms	2908 KiB

shortcut

#include "shortcut.h"

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

long long find_shortcut(int n, std::vector<int> l, std::vector<int> d, int c) {
        vector<int64_t> a(n), b(n);  // a = x + d, b = x - d
        vector<int64_t> x(n);
        for (int i = 1; i < n; i++) x[i] = x[i - 1] + l[i - 1];
        for (int i = 0; i < n; i++) a[i] = x[i] + d[i], b[i] = x[i] - d[i];
        vector<int64_t> dx = x;
        for (auto& v : dx) v *= 2;

        // abs(x[i] - x[p]) + abs(x[j] - x[q]) + d[i] + d[j] + c <= target
        // x[i] - x[p] + x[j] - x[q] + d[i] + d[j] + c <= target
        // x[p] - x[i] + x[j] - x[q] + d[i] + d[j] + c <= target
        // x[i] - x[p] + x[q] - x[j] + d[i] + d[j] + c <= target
        // x[p] - x[i] + x[q] - x[j] + d[i] + d[j] + c <= target

        // x[p] + x[q] >= x[i] + x[j] + d[i] + d[j] + c - target
        // x[p] + x[q] <= x[i] + x[j] - d[i] - d[j] - c + target
        // x[q] - x[p] <= x[j] - x[i] - d[i] - d[j] - c + target
        // x[q] - q[p] >= x[j] - x[i] + d[i] + d[j] + c - target

        // k := c - target
        // x[p] + x[q] >= (x[i] + d[i]) + (x[j] + d[j]) + k
        // x[p] + x[q] <= (x[i] - d[i]) + (x[j] - d[j]) - k
        // x[q] - x[p] <= (x[j] - d[j]) - (x[i] + d[i]) - k
        // x[q] - x[p] >= (x[j] + d[j]) - (x[i] - d[i]) + k

        // x[p] + x[q] >= a[i] + a[j] + k
        // x[p] + x[q] <= b[i] + b[j] - k
        // x[q] - x[p] <= b[j] - a[i] - k
        // x[q] - x[p] >= a[j] - b[i] + k

        auto check = [&](int64_t target) {
                int64_t low_sum = -1e18, high_sum = +1e18;
                int64_t low_diff = -1e18, high_diff = +1e18;
                int64_t k = c - target;
                for (int i = 0; i < n; i++) {
                        for (int j = i + 1; j < n; j++) {
                                if (x[j] - x[i] + d[i] + d[j] > target) {
                                        low_sum = max(low_sum, a[i] + a[j] + k);
                                        high_sum = min(high_sum, b[i] + b[j] - k);
                                        low_diff = max(low_diff, a[j] - b[i] + k);
                                        high_diff = min(high_diff, b[j] - a[i] - k);
                                }
                        }
                }

                if (low_sum > high_sum || low_diff > high_diff) return 0;
                int low_sum_q = n - 1, low_diff_q = 0, high_sum_q = n - 1, high_diff_q = 0;
                for (int p = 0; p < n; p++) {
                        low_diff_q = max(low_diff_q, p + 1);
                        while (low_sum_q > p && x[p] + x[low_sum_q] >= low_sum) low_sum_q--;
                        while (high_sum_q >= 0 && x[p] + x[high_sum_q] > high_sum) high_sum_q--;
                        // (low_sum_q, high_sum_q]
                        while (low_diff_q < n && x[low_diff_q] - x[p] < low_diff) low_diff_q++;
                        while (high_diff_q < n && x[high_diff_q] - x[p] <= high_diff) high_diff_q++;
                        // [low_diff_q, high_diff_q)

                        low_sum_q = max(low_sum_q, p);
                        if (low_sum_q >= high_sum_q || low_diff_q >= high_diff_q) continue;
                        int max_l = max(low_sum_q + 1, low_diff_q);
                        int min_r = min(high_sum_q, high_diff_q - 1);
                        if (max_l <= min_r) {
                                return 1;
                        }
                }

                return 0;
        };

        int64_t low = 0, high = 1ll << 60;
        while (low < high) {
                int64_t mid = low + high >> 1;
                if (check(mid)) {
                        high = mid;
                } else {
                        low = mid + 1;
                }
        }
        return high;
}

Compilation message (stderr)

shortcut.cpp: In function 'long long int find_shortcut(int, std::vector<int>, std::vector<int>, int)':
shortcut.cpp:76:35: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   76 |                 int64_t mid = low + high >> 1;
      |                               ~~~~^~~~~~

• Subtask 1: 9 / 9
• Subtask 2: 14 / 14
• Subtask 3: 8 / 8
• Subtask 4: 7 / 7
• Subtask 5: 33 / 33
• Subtask 6: 0 / 22
• Subtask 7: 0 / 4
• Subtask 8: 0 / 3