Submission #162764

#	Time	Username	Problem	Language	Result	Execution time	Memory
162764		rama_pang	Shortcut (IOI16_shortcut)	C++14	100 / 100	1711 ms	104196 KiB

shortcut

#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
const lint INF = 2e15;
 
struct SumDif {
    lint sum, dif;
    lint X, D;
    int id;
};
 
int N, C;
 
SumDif SUM[1000000]; // increasing X[i] + D[i]
SumDif DIF[1000000]; // increasing X[i] - D[i]
 
lint X[1000000]; // location of main stations

bool is_valid(lint T) {
    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
    int  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
    int  dif_idx = -1;   // index of dif_sml
 
    for (int j = 0, pos = 0; j < N; j++) {
        while (pos < N && SUM[j].sum - DIF[pos].dif > T) {
            lint sum_val = DIF[pos].sum, dif_val = DIF[pos].dif;
 
            if (sum_big < sum_val) {
                sum_sml = sum_big;
                sum_big = sum_val;
                sum_idx = DIF[pos].id;
            } else if (sum_sml < sum_val) {
                sum_sml = sum_val;
            }
 
            if (dif_sml > dif_val) {
                dif_big = dif_sml;
                dif_sml = dif_val;
                dif_idx = DIF[pos].id;
            } else if (dif_big > dif_val) {
                dif_big = dif_val;
            }
 
            pos++;
        }
 
        lint valid_sum = ((SUM[j].id != sum_idx)? sum_big : sum_sml);
        lint valid_dif = ((SUM[j].id != dif_idx)? dif_sml : dif_big);
        lint sum_val = SUM[j].sum, dif_val = SUM[j].dif;
 
        max_sum = min(max_sum, + T + valid_dif + dif_val - C);        
        min_sum = max(min_sum, - T + valid_sum + sum_val + C);
        max_dif = min(max_dif, + T + valid_dif - sum_val - C);
        min_dif = max(min_dif, - T + valid_sum - dif_val + C);
    }
 
    if (min_sum > max_sum || min_dif > max_dif)
        return false;
    
    for (int i = 0, ptl = 0, ptr = N - 1, pos; i < N; 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);
        if (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 true;
    }
 
    return false;
}
 
lint find_shortcut(int n_, vector<int> l_, vector<int> D, int c_) {
    N = n_, C = c_;
    for (int i = 0; i < l_.size(); i++)
        X[i + 1] = X[i] + l_[i];
    for (int i = 0; i < N; i++) {
        SUM[i] = SumDif{X[i] + D[i], X[i] - D[i], X[i], D[i], i};
        DIF[i] = SumDif{X[i] + D[i], X[i] - D[i], X[i], D[i], i};
    }
 
    sort(SUM, SUM + N, [&] (SumDif &l, SumDif &r) { return l.sum < r.sum; });
    sort(DIF, DIF + N, [&] (SumDif &l, SumDif &r) { return l.dif < r.dif; });
 
    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:85:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int i = 0; i < l_.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: 3 / 3