Submission #785900

#	Time	Username	Problem	Language	Result	Execution time	Memory
785900		canadavid1	Teleporters (IOI08_teleporters)	C++14	100 / 100	503 ms	50476 KiB

teleporters

#include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
#define all(x) begin(x),end(x)
/*
Idea:
traverse without any added
enumerate and group up unreachable regions
need only count of number of teles in each region

only 2(teleporters)+1 states, changing takes exactly one teleport => optimal 2(n+m) points
any new teleporter added can only increase region count by 2, and should ideally connect a reachable and unreachable
section together (this makes the unreachable section a "subroutine" at the other point)

*/

// adding each teleporter:
    // if both endpoints are the same group, partition the group into "inside" and "outside"
    // if enpoints are different, the ends become the same group
    // sounds like union find

// size of the path. Made smaller for debugging purposes. Should be strictly bigger than the last paths end.
#define PATHLEN 2000010

signed main()
{
    int N,M;
    cin >> N >> M;
    vector<pair<int,int>> tele(N);
    for(int i = 0; i < N; i++) cin >> tele[i].first >> tele[i].second;
    // sorting the teleporters
    vector<int> to(PATHLEN,-1);
    for(auto i : tele) {to[i.first] = i.second;to[i.second] = i.first;}
    int c = 0;
    to.back() = 0;
    // tele contains now both ways, sorted by entrance -> exit. Though using to is more useful.
    vector<bool> group(PATHLEN,0);
    vector<int> gcs;
    for(int start = 0; start < PATHLEN; start++)
    {
        if(group[start]) continue;
        int gc = 0;
        int i = start;
        while(!group[i])
        {
            group[i] = true;
            if(to[i]==-1) {i++; continue;}
            i = to[i]+1;
            gc++;
        } 
        gcs.push_back(gc);
    }
    i64 sum_count = 0;
    if(M <= gcs.size()-1)
    {
        // group 0 is the one we start with.
        sum_count = gcs[0]-1;
        //sort(all(gcs)); // this can be problematic if ie all the paths are disjoint, giving 1e6 different groups
        // counting sort to the rescue again!
        vector<int> count(2*PATHLEN,0);
        for(auto i : gcs) count[i]++;
        // make the longest M groups accessible
        count[gcs[0]]--; // don't count the original path
        for(int i = count.size()-1; M > 0; i--)
        {
            if(!count[i]) continue;
            sum_count += i+2;
            count[i]--;
            i++;
            M--;
        }
    }
    else
    {
        // include all closed off paths
        for(auto i : gcs) sum_count += i+2; // +1 for going into (and out) of the group
        sum_count -= 3; // a little overcounting for the first group
        M -= gcs.size()-1;
        // adding two teleporters adds four
        sum_count += 4*(M/2);
        if(M%2) sum_count++;
    }
    cout << sum_count << "\n";
}

Compilation message (stderr)

teleporters.cpp: In function 'int main()':
teleporters.cpp:54:10: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   54 |     if(M <= gcs.size()-1)
      |        ~~^~~~~~~~~~~~~~~
teleporters.cpp:34:9: warning: unused variable 'c' [-Wunused-variable]
   34 |     int c = 0;
      |         ^

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