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Submission #426391

# Submission time Handle Problem Language Result Execution time Memory
426391 2021-06-13T22:54:43 Z timmyfeng Shortcut (IOI16_shortcut) C++17
0 / 100
 2 ms 460 KB 
#include <bits/stdc++.h>
using namespace std;
 
const int N = 1000001;
 
int sum_order[N], diff_order[N], n;
long long sum[N], diff[N], x[N];
 
long long find_shortcut(int n, vector<int> l, vector<int> d, int c) {
    ::n = n;
 
    for (int i = 0; i < n - 1; ++i) {
        x[i + 1] = x[i] + l[i];
    }
 
    for (int i = 0; i < n; ++i) {
        sum[i] = x[i] + d[i];
        diff[i] = x[i] - d[i];
    }
 
    iota(sum_order, sum_order + n, 0);
    sort(sum_order, sum_order + n, [&](int a, int b) {
        return sum[a] < sum[b];
    });
 
    iota(diff_order, diff_order + n, 0);
    sort(diff_order, diff_order + n, [&](int a, int b) {
        return diff[a] < diff[b];
    });
 
    long long low = 0, high = sum[sum_order[n - 1]] - diff[diff_order[0]];
    while (low < high) {
        long long mid = (low + high) / 2;
 
        long long min_sum = LLONG_MIN, max_sum = LLONG_MAX;
        long long min_diff = LLONG_MIN, max_diff = LLONG_MAX;
 
        long long sum_1 = LLONG_MIN, sum_2 = LLONG_MIN;
        long long diff_1 = LLONG_MAX, diff_2 = LLONG_MAX;
 
        for (int i = 0, j = 0; j < n; ++j) {
            while (i < n && sum[sum_order[j]] - diff[diff_order[i]] > mid) {
                long long s = sum[diff_order[i]], d = diff[diff_order[i]];
                ++i;
 
                if (s > sum_1) {
                    sum_2 = sum_1, sum_1 = s;
                } else if (s > sum_2) {
                    sum_2 = s;
                }
 
                if (d < diff_1) {
                    diff_2 = diff_1, diff_1 = d;
                } else if (d < diff_2) {
                    diff_2 = d;
                }
            }
 
            long long s = sum[sum_order[j]] == sum_1 ? sum_2 : sum_1;
            long long d = diff[sum_order[j]] == diff_1 ? diff_2 : diff_1;
 
            if (s > LLONG_MIN) {
                min_sum = max(min_sum, -mid + c + sum[sum_order[j]] + s);
                max_sum = min(max_sum, mid - c + diff[sum_order[j]] + d);
                min_diff = max(min_diff, -mid + c + sum[sum_order[j]] - d);
                max_diff = min(max_diff, mid - c + diff[sum_order[j]] - s);
            }
        }
 
        if (n <= 3000) {
            long long alt_min_sum = LLONG_MIN, alt_max_sum = LLONG_MAX;
            long long alt_min_diff = LLONG_MIN, alt_max_diff = LLONG_MAX;
 
            for (int i = 0; i < n; ++i) {
                for (int j = i + 1; j < n; ++j) {
                    if (sum[j] - diff[i] > mid) {
                        alt_min_sum = max(min_sum, -mid + c + sum[j] + sum[i]);
                        alt_max_sum = min(max_sum, mid - c + diff[j] + diff[i]);
                        alt_min_diff = max(min_diff, -mid + c + sum[j] - diff[i]);
                        alt_max_diff = min(max_diff, mid - c + diff[j] - sum[i]);
                    }
                }
            }
 
            assert(
                alt_min_sum <= min_sum &&
                alt_max_sum >= max_sum &&
                alt_min_diff <= min_diff &&
                alt_max_diff >= max_diff
            );
        }
 
        bool ok = false;
        int l1 = n - 1, l2 = 0, r1 = n - 1, r2 = 0;
        for (int i = 0; i < n; ++i) {
            while (l1 >= 0 && x[i] + x[l1] >= min_sum) {
                --l1;
            }
            while (r1 >= 0 && x[i] + x[r1] > max_sum) {
                --r1;
            }
            while (l2 < n && x[i] - x[l2] > max_diff) {
                ++l2;
            }
            while (r2 < n && x[i] - x[r2] >= min_diff) {
                ++r2;
            }
            ok |= max(l1 + 1, l2) < min(r1 + 1, r2);
        }
 
        if (ok) {
            high = mid;
        } else {
            low = mid + 1;
        }
    }
 
    return low;
}

Subtask #1
0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB n = 4, 80 is a correct answer
2 Correct 1 ms 332 KB n = 9, 110 is a correct answer
3 Correct 1 ms 332 KB n = 4, 21 is a correct answer
4 Correct 1 ms 332 KB n = 3, 4 is a correct answer
5 Correct 1 ms 332 KB n = 2, 62 is a correct answer
6 Correct 1 ms 332 KB n = 2, 3 is a correct answer
7 Correct 1 ms 332 KB n = 3, 29 is a correct answer
8 Correct 1 ms 332 KB n = 2, 3 is a correct answer
9 Correct 1 ms 332 KB n = 2, 3 is a correct answer
10 Correct 1 ms 332 KB n = 2, 2000000001 is a correct answer
11 Correct 1 ms 332 KB n = 2, 3000000000 is a correct answer
12 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
13 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
14 Correct 1 ms 332 KB n = 4, 3000000001 is a correct answer
15 Correct 1 ms 304 KB n = 4, 4000000000 is a correct answer
16 Correct 1 ms 332 KB n = 5, 4000000000 is a correct answer
17 Correct 1 ms 332 KB n = 10, 1000000343 is a correct answer
18 Correct 1 ms 332 KB n = 10, 3189 is a correct answer
19 Correct 1 ms 332 KB n = 10, 7000000000 is a correct answer
20 Runtime error 2 ms 460 KB Execution killed with signal 6
21 Halted 0 ms 0 KB -

Subtask #2
0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB n = 4, 80 is a correct answer
2 Correct 1 ms 332 KB n = 9, 110 is a correct answer
3 Correct 1 ms 332 KB n = 4, 21 is a correct answer
4 Correct 1 ms 332 KB n = 3, 4 is a correct answer
5 Correct 1 ms 332 KB n = 2, 62 is a correct answer
6 Correct 1 ms 332 KB n = 2, 3 is a correct answer
7 Correct 1 ms 332 KB n = 3, 29 is a correct answer
8 Correct 1 ms 332 KB n = 2, 3 is a correct answer
9 Correct 1 ms 332 KB n = 2, 3 is a correct answer
10 Correct 1 ms 332 KB n = 2, 2000000001 is a correct answer
11 Correct 1 ms 332 KB n = 2, 3000000000 is a correct answer
12 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
13 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
14 Correct 1 ms 332 KB n = 4, 3000000001 is a correct answer
15 Correct 1 ms 304 KB n = 4, 4000000000 is a correct answer
16 Correct 1 ms 332 KB n = 5, 4000000000 is a correct answer
17 Correct 1 ms 332 KB n = 10, 1000000343 is a correct answer
18 Correct 1 ms 332 KB n = 10, 3189 is a correct answer
19 Correct 1 ms 332 KB n = 10, 7000000000 is a correct answer
20 Runtime error 2 ms 460 KB Execution killed with signal 6
21 Halted 0 ms 0 KB -

Subtask #3
0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB n = 4, 80 is a correct answer
2 Correct 1 ms 332 KB n = 9, 110 is a correct answer
3 Correct 1 ms 332 KB n = 4, 21 is a correct answer
4 Correct 1 ms 332 KB n = 3, 4 is a correct answer
5 Correct 1 ms 332 KB n = 2, 62 is a correct answer
6 Correct 1 ms 332 KB n = 2, 3 is a correct answer
7 Correct 1 ms 332 KB n = 3, 29 is a correct answer
8 Correct 1 ms 332 KB n = 2, 3 is a correct answer
9 Correct 1 ms 332 KB n = 2, 3 is a correct answer
10 Correct 1 ms 332 KB n = 2, 2000000001 is a correct answer
11 Correct 1 ms 332 KB n = 2, 3000000000 is a correct answer
12 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
13 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
14 Correct 1 ms 332 KB n = 4, 3000000001 is a correct answer
15 Correct 1 ms 304 KB n = 4, 4000000000 is a correct answer
16 Correct 1 ms 332 KB n = 5, 4000000000 is a correct answer
17 Correct 1 ms 332 KB n = 10, 1000000343 is a correct answer
18 Correct 1 ms 332 KB n = 10, 3189 is a correct answer
19 Correct 1 ms 332 KB n = 10, 7000000000 is a correct answer
20 Runtime error 2 ms 460 KB Execution killed with signal 6
21 Halted 0 ms 0 KB -

Subtask #4
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB n = 4, 80 is a correct answer
2 Correct 1 ms 332 KB n = 9, 110 is a correct answer
3 Correct 1 ms 332 KB n = 4, 21 is a correct answer
4 Correct 1 ms 332 KB n = 3, 4 is a correct answer
5 Correct 1 ms 332 KB n = 2, 62 is a correct answer
6 Correct 1 ms 332 KB n = 2, 3 is a correct answer
7 Correct 1 ms 332 KB n = 3, 29 is a correct answer
8 Correct 1 ms 332 KB n = 2, 3 is a correct answer
9 Correct 1 ms 332 KB n = 2, 3 is a correct answer
10 Correct 1 ms 332 KB n = 2, 2000000001 is a correct answer
11 Correct 1 ms 332 KB n = 2, 3000000000 is a correct answer
12 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
13 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
14 Correct 1 ms 332 KB n = 4, 3000000001 is a correct answer
15 Correct 1 ms 304 KB n = 4, 4000000000 is a correct answer
16 Correct 1 ms 332 KB n = 5, 4000000000 is a correct answer
17 Correct 1 ms 332 KB n = 10, 1000000343 is a correct answer
18 Correct 1 ms 332 KB n = 10, 3189 is a correct answer
19 Correct 1 ms 332 KB n = 10, 7000000000 is a correct answer
20 Runtime error 2 ms 460 KB Execution killed with signal 6
21 Halted 0 ms 0 KB -

Subtask #5
0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB n = 4, 80 is a correct answer
2 Correct 1 ms 332 KB n = 9, 110 is a correct answer
3 Correct 1 ms 332 KB n = 4, 21 is a correct answer
4 Correct 1 ms 332 KB n = 3, 4 is a correct answer
5 Correct 1 ms 332 KB n = 2, 62 is a correct answer
6 Correct 1 ms 332 KB n = 2, 3 is a correct answer
7 Correct 1 ms 332 KB n = 3, 29 is a correct answer
8 Correct 1 ms 332 KB n = 2, 3 is a correct answer
9 Correct 1 ms 332 KB n = 2, 3 is a correct answer
10 Correct 1 ms 332 KB n = 2, 2000000001 is a correct answer
11 Correct 1 ms 332 KB n = 2, 3000000000 is a correct answer
12 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
13 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
14 Correct 1 ms 332 KB n = 4, 3000000001 is a correct answer
15 Correct 1 ms 304 KB n = 4, 4000000000 is a correct answer
16 Correct 1 ms 332 KB n = 5, 4000000000 is a correct answer
17 Correct 1 ms 332 KB n = 10, 1000000343 is a correct answer
18 Correct 1 ms 332 KB n = 10, 3189 is a correct answer
19 Correct 1 ms 332 KB n = 10, 7000000000 is a correct answer
20 Runtime error 2 ms 460 KB Execution killed with signal 6
21 Halted 0 ms 0 KB -

Subtask #6
0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB n = 4, 80 is a correct answer
2 Correct 1 ms 332 KB n = 9, 110 is a correct answer
3 Correct 1 ms 332 KB n = 4, 21 is a correct answer
4 Correct 1 ms 332 KB n = 3, 4 is a correct answer
5 Correct 1 ms 332 KB n = 2, 62 is a correct answer
6 Correct 1 ms 332 KB n = 2, 3 is a correct answer
7 Correct 1 ms 332 KB n = 3, 29 is a correct answer
8 Correct 1 ms 332 KB n = 2, 3 is a correct answer
9 Correct 1 ms 332 KB n = 2, 3 is a correct answer
10 Correct 1 ms 332 KB n = 2, 2000000001 is a correct answer
11 Correct 1 ms 332 KB n = 2, 3000000000 is a correct answer
12 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
13 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
14 Correct 1 ms 332 KB n = 4, 3000000001 is a correct answer
15 Correct 1 ms 304 KB n = 4, 4000000000 is a correct answer
16 Correct 1 ms 332 KB n = 5, 4000000000 is a correct answer
17 Correct 1 ms 332 KB n = 10, 1000000343 is a correct answer
18 Correct 1 ms 332 KB n = 10, 3189 is a correct answer
19 Correct 1 ms 332 KB n = 10, 7000000000 is a correct answer
20 Runtime error 2 ms 460 KB Execution killed with signal 6
21 Halted 0 ms 0 KB -

Subtask #7
0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB n = 4, 80 is a correct answer
2 Correct 1 ms 332 KB n = 9, 110 is a correct answer
3 Correct 1 ms 332 KB n = 4, 21 is a correct answer
4 Correct 1 ms 332 KB n = 3, 4 is a correct answer
5 Correct 1 ms 332 KB n = 2, 62 is a correct answer
6 Correct 1 ms 332 KB n = 2, 3 is a correct answer
7 Correct 1 ms 332 KB n = 3, 29 is a correct answer
8 Correct 1 ms 332 KB n = 2, 3 is a correct answer
9 Correct 1 ms 332 KB n = 2, 3 is a correct answer
10 Correct 1 ms 332 KB n = 2, 2000000001 is a correct answer
11 Correct 1 ms 332 KB n = 2, 3000000000 is a correct answer
12 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
13 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
14 Correct 1 ms 332 KB n = 4, 3000000001 is a correct answer
15 Correct 1 ms 304 KB n = 4, 4000000000 is a correct answer
16 Correct 1 ms 332 KB n = 5, 4000000000 is a correct answer
17 Correct 1 ms 332 KB n = 10, 1000000343 is a correct answer
18 Correct 1 ms 332 KB n = 10, 3189 is a correct answer
19 Correct 1 ms 332 KB n = 10, 7000000000 is a correct answer
20 Runtime error 2 ms 460 KB Execution killed with signal 6
21 Halted 0 ms 0 KB -

Subtask #8
0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB n = 4, 80 is a correct answer
2 Correct 1 ms 332 KB n = 9, 110 is a correct answer
3 Correct 1 ms 332 KB n = 4, 21 is a correct answer
4 Correct 1 ms 332 KB n = 3, 4 is a correct answer
5 Correct 1 ms 332 KB n = 2, 62 is a correct answer
6 Correct 1 ms 332 KB n = 2, 3 is a correct answer
7 Correct 1 ms 332 KB n = 3, 29 is a correct answer
8 Correct 1 ms 332 KB n = 2, 3 is a correct answer
9 Correct 1 ms 332 KB n = 2, 3 is a correct answer
10 Correct 1 ms 332 KB n = 2, 2000000001 is a correct answer
11 Correct 1 ms 332 KB n = 2, 3000000000 is a correct answer
12 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
13 Correct 1 ms 332 KB n = 3, 3000000000 is a correct answer
14 Correct 1 ms 332 KB n = 4, 3000000001 is a correct answer
15 Correct 1 ms 304 KB n = 4, 4000000000 is a correct answer
16 Correct 1 ms 332 KB n = 5, 4000000000 is a correct answer
17 Correct 1 ms 332 KB n = 10, 1000000343 is a correct answer
18 Correct 1 ms 332 KB n = 10, 3189 is a correct answer
19 Correct 1 ms 332 KB n = 10, 7000000000 is a correct answer
20 Runtime error 2 ms 460 KB Execution killed with signal 6
21 Halted 0 ms 0 KB -