Submission #162730

#	Time	Username	Problem	Language	Result	Execution time	Memory
162730		rama_pang	Shortcut (IOI16_shortcut)	C++14	97 / 100	2045 ms	40568 KiB

shortcut

#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
const lint INF = 2e15;

int N, C;
vector<lint> X;
vector<lint> D;
vector<int> SUM; // index of increasing X[i] + D[i]
vector<int> DIF; // index of increasing X[i] - D[i]

bool is_valid(lint T) {
    bool valid   = false;
    lint max_sum = +INF; // maximum of S1 + S2 that is valid
    lint min_sum = -INF; // minimum of S1 + S2 that is valid
    lint max_dif = +INF; // maximum of S1 - S2 that is valid
    lint min_dif = -INF; // minimum of S1 - S2 that is valid
    lint sum_big = -INF; // maximum X[i] + D[i], for all valid i
    lint sum_sml = -INF; // second maximum X[i] + D[i], for all valid i
    lint sum_idx = -1;   // index of sum_big
    lint dif_sml = +INF; // minimum X[i] - D[i], for all valid i
    lint dif_big = +INF; // second minimum X[i] - D[i], for all valid i
    lint dif_idx = -1;   // index of dif_sml 
    lint new_sum = X[DIF[0]] + D[DIF[0]];
    lint new_dif = X[DIF[0]] - D[DIF[0]];
    lint cur_sum;
    lint cur_dif;
    lint valid_sum;
    lint valid_dif;

    for (int j = 0, pos = 0; j < N; j++) {
        cur_sum = X[SUM[j]] + D[SUM[j]];
        cur_dif = X[SUM[j]] - D[SUM[j]];

        while (pos < N && cur_sum - new_dif > T) {
            if (sum_big < new_sum) {
                sum_sml = sum_big;
                sum_big = new_sum;
                sum_idx = DIF[pos];
            } else if (sum_sml < new_sum) {
                sum_sml = new_sum;
            }

            if (dif_sml > new_dif) {
                dif_big = dif_sml;
                dif_sml = new_dif;
                dif_idx = DIF[pos];
            } else if (dif_big > new_dif) {
                dif_big = new_dif;
            }

            pos++;
            if (pos < N) new_sum = X[DIF[pos]] + D[DIF[pos]];
            if (pos < N) new_dif = X[DIF[pos]] - D[DIF[pos]];
        }
        
        valid_sum = ((SUM[j] == sum_idx)? sum_sml : sum_big);
        valid_dif = ((SUM[j] == dif_idx)? dif_big : dif_sml);

        max_sum = min(max_sum, + T + valid_dif + cur_dif - C);        
        min_sum = max(min_sum, - T + valid_sum + cur_sum + C);
        max_dif = min(max_dif, + T + valid_dif - cur_sum - C);
        min_dif = max(min_dif, - T + valid_sum - cur_dif + C);

    }

    for (int i = 0, ptl = 0, ptr = N - 1, pos; i < N && !valid; i++) {
        while (ptl <  N && X[ptl] - X[i] <  min_dif) ptl++;
        while (ptr >= 0 && X[ptr] + X[i] >= min_sum) ptr--;
        pos = max(ptl, ptr + 1);
        valid |= (pos < N && min_sum <= X[pos] + X[i] && X[pos] + X[i] <= max_sum 
                          && min_dif <= X[pos] - X[i] && X[pos] - X[i] <= max_dif);
    }

    return valid;
}

lint find_shortcut(int n_, vector<int> l_, vector<int> d_, int c_) {
    N = n_, C = c_;
    X.reserve(N), D.reserve(N), SUM.reserve(N), DIF.reserve(N);
    X.resize(N), D.resize(N), SUM.resize(N), DIF.resize(N);

    for (int i = 0; i < l_.size(); i++)
        X[i + 1] = X[i] + l_[i];
    for (int i = 0; i < d_.size(); i++)
        D[i] = d_[i];
    
    iota(SUM.begin(), SUM.end(), 0), iota(DIF.begin(), DIF.end(), 0);
    sort(SUM.begin(), SUM.end(), [&] (int l, int r) { return X[l] + D[l] < X[r] + D[r]; });
    sort(DIF.begin(), DIF.end(), [&] (int l, int r) { return X[l] - D[l] < X[r] - D[r]; });

    lint res = 0;
    
    for (lint L = 0, R = INF, M = (L + R) / 2; L <= R; M = (L + R) / 2) 
        if (is_valid(M))
            R = M - 1, res = M;
        else
            L = M + 1;
    
    return res;
}

Compilation message (stderr)

shortcut.cpp: In function 'lint find_shortcut(int, std::vector<int>, std::vector<int>, int)':
shortcut.cpp:84:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 0; i < l_.size(); i++)
                     ~~^~~~~~~~~~~
shortcut.cpp:86:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 0; i < d_.size(); i++)
                     ~~^~~~~~~~~~~

• 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: 0 / 3