oj.uz

Submission #432275

# Submission time Handle Problem Language Result Execution time Memory
432275 2021-06-18T07:04:35 Z blue Road Construction (JOI21_road_construction) C++17
11 / 100
 10000 ms 59524 KB 
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <set>
using namespace std;

/*
We transform each point (x, y) into a point (x', y') where x' = x+y and y' = x-y. The Manhattan
distance between (x1, y1) and (x2, y2) = |x1-x2| + |y1-y2| = max( |x1'-x2'|, |y1'-y2'| ).

1. Transform each point (x, y) into a point (x1, y1) where x1 = x+y and y1 = x-y. √
2. Sort the points (x1, y1) twice, once by x1 and once by y1. √
3. Iterate over points sorted by x1:
4.      Maintain a set of these points sorted by the distance to the closest neighbor.
5.      Repeatedly, find the smallest such distance.
6.      If this distance is larger than the X-Y distance, add it to the result set.
*/

long long long_absval(long long x)
{
    return max(x, -x);
}

const int maxN = 250000;
const long long INF = 1'000'000'000'000'000'000LL;

vector<long long> A(1+maxN), B(1+maxN);
vector<int> I_A, I_B;

int N, K;

struct loc
{
    int i;
    long long v;
};

bool operator < (loc P, loc Q)
{
    if(P.v == Q.v) return P.i < Q.i;
    return P.v < Q.v;
}


vector<int> nxtA, nxtB;
vector<long long> valA, valB;

void compute_score_A(int i)
{
    valA[i] = INF;
    if(nxtA[i] <= N-1)
    {
        valA[i] = A[ I_A[nxtA[i]] ] - A[ I_A[i] ];
    }
}

void compute_score_B(int i)
{
    valB[i] = INF;

    if(nxtB[i] <= N-1)
    {
        valB[i] = B[ I_B[nxtB[i]] ] - B[ I_B[i] ];
    }
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    cin >> N >> K;

    for(int i = 1; i <= N; i++)
    {
        long long X, Y;
        cin >> X >> Y;
        A[i] = X+Y;
        B[i] = X-Y;
    }

    I_A = I_B = vector<int>(N);
    for(int i = 0; i < N; i++)
    {
        I_A[i] = i+1;
        I_B[i] = i+1;
    }

    sort(I_A.begin(), I_A.end(), [] (int p, int q)
    {
        return A[p] < A[q];
    });

    sort(I_B.begin(), I_B.end(), [] (int p, int q)
    {
        return B[p] < B[q];
    });

    multiset<long long> res;







    nxtA = vector<int>(N);
    for(int i = 0; i < N; i++)
    {
        nxtA[i] = i+1;
    }

    valA = vector<long long>(N, INF);
    for(int i = 0; i < N; i++)
    {
        compute_score_A(i);
    }
    set<loc> LA;
    for(int i = 0; i < N; i++) LA.insert(loc{i, valA[i]});









    nxtB = vector<int>(N);
    for(int i = 0; i < N; i++)
    {
        nxtB[i] = i+1;
    }

    valB = vector<long long>(N, INF);
    for(int i = 0; i < N; i++)
    {
        compute_score_B(i);
    }

    set<loc> LB;
    for(int i = 0; i < N; i++) LB.insert(loc{i, valB[i]});






    while(res.size() < K)
    {
        if(valA[LA.begin()->i] < valB[LB.begin()->i])
        {
            int i = LA.begin()->i;

            LA.erase(LA.begin());

            // cerr << i << ' ' << val[i] << ' ' << nxt[i] << '\n';

            // if(val[i] >= INF) break;

            int j = nxtA[i];               //!!!!!

            if(j > N-1) break;

            if(long_absval(A[ I_A[i] ] - A[ I_A[j] ]) >= long_absval(B[ I_A[i] ] - B[ I_A[j] ]))
            {
                res.insert(long_absval(A[ I_A[i] ] - A[ I_A[j] ]));
                // cerr << I_A[i] << ' ' << I_A[j] << ' ' << abs(A[ I_A[i] ] - A[ I_A[j] ]) << '\n';
            }
            nxtA[i]++;
            compute_score_A(i);

            LA.insert(loc{i, valA[i]});
        }
        else
        {
            int i = LB.begin()->i;

            LB.erase(LB.begin());

            int j = nxtB[i];               //!!!!!

            // cerr << i << ' ' << val[i] << ' ' << nxt[i] << '\n';

            if(j > N-1) break;

            if(long_absval(B[ I_B[i] ] - B[ I_B[j] ]) > long_absval(A[ I_B[i] ] - A[ I_B[j] ]))
            {
                res.insert(long_absval(B[ I_B[i] ] - B[ I_B[j] ]));
                // cerr << I_B[i] << ' ' << I_B[j] << ' ' << abs(B[ I_B[i] ] - B[ I_B[j] ]) << '\n';
            }
            nxtB[i]++;
            compute_score_B(i);

            LB.insert(loc{i, valB[i]});
        }
    }







    int ct = 0;
    for(long long r:res)
    {
        ct++;
        if(ct > K) break;
        cout << r << '\n';
    }
}

/* Version 1


//Part 1: iterate over I_A;
nxtA = vector<int>(N);
for(int i = 0; i < N; i++)
{
    nxtA[i] = i+1;
}

valA = vector<long long>(N, INF);
for(int i = 0; i < N; i++)
{
    compute_score_A(i);
}

set<loc> LA;
for(int i = 0; i < N; i++) LA.insert(loc{i, valA[i]});

++++

while(res.size() < K)
{
    int i = LA.begin()->i;

    LA.erase(LA.begin());

    // cerr << i << ' ' << val[i] << ' ' << nxt[i] << '\n';

    // if(val[i] >= INF) break;

    int j = nxtA[i];               //!!!!!

    if(j > N-1) break;

    if(long_absval(A[ I_A[i] ] - A[ I_A[j] ]) >= long_absval(B[ I_A[i] ] - B[ I_A[j] ]))
    {
        res.insert(long_absval(A[ I_A[i] ] - A[ I_A[j] ]));
        // cerr << I_A[i] << ' ' << I_A[j] << ' ' << abs(A[ I_A[i] ] - A[ I_A[j] ]) << '\n';
    }
    nxtA[i]++;
    compute_score_A(i);

    LA.insert(loc{i, valA[i]});
}












// cerr << "switching \n";





//Part 2: iterate over I_B;
nxtB = vector<int>(N);
for(int i = 0; i < N; i++)
{
    nxtB[i] = i+1;
}

valB = vector<long long>(N, INF);
for(int i = 0; i < N; i++)
{
    compute_score_B(i);
}

set<loc> LB;
for(int i = 0; i < N; i++) LB.insert(loc{i, valB[i]});


++++++++++++

// cerr << "hello\n";

while(res.size() < 2*K)
{
    int i = LB.begin()->i;

    LB.erase(LB.begin());

    int j = nxtB[i];               //!!!!!

    // cerr << i << ' ' << val[i] << ' ' << nxt[i] << '\n';

    if(j > N-1) break;

    if(long_absval(B[ I_B[i] ] - B[ I_B[j] ]) > long_absval(A[ I_B[i] ] - A[ I_B[j] ]))
    {
        res.insert(long_absval(B[ I_B[i] ] - B[ I_B[j] ]));
        // cerr << I_B[i] << ' ' << I_B[j] << ' ' << abs(B[ I_B[i] ] - B[ I_B[j] ]) << '\n';
    }
    nxtB[i]++;
    compute_score_B(i);

    LB.insert(loc{i, valB[i]});
}




*/

Compilation message

road_construction.cpp: In function 'int main()':
road_construction.cpp:150:22: warning: comparison of integer expressions of different signedness: 'std::multiset<long long int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  150 |     while(res.size() < K)
      |           ~~~~~~~~~~~^~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 272 ms 18756 KB Output is correct
2 Correct 268 ms 18592 KB Output is correct
3 Correct 217 ms 18612 KB Output is correct
4 Correct 212 ms 18712 KB Output is correct
5 Correct 220 ms 17476 KB Output is correct
6 Correct 12 ms 4432 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 1667 ms 56340 KB Output is correct
2 Correct 1644 ms 59524 KB Output is correct
3 Correct 205 ms 18496 KB Output is correct
4 Correct 586 ms 59056 KB Output is correct
5 Correct 728 ms 59204 KB Output is correct
6 Correct 752 ms 59344 KB Output is correct
7 Correct 663 ms 58672 KB Output is correct

Subtask #3
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1108 ms 43388 KB Output is correct
2 Correct 1508 ms 43460 KB Output is correct
3 Correct 2 ms 4172 KB Output is correct
4 Correct 373 ms 43344 KB Output is correct
5 Execution timed out 10014 ms 48580 KB Time limit exceeded

Subtask #4
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1108 ms 43388 KB Output is correct
2 Correct 1508 ms 43460 KB Output is correct
3 Correct 2 ms 4172 KB Output is correct
4 Correct 373 ms 43344 KB Output is correct
5 Execution timed out 10014 ms 48580 KB Time limit exceeded

Subtask #5
0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 272 ms 18756 KB Output is correct
2 Correct 268 ms 18592 KB Output is correct
3 Correct 217 ms 18612 KB Output is correct
4 Correct 212 ms 18712 KB Output is correct
5 Correct 220 ms 17476 KB Output is correct
6 Correct 12 ms 4432 KB Output is correct
7 Execution timed out 10051 ms 19896 KB Time limit exceeded
8 Halted 0 ms 0 KB -

Subtask #6
0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 272 ms 18756 KB Output is correct
2 Correct 268 ms 18592 KB Output is correct
3 Correct 217 ms 18612 KB Output is correct
4 Correct 212 ms 18712 KB Output is correct
5 Correct 220 ms 17476 KB Output is correct
6 Correct 12 ms 4432 KB Output is correct
7 Correct 1667 ms 56340 KB Output is correct
8 Correct 1644 ms 59524 KB Output is correct
9 Correct 205 ms 18496 KB Output is correct
10 Correct 586 ms 59056 KB Output is correct
11 Correct 728 ms 59204 KB Output is correct
12 Correct 752 ms 59344 KB Output is correct
13 Correct 663 ms 58672 KB Output is correct
14 Correct 1108 ms 43388 KB Output is correct
15 Correct 1508 ms 43460 KB Output is correct
16 Correct 2 ms 4172 KB Output is correct
17 Correct 373 ms 43344 KB Output is correct
18 Execution timed out 10014 ms 48580 KB Time limit exceeded