Submission #171541

#	Time	Username	Problem	Language	Result	Execution time	Memory
171541		ho94949	Long Distance Coach (JOI17_coach)	C++17	100 / 100	853 ms	39728 KiB

coach

#include<bits/stdc++.h>
using namespace std;
const int MAXN = 202020;
long long X, N, M, W, T;
long long S[MAXN];
long long D[MAXN], C[MAXN];

// used water before kickout
long long nw[MAXN];

//1~(i-1) customer minimum value when ith person do not kicked
// -(C_1+...+C_i)+ WV[i] customer's required value.
long long DP[MAXN];

// drank water of ith customer if none was kicked
long long WV[MAXN];

int pv[MAXN];

// min li-chao tree
struct Line
{
    long long a;
    long long b;
};
const long long INFV = (long long)1e18;
Line emptyl = {INFV, INFV};
struct Node
{
    long long s, e;
    Node* l;
    Node* r;
    Line v;
    Node(long long _s, long long _e)
    :s(_s), e(_e), l(nullptr), r(nullptr), v(emptyl)
    {

    }
    __int128 getv(long long x)
    {
        assert(v.a != INFV);
        __int128 ans = (__int128)v.a*x+v.b;
        long long m = (s+e)>>1;
        if(x<=m && l) ans = min(ans, l->getv(x));
        if(x>m && r) ans = min(ans, r->getv(x));
        return ans;
    }
    void setv(Line x)
    {
        if(v.a==INFV && v.b==INFV)
        {
            v = x;
            return;
        }
        if(s==e)
        {
            if((__int128)s*v.a+v.b > (__int128)s*x.a+x.b)
                swap(v, x);
            return;
        }
        long long m = (s+e)>>1;
        long long pt = 2*m+1;
        __int128 exist = (__int128)v.a*pt+2*v.b;
        __int128 nv = (__int128)x.a*pt+2*x.b;
        if(exist > nv)
            swap(v, x);
        
        if(v.a < x.a)
        {
            if(!l) l = new Node(s, m);
            l->setv(x);
        }
        else
        {
            if(!r) r = new Node(m+1, e);
            r->setv(x);
        }
    }
};


long long do_dp()
{
    Node* root = new Node(-INFV, INFV);
    DP[0] = 0; root->setv({-0, DP[0]});
    for(int i=1; i<=M+1; ++i)
    {
        DP[i] = DP[i-1]; // not kicking (i-1)th customer

        if(nw[i] != -1) // if can start kicking strategy,
        {
            DP[i] = min(DP[i], (long long)(root->getv(nw[i])+(i-1)*nw[i]));
            
            /*
            for(int j=i-2; j>=0; --j) //not kicking jth customer, kicking all
            
                DP[i] = min(DP[i], DP[j]+(i-j-1)*nw[i]);
            */    
        }
        if(pv[i] != 0) //kick through pv player and let what they want.
        {
            //cout << "!" << i << " " << pv[i] << endl;
            DP[i] = min(DP[i], DP[pv[i]] - WV[pv[i]] +C[pv[i]] + (i-pv[i])*nw[i]);
        }
        DP[i] += -C[i] + WV[i];
        root->setv({-i, DP[i]});
        //printf("%d %lld %lld\n", i, nw[i], DP[i]);
    }

    long long ans = DP[M+1]; //basic DP value;
    //we remove C_1...C_M
    for(int i=1; i<=M; ++i) ans += C[i];
    // WV[M+1] is defined as 0
    // we should add bus drivers' cost
    ans += W*(1+X/T);
    return ans;
}
int main()
{
    cin >> X >> N >> M >> W >> T;
    for(int i=0; i<N; ++i) cin >> S[i];
    vector<pair<long long, long long> > VDC;
    for(int i=0; i<M; ++i)
    {
        long long d, c;
        cin >> d >> c;
        VDC.emplace_back(d, c);
    }
    sort(VDC.begin(), VDC.end());
    for(int i=1; i<=M; ++i)
    {
        tie(D[i], C[i]) = VDC[i-1];
        WV[i] = W*(1+(X-D[i])/T);
        //printf("%d: %lld %lld\n", i, WV[i], C[i]);
    }
    S[N] = X;
    sort(S, S+N+1);

    memset(nw, -1, sizeof nw);
    set<int> SS;
    for(int i=0; i<=N; ++i)
    {
        long long kickout_water = W*(S[i]/T);
        int kick_index = lower_bound(D+1, D+1+M, S[i]%T) - D;
        //printf("%lld %d\n", kickout_water, kick_index);
        // we will decide whether kick 1~kick_index
        if(kick_index == 1) continue;
        if(nw[kick_index] != -1) continue;
        nw[kick_index] = kickout_water;

        SS.insert(kick_index);
        auto it = SS.find(kick_index);
        if(it != SS.begin())
            pv[kick_index] = *(--it);
    }

    printf("%lld\n", do_dp());
}

• Subtask 1: 16 / 16
• Subtask 2: 30 / 30
• Subtask 3: 25 / 25
• Subtask 4: 29 / 29