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Submission #842432

# Submission time Handle Problem Language Result Execution time Memory
842432 2023-09-02T21:42:09 Z arnold518 Overtaking (IOI23_overtaking) C++17
100 / 100
 406 ms 46196 KB 
#include "overtaking.h"
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int MAXN = 1000;
const ll INF = 1e18;

int L, N;
pll P[MAXN+10];
int M, S[MAXN+10];
ll X;

int C[MAXN+10];
ll A[MAXN+10], B[MAXN+10], A2[MAXN+10][MAXN+10], ans[MAXN+10][MAXN+10];

struct Frac
{
    ll a, b;
    Frac(ll a, ll b) : a(a), b(b) {}
};
bool operator <= (Frac p, Frac q)
{
    if(p.a<0) p.a*=-1, p.b*=-1;
    if(q.a<0) q.a*=-1, q.b*=-1;
    return (__int128)p.b*q.a<=(__int128)q.b*p.a;
}

struct CHT
{
    vector<pair<pll, int>> V;
    CHT() {}
    Frac cross(pll p, pll q) { return {p.first-q.first, q.second-p.second}; }
    Frac f(pll p, ll y) { return {p.first, y-p.second}; }
    ll f2(pll p, ll y) { return (y-p.second+p.first-1)/p.first; }
    void push(pll p, int q)
    {
        while(!V.empty() && V.back().first.first<=p.first) V.pop_back();
        while(V.size()>1 && (V.back().first.first==p.first || cross(V[V.size()-2].first, V[V.size()-1].first)<=cross(V[V.size()-1].first, p))) V.pop_back();
        V.push_back({p, q});
    }
    pll query(ll y)
    {
        while(V.size()>1 && f(V[V.size()-2].first, y)<=f(V[V.size()-1].first, y)) V.pop_back();
        if(V.empty()) return {0, 0};
        else
        {
            return {V.back().second, f2(V.back().first, y)};
        }
    }
};
vector<ll> V1;
vector<CHT> V2;

void init(int _L, int _N, vector<ll> _T, vector<int> _W, int _X, int _M, vector<int> _S)
{
    L=_L; N=_N;
    for(int i=1; i<=N; i++) P[i]=pll(_W[i-1], _T[i-1]);
    M=_M; X=_X;
    for(int i=0; i<M; i++) S[i]=_S[i];
    M--;

    sort(P+1, P+N+1);
    reverse(P+1, P+N+1);
    while(N && P[N].first<=X) N--;

    for(int i=1; i<=N; i++) C[i]=i;
    for(int i=1; i<=N; i++) A[i]=P[i].second;
    for(int i=1; i<=N; i++) A2[i][0]=A[i];
    for(int i=1; i<=M; i++)
    {
        for(int j=1; j<=N; j++) B[j]=A[j]+(ll)(S[i]-S[i-1])*P[j].first;
        sort(C+1, C+N+1, [&](const int &p, const int &q) { return pll(A[p], B[p])<pll(A[q], B[q]); });
        ll t=0;
        for(int j=1; j<=N; j++) A[C[j]]=t=max(t, B[C[j]]);
        for(int j=1; j<=N; j++) A2[j][i]=A[j];
    }

    for(int i=M; i>=0; i--)
    {
        sort(C+1, C+N+1, [&](const int &p, const int &q) { return A2[p][i]<A2[q][i]; });
        CHT cht;
        for(int j=1; j<=N;)
        {
            auto p=cht.query(A2[C[j]][i]); p.second+=S[i];
            ll val;
            if(p.first==0) val=A2[C[j]][i]+X*(L-S[i]);
            else
            {
                if(p.second>L) val=A2[C[j]][i]+X*(L-S[i]);
                else
                {
                    int it=lower_bound(S, S+M+1, p.second)-S;
                    val=ans[p.first][it];
                }
            }
            ll tt=A2[C[j]][i];
            for(; j<=N && A2[C[j]][i]==tt; j++)
            {
                ans[C[j]][i]=val;
                cht.push({P[C[j]].first-X, A2[C[j]][i]}, C[j]);
            }
            if(i==0) V1.push_back(tt), V2.push_back(cht);
        }
    }
}

ll arrival_time(ll Y)
{
    auto it=lower_bound(V1.begin(), V1.end(), Y);
    if(it==V1.begin()) return Y+X*L;
    it--;
    auto &cht = V2[it-V1.begin()];
    int lo=0, hi=cht.V.size();
    while(lo+1<hi)
    {
        int mid=lo+hi>>1;
        if(cht.f(cht.V[mid].first, Y)<=cht.f(cht.V[mid-1].first, Y)) lo=mid;
        else hi=mid;
    }
    pll p;
    if(cht.V.empty()) p={0, 0};
    else p=pll(cht.V[lo].second, cht.f2(cht.V[lo].first, Y));
    
    if(p.first==0) return Y+X*L;
    else
    {
        if(p.second>L) return Y+X*L;
        else
        {
            int it=lower_bound(S, S+M+1, p.second)-S;
            return ans[p.first][it];
        }
    }
}

Compilation message

overtaking.cpp: In function 'll arrival_time(ll)':
overtaking.cpp:120:19: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  120 |         int mid=lo+hi>>1;
      |                 ~~^~~

Subtask #0
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2592 KB Output is correct
2 Correct 1 ms 2392 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 0 ms 344 KB Output is correct
5 Correct 1 ms 2392 KB Output is correct
6 Correct 1 ms 2392 KB Output is correct
7 Correct 1 ms 2392 KB Output is correct
8 Correct 1 ms 2392 KB Output is correct
9 Correct 1 ms 2392 KB Output is correct
10 Correct 1 ms 2392 KB Output is correct
11 Correct 1 ms 348 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6488 KB Output is correct
2 Correct 1 ms 6488 KB Output is correct
3 Correct 1 ms 6488 KB Output is correct
4 Correct 1 ms 6488 KB Output is correct
5 Correct 2 ms 10840 KB Output is correct
6 Correct 2 ms 14936 KB Output is correct
7 Correct 3 ms 15704 KB Output is correct
8 Correct 3 ms 15708 KB Output is correct
9 Correct 4 ms 15704 KB Output is correct
10 Correct 2 ms 15704 KB Output is correct
11 Correct 2 ms 15704 KB Output is correct
12 Correct 2 ms 15708 KB Output is correct
13 Correct 1 ms 344 KB Output is correct
14 Correct 1 ms 344 KB Output is correct

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2592 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 1 ms 2392 KB Output is correct
5 Correct 0 ms 344 KB Output is correct
6 Correct 1 ms 6488 KB Output is correct
7 Correct 1 ms 6488 KB Output is correct
8 Correct 1 ms 6488 KB Output is correct
9 Correct 2 ms 6488 KB Output is correct
10 Correct 2 ms 6496 KB Output is correct
11 Correct 1 ms 6488 KB Output is correct
12 Correct 1 ms 6492 KB Output is correct
13 Correct 1 ms 6488 KB Output is correct
14 Correct 1 ms 6492 KB Output is correct
15 Correct 2 ms 6744 KB Output is correct
16 Correct 2 ms 6744 KB Output is correct
17 Correct 2 ms 6744 KB Output is correct
18 Correct 2 ms 6744 KB Output is correct
19 Correct 2 ms 6488 KB Output is correct
20 Correct 2 ms 6488 KB Output is correct
21 Correct 1 ms 6488 KB Output is correct
22 Correct 1 ms 6488 KB Output is correct
23 Correct 1 ms 6488 KB Output is correct
24 Correct 2 ms 6488 KB Output is correct
25 Correct 2 ms 6488 KB Output is correct
26 Correct 2 ms 6488 KB Output is correct
27 Correct 2 ms 6744 KB Output is correct
28 Correct 1 ms 6492 KB Output is correct
29 Correct 1 ms 6488 KB Output is correct
30 Correct 1 ms 6492 KB Output is correct
31 Correct 1 ms 6492 KB Output is correct
32 Correct 1 ms 6488 KB Output is correct
33 Correct 1 ms 6488 KB Output is correct
34 Correct 1 ms 6488 KB Output is correct
35 Correct 1 ms 6488 KB Output is correct
36 Correct 1 ms 6488 KB Output is correct
37 Correct 2 ms 6488 KB Output is correct
38 Correct 0 ms 344 KB Output is correct
39 Correct 0 ms 344 KB Output is correct
40 Correct 1 ms 6488 KB Output is correct

Subtask #4
26.0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2592 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 1 ms 2392 KB Output is correct
5 Correct 0 ms 344 KB Output is correct
6 Correct 1 ms 2392 KB Output is correct
7 Correct 1 ms 2392 KB Output is correct
8 Correct 1 ms 2392 KB Output is correct
9 Correct 1 ms 2392 KB Output is correct
10 Correct 1 ms 2392 KB Output is correct
11 Correct 1 ms 2392 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 6488 KB Output is correct
14 Correct 1 ms 6488 KB Output is correct
15 Correct 1 ms 6488 KB Output is correct
16 Correct 2 ms 6488 KB Output is correct
17 Correct 2 ms 6496 KB Output is correct
18 Correct 1 ms 6488 KB Output is correct
19 Correct 1 ms 6492 KB Output is correct
20 Correct 1 ms 6488 KB Output is correct
21 Correct 1 ms 6492 KB Output is correct
22 Correct 2 ms 6744 KB Output is correct
23 Correct 2 ms 6744 KB Output is correct
24 Correct 2 ms 6744 KB Output is correct
25 Correct 2 ms 6744 KB Output is correct
26 Correct 2 ms 6488 KB Output is correct
27 Correct 2 ms 6488 KB Output is correct
28 Correct 1 ms 6488 KB Output is correct
29 Correct 1 ms 6488 KB Output is correct
30 Correct 1 ms 6488 KB Output is correct
31 Correct 2 ms 6488 KB Output is correct
32 Correct 2 ms 6488 KB Output is correct
33 Correct 2 ms 6488 KB Output is correct
34 Correct 2 ms 6744 KB Output is correct
35 Correct 1 ms 6492 KB Output is correct
36 Correct 1 ms 6488 KB Output is correct
37 Correct 1 ms 6492 KB Output is correct
38 Correct 1 ms 6492 KB Output is correct
39 Correct 1 ms 6488 KB Output is correct
40 Correct 1 ms 6488 KB Output is correct
41 Correct 1 ms 6488 KB Output is correct
42 Correct 1 ms 6488 KB Output is correct
43 Correct 1 ms 6488 KB Output is correct
44 Correct 2 ms 6488 KB Output is correct
45 Correct 0 ms 344 KB Output is correct
46 Correct 0 ms 344 KB Output is correct
47 Correct 1 ms 6488 KB Output is correct
48 Correct 86 ms 16464 KB Output is correct
49 Correct 82 ms 16464 KB Output is correct
50 Correct 96 ms 16376 KB Output is correct
51 Correct 84 ms 16464 KB Output is correct
52 Correct 86 ms 16464 KB Output is correct
53 Correct 84 ms 16464 KB Output is correct
54 Correct 88 ms 16464 KB Output is correct
55 Correct 69 ms 16460 KB Output is correct
56 Correct 82 ms 16464 KB Output is correct
57 Correct 71 ms 16652 KB Output is correct
58 Correct 87 ms 16556 KB Output is correct
59 Correct 77 ms 16468 KB Output is correct
60 Correct 78 ms 16416 KB Output is correct
61 Correct 82 ms 16660 KB Output is correct
62 Correct 2 ms 2648 KB Output is correct
63 Correct 4 ms 15708 KB Output is correct
64 Correct 38 ms 10840 KB Output is correct
65 Correct 39 ms 16468 KB Output is correct
66 Correct 52 ms 16416 KB Output is correct
67 Correct 75 ms 16464 KB Output is correct
68 Correct 84 ms 16464 KB Output is correct
69 Correct 43 ms 16464 KB Output is correct
70 Correct 45 ms 16464 KB Output is correct
71 Correct 48 ms 16464 KB Output is correct
72 Correct 73 ms 16724 KB Output is correct
73 Correct 51 ms 16424 KB Output is correct
74 Correct 47 ms 16464 KB Output is correct
75 Correct 1 ms 600 KB Output is correct
76 Correct 2 ms 600 KB Output is correct
77 Correct 1 ms 600 KB Output is correct
78 Correct 46 ms 16720 KB Output is correct

Subtask #5
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2592 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 1 ms 2392 KB Output is correct
5 Correct 0 ms 344 KB Output is correct
6 Correct 1 ms 2392 KB Output is correct
7 Correct 1 ms 2392 KB Output is correct
8 Correct 1 ms 2392 KB Output is correct
9 Correct 1 ms 2392 KB Output is correct
10 Correct 1 ms 2392 KB Output is correct
11 Correct 1 ms 2392 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 6488 KB Output is correct
14 Correct 1 ms 6488 KB Output is correct
15 Correct 1 ms 6488 KB Output is correct
16 Correct 1 ms 6488 KB Output is correct
17 Correct 2 ms 10840 KB Output is correct
18 Correct 2 ms 14936 KB Output is correct
19 Correct 3 ms 15704 KB Output is correct
20 Correct 3 ms 15708 KB Output is correct
21 Correct 4 ms 15704 KB Output is correct
22 Correct 2 ms 15704 KB Output is correct
23 Correct 2 ms 15704 KB Output is correct
24 Correct 2 ms 15708 KB Output is correct
25 Correct 1 ms 344 KB Output is correct
26 Correct 1 ms 344 KB Output is correct
27 Correct 2 ms 6488 KB Output is correct
28 Correct 2 ms 6496 KB Output is correct
29 Correct 1 ms 6488 KB Output is correct
30 Correct 1 ms 6492 KB Output is correct
31 Correct 1 ms 6488 KB Output is correct
32 Correct 1 ms 6492 KB Output is correct
33 Correct 2 ms 6744 KB Output is correct
34 Correct 2 ms 6744 KB Output is correct
35 Correct 2 ms 6744 KB Output is correct
36 Correct 2 ms 6744 KB Output is correct
37 Correct 2 ms 6488 KB Output is correct
38 Correct 2 ms 6488 KB Output is correct
39 Correct 1 ms 6488 KB Output is correct
40 Correct 1 ms 6488 KB Output is correct
41 Correct 1 ms 6488 KB Output is correct
42 Correct 2 ms 6488 KB Output is correct
43 Correct 2 ms 6488 KB Output is correct
44 Correct 2 ms 6488 KB Output is correct
45 Correct 2 ms 6744 KB Output is correct
46 Correct 1 ms 6492 KB Output is correct
47 Correct 1 ms 6488 KB Output is correct
48 Correct 1 ms 6492 KB Output is correct
49 Correct 1 ms 6492 KB Output is correct
50 Correct 1 ms 6488 KB Output is correct
51 Correct 1 ms 6488 KB Output is correct
52 Correct 1 ms 6488 KB Output is correct
53 Correct 1 ms 6488 KB Output is correct
54 Correct 1 ms 6488 KB Output is correct
55 Correct 2 ms 6488 KB Output is correct
56 Correct 0 ms 344 KB Output is correct
57 Correct 0 ms 344 KB Output is correct
58 Correct 1 ms 6488 KB Output is correct
59 Correct 86 ms 16464 KB Output is correct
60 Correct 82 ms 16464 KB Output is correct
61 Correct 96 ms 16376 KB Output is correct
62 Correct 84 ms 16464 KB Output is correct
63 Correct 86 ms 16464 KB Output is correct
64 Correct 84 ms 16464 KB Output is correct
65 Correct 88 ms 16464 KB Output is correct
66 Correct 69 ms 16460 KB Output is correct
67 Correct 82 ms 16464 KB Output is correct
68 Correct 71 ms 16652 KB Output is correct
69 Correct 87 ms 16556 KB Output is correct
70 Correct 77 ms 16468 KB Output is correct
71 Correct 78 ms 16416 KB Output is correct
72 Correct 82 ms 16660 KB Output is correct
73 Correct 2 ms 2648 KB Output is correct
74 Correct 4 ms 15708 KB Output is correct
75 Correct 38 ms 10840 KB Output is correct
76 Correct 39 ms 16468 KB Output is correct
77 Correct 52 ms 16416 KB Output is correct
78 Correct 75 ms 16464 KB Output is correct
79 Correct 84 ms 16464 KB Output is correct
80 Correct 43 ms 16464 KB Output is correct
81 Correct 45 ms 16464 KB Output is correct
82 Correct 48 ms 16464 KB Output is correct
83 Correct 73 ms 16724 KB Output is correct
84 Correct 51 ms 16424 KB Output is correct
85 Correct 47 ms 16464 KB Output is correct
86 Correct 1 ms 600 KB Output is correct
87 Correct 2 ms 600 KB Output is correct
88 Correct 1 ms 600 KB Output is correct
89 Correct 46 ms 16720 KB Output is correct
90 Correct 106 ms 18768 KB Output is correct
91 Correct 315 ms 41808 KB Output is correct
92 Correct 331 ms 41552 KB Output is correct
93 Correct 314 ms 41812 KB Output is correct
94 Correct 318 ms 41808 KB Output is correct
95 Correct 322 ms 41812 KB Output is correct
96 Correct 332 ms 42012 KB Output is correct
97 Correct 93 ms 18928 KB Output is correct
98 Correct 325 ms 41644 KB Output is correct
99 Correct 326 ms 42320 KB Output is correct
100 Correct 356 ms 41808 KB Output is correct
101 Correct 317 ms 41804 KB Output is correct
102 Correct 337 ms 41808 KB Output is correct
103 Correct 333 ms 41808 KB Output is correct
104 Correct 275 ms 35664 KB Output is correct
105 Correct 304 ms 43344 KB Output is correct
106 Correct 310 ms 46160 KB Output is correct
107 Correct 354 ms 45984 KB Output is correct
108 Correct 379 ms 46160 KB Output is correct
109 Correct 350 ms 46196 KB Output is correct
110 Correct 405 ms 46160 KB Output is correct
111 Correct 254 ms 42084 KB Output is correct
112 Correct 269 ms 42064 KB Output is correct
113 Correct 318 ms 43344 KB Output is correct
114 Correct 382 ms 44368 KB Output is correct
115 Correct 311 ms 43124 KB Output is correct
116 Correct 280 ms 43088 KB Output is correct
117 Correct 173 ms 27984 KB Output is correct
118 Correct 179 ms 27996 KB Output is correct
119 Correct 167 ms 27056 KB Output is correct
120 Correct 182 ms 27984 KB Output is correct
121 Correct 174 ms 29008 KB Output is correct
122 Correct 264 ms 38996 KB Output is correct
123 Correct 406 ms 44112 KB Output is correct
124 Correct 399 ms 44112 KB Output is correct
125 Correct 397 ms 44012 KB Output is correct