Submission #633460

#	Time	Username	Problem	Language	Result	Execution time	Memory
633460		Lawliet	Radio Towers (IOI22_towers)	C++17	0 / 100	933 ms	28192 KiB

towers

#include "towers.h"
#include <bits/stdc++.h>

using namespace std;

const int maxl = 20;
const int maxn = 100010;
const int inf = 1000000010;

class SparseTable
{
    public:

        void build(int n, vector<int> v, bool mn = false)
        {
            isMin = mn;

            for(int i = 1 ; i <= n ; i++)
                tab[0][i] = (mn ? -v[i] : v[i]);

            for(int k = 1 ; k < maxl ; k++)
                for(int i = 1 ; i + (1 << k) - 1 <= n ; i++)
                    tab[k][i] = max( tab[k - 1][i] , tab[k - 1][i + (1 << (k - 1))] ); 
        }

        int query(int l, int r)
        {
            if( l > r )
                return (isMin ? inf : -inf);

            int t = 31 - __builtin_clz(r - l + 1);
            int ans = max( tab[t][l] , tab[t][r - (1 << t) + 1] );

            return (isMin ? -ans : ans);
        }

    protected:

        bool isMin;
        int tab[maxl][maxn];
};

int n;

int v[maxn];

bool hasBuilt = false;

SparseTable stV, stR, stL, corner;

vector<int> valleys, optL, optR, cL, cR;

bool isValid(int i, int j, int D)
{
    int peak = stV.query( i + 1 , j - 1 );

    if( v[i] <= peak - D && v[j] <= peak - D )
        return true;

    return false;
}

int findOptL(int i, int D)
{
    int l = 1, r = i - 1;

    if( v[i] > stV.query( l , i - 1 ) - D )
        return 0;

    while( l < r )
    {
        int m = ( l + r )/2;
        if( l == r - 1 ) m = r;

        if( v[i] <= stV.query( m , i - 1 ) - D )
            l = m;
        else
            r = m - 1;
    }

    return l;
}

int findOptR(int i, int D)
{
    int l = i + 1, r = n;

    if( v[i] > stV.query( i + 1 , r ) - D )
        return n + 1;

    while( l < r )
    {
        int m = ( l + r )/2;

        if( v[i] <= stV.query( i + 1 , m ) - D )
            r = m;
        else
            l = m + 1;
    }

    return r;
}

void buildHistogram(int D)
{
    optL.resize( n + 1 );
    optR.resize( n + 1 );

    for(int i = 1 ; i <= n ; i++)
    {
        optL[i] = findOptL(i, D);
        optR[i] = findOptR(i, D);
    }
}

void build(int D)
{
    buildHistogram(D);

    stR.build( n , optR , true );
    stL.build( n , optL );

    // Corner Case

    cL.resize( n + 1 , 0 );
    cR.resize( n + 1 , n + 1 );

    for(int i = 1 ; i <= n ; i++)
    {
        cL[ optR[i] ] = max( cL[ optR[i] ] , i );
        cR[ optL[i] ] = min( cR[ optL[i] ] , i );
    }

    vector<int> tmp(n + 1, n + 1);

    for(int i = 1 ; i <= n ; i++)
        tmp[ cL[i] ] = min( tmp[ cL[i] ] , cR[i] );

    corner.build( n , tmp );

    // 

    for(int i = 1 ; i <= n ; i++)
    {
        while( !valleys.empty() )
        {
            int j = valleys.back();

            if( isValid( j , i , D ) )
            {
                valleys.push_back( i );
                break;
            }

            if( v[j] < v[i] )
                break;

            valleys.pop_back();
        }

        if( valleys.empty() )
            valleys.push_back( i );
    }

    hasBuilt = true;
}

void init(int N, vector<int> H) {
    n = N;

    H.insert( H.begin() , 0 );

    for(int i = 1 ; i <= n ; i++)
        v[i] = H[i];

    stV.build( n , H );
}

bool newPairL(int L, int opt)
{
    int l = L, r = optL[opt] - 1;

    if( stR.query( l , r ) < opt )
        return true;

    return false;
}

bool newPairR(int R, int opt)
{
    int l = optR[opt] + 1, r = R;

    if( opt < stL.query( l , r ) )
        return true;

    return false;
}

int max_towers(int L, int R, int D) 
{
    if( !hasBuilt )
        build( D );

    L++; R++;

    if( R - L + 1 <= 2 )
        return 1;

    int pL = lower_bound( valleys.begin() , valleys.end() , L ) - valleys.begin();
    int pR = upper_bound( valleys.begin() , valleys.end() , R ) - valleys.begin();

    if( pL == pR )
    {
        if( corner.query( L , R ) <= R )
            return 2;

        return 1;
    }

    int ans = pR - pL;

    if( newPairL( L , valleys[pL] ) )
        ans++;

    if( newPairR( R , valleys[pR - 1] ) )
        ans++;

    return ans;
}

• Subtask 1: 0 / 4
• Subtask 2: 0 / 11
• Subtask 3: 0 / 12
• Subtask 4: 0 / 14
• Subtask 5: 0 / 17
• Subtask 6: 0 / 19
• Subtask 7: 0 / 23