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Submission #1037032

# Submission time Handle Problem Language Result Execution time Memory
1037032 2024-07-27T22:34:18 Z model_code Tricks of the Trade (CEOI23_trade) C++17
100 / 100
 968 ms 142196 KB 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
constexpr ll inf = 1e18;

struct Answer{
    ll maximum;
    ll rangeCnt;
    string optimalIndices;
};

int n, k;
vector<ll> a, b, bpr, result;
vector<int> opt, opt2;

constexpr int NODES = 1e7;
int nodeCnt, L[NODES], R[NODES], scnt[NODES];
ll ssum[NODES];

int supd(int p, ll v, int a, int b, int i){
    int node = nodeCnt++;
    L[node] = L[i];
    R[node] = R[i];
    if(a == b){
        ssum[node] = v;
        scnt[node] = 1;
        return node;
    }
    int m = (a+b)/2;
    if(p <= m) L[node] = supd(p, v, a, m, L[i]);
    else R[node] = supd(p, v, m+1, b, R[i]);
    scnt[node] = scnt[L[node]] + scnt[R[node]];
    ssum[node] = ssum[L[node]] + ssum[R[node]];
    return node;
}

// (sum, k-biggest)
pair<ll, ll> sqry(int goal, int add, int sub, int siz){
    if(siz == 1){
        assert(scnt[sub] == 0);
        return {ssum[add], ssum[add]};
    }
    int cr = scnt[R[add]] - scnt[R[sub]];
    if(cr < goal){
        auto [lsum, lkbig] = sqry(goal-cr, L[add], L[sub], siz/2);
        return {lsum + ssum[R[add]] - ssum[R[sub]], lkbig};
    }
    else{
        return sqry(goal, R[add], R[sub], siz/2);
    }
}

vector<int> roots;
int cap;

pair<ll, ll> qry(int l, int r){
    auto [sum, kbig] = sqry(k, roots[r+1], roots[l], cap);
    sum -= bpr[r+1] - bpr[l];
    return {sum, kbig};
}

void init(){
    roots.resize(n+1);
    for(cap=1; cap<n; cap*=2);
    roots[0] = 1;
    for(int i = cap-1; i >= 1; i--) L[i] = 2*i, R[i] = 2*i+1;
    nodeCnt = 2*cap;

    vector<pair<ll, int>> aind;
    for(int i = 0; i < n; i++) aind.emplace_back(a[i], i);
    sort(aind.begin(), aind.end());
    vector<int> ind(n);
    for(int i = 0; i < n; i++) ind[aind[i].second] = i;
    for(int i = 0; i < n; i++) roots[i+1] = supd(ind[i], a[i], 0, cap-1, roots[i]);

    bpr.resize(n+1);
    for(int i = 0; i < n; i++) bpr[i+1] = bpr[i] + b[i];
}

ll ans = -inf;

// minimum optimal index
void dc(int l, int r, int optL, int optR){
    if(l > r) return;
    int m = (l+r)/2;
    ll res = -inf; int ind = optR;
    for(int i = max(m+k-1, optL); i <= optR; i++){
        ll val = qry(m, i).first;
        if(val > res){
            res = val;
            ind = i;
        }
    }
    ans = max(ans, res);
    opt[m] = ind;
    result[m] = res;
    dc(l, m-1, optL, ind);
    dc(m+1, r, ind, optR);
}

Answer solve(){
    init();
    ans = -inf;
    opt.assign(n, -1);
    opt2.assign(n, -1);
    result.assign(n, -inf);

    dc(0, n-1, 0, n-1);
    Answer answer;
    answer.maximum = ans;
    // ans is calculated now.

    // optimal indices
    {
        vector<vector<ll>> add(n), rem(n+1);
        int nxt = 0;
        for(int i = 0; i < n; i++){
            if(result[i] != ans) continue;
            nxt = max(nxt, i+1);
            while(nxt < n && result[nxt] != ans) nxt++;
            int r = n-1;
            if(nxt != n) r = opt[nxt];
            for(int j = opt[i]; j <= r; j++){
                auto [val, kth] = qry(i, j);
                if(val == ans){
                    add[i].push_back(kth);
                    rem[j+1].push_back(kth);
                }
            }
        }
        string optimalIndices(n, '0');
        multiset<ll> active;
        for(int i = 0; i < n; i++){
            for(ll x : add[i]) active.insert(x);
            for(ll x : rem[i]) active.erase(active.find(x));
            if(active.empty()) continue;
            if(a[i] >= *active.begin()) optimalIndices[i] = '1';
        }
        answer.optimalIndices = optimalIndices;
    }

    return answer;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin >> n >> k;
    a.resize(n), b.resize(n);
    for(int i = 0; i < n; i++) cin >> b[i];
    for(int i = 0; i < n; i++) cin >> a[i];
    Answer ans = solve();
    cout << ans.maximum << "\n";
    cout << ans.optimalIndices << "\n";
}

Subtask #0
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6492 KB Output is correct
2 Correct 1 ms 6492 KB Output is correct

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6492 KB Output is correct
2 Correct 1 ms 6492 KB Output is correct
3 Correct 1 ms 6488 KB Output is correct
4 Correct 1 ms 6492 KB Output is correct
5 Correct 1 ms 6492 KB Output is correct
6 Correct 1 ms 6492 KB Output is correct
7 Correct 1 ms 6492 KB Output is correct
8 Correct 1 ms 6492 KB Output is correct
9 Correct 1 ms 6492 KB Output is correct
10 Correct 1 ms 6488 KB Output is correct
11 Correct 1 ms 6488 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6492 KB Output is correct
2 Correct 1 ms 6492 KB Output is correct
3 Correct 1 ms 6488 KB Output is correct
4 Correct 1 ms 6492 KB Output is correct
5 Correct 1 ms 6492 KB Output is correct
6 Correct 1 ms 6492 KB Output is correct
7 Correct 1 ms 6492 KB Output is correct
8 Correct 1 ms 6492 KB Output is correct
9 Correct 1 ms 6492 KB Output is correct
10 Correct 1 ms 6488 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 6492 KB Output is correct
14 Correct 1 ms 6492 KB Output is correct
15 Correct 1 ms 6492 KB Output is correct
16 Correct 1 ms 6492 KB Output is correct
17 Correct 1 ms 6492 KB Output is correct
18 Correct 1 ms 6492 KB Output is correct
19 Correct 1 ms 6488 KB Output is correct
20 Correct 1 ms 6744 KB Output is correct
21 Correct 1 ms 6492 KB Output is correct
22 Correct 1 ms 6492 KB Output is correct
23 Correct 3 ms 9208 KB Output is correct
24 Correct 7 ms 9212 KB Output is correct
25 Correct 8 ms 9420 KB Output is correct
26 Correct 8 ms 9356 KB Output is correct
27 Correct 5 ms 9468 KB Output is correct
28 Correct 6 ms 9212 KB Output is correct
29 Correct 5 ms 9212 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6492 KB Output is correct
2 Correct 355 ms 137868 KB Output is correct
3 Correct 298 ms 130008 KB Output is correct
4 Correct 446 ms 130164 KB Output is correct
5 Correct 721 ms 135856 KB Output is correct
6 Correct 708 ms 135544 KB Output is correct
7 Correct 360 ms 140580 KB Output is correct
8 Correct 343 ms 130056 KB Output is correct
9 Correct 318 ms 130164 KB Output is correct
10 Correct 344 ms 135144 KB Output is correct

Subtask #4
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6492 KB Output is correct
2 Correct 355 ms 137868 KB Output is correct
3 Correct 298 ms 130008 KB Output is correct
4 Correct 446 ms 130164 KB Output is correct
5 Correct 721 ms 135856 KB Output is correct
6 Correct 708 ms 135544 KB Output is correct
7 Correct 360 ms 140580 KB Output is correct
8 Correct 343 ms 130056 KB Output is correct
9 Correct 318 ms 130164 KB Output is correct
10 Correct 344 ms 135144 KB Output is correct
11 Correct 1 ms 6488 KB Output is correct
12 Correct 338 ms 137904 KB Output is correct
13 Correct 313 ms 129932 KB Output is correct
14 Correct 509 ms 129924 KB Output is correct
15 Correct 764 ms 136076 KB Output is correct
16 Correct 706 ms 135600 KB Output is correct
17 Correct 367 ms 140660 KB Output is correct
18 Correct 326 ms 129912 KB Output is correct
19 Correct 313 ms 129908 KB Output is correct
20 Correct 373 ms 135240 KB Output is correct
21 Correct 1 ms 6492 KB Output is correct
22 Correct 1 ms 6492 KB Output is correct
23 Correct 1 ms 6492 KB Output is correct
24 Correct 1 ms 6492 KB Output is correct
25 Correct 1 ms 6636 KB Output is correct
26 Correct 1 ms 6492 KB Output is correct
27 Correct 1 ms 6492 KB Output is correct
28 Correct 1 ms 6492 KB Output is correct
29 Correct 1 ms 6492 KB Output is correct
30 Correct 1 ms 6492 KB Output is correct
31 Correct 305 ms 129964 KB Output is correct
32 Correct 748 ms 134068 KB Output is correct
33 Correct 789 ms 136876 KB Output is correct
34 Correct 667 ms 133496 KB Output is correct
35 Correct 694 ms 132236 KB Output is correct
36 Correct 329 ms 129972 KB Output is correct
37 Correct 352 ms 136632 KB Output is correct

Subtask #5
45.0 / 45.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 6492 KB Output is correct
2 Correct 1 ms 6492 KB Output is correct
3 Correct 1 ms 6492 KB Output is correct
4 Correct 1 ms 6492 KB Output is correct
5 Correct 1 ms 6488 KB Output is correct
6 Correct 1 ms 6492 KB Output is correct
7 Correct 1 ms 6492 KB Output is correct
8 Correct 1 ms 6492 KB Output is correct
9 Correct 1 ms 6492 KB Output is correct
10 Correct 1 ms 6492 KB Output is correct
11 Correct 1 ms 6492 KB Output is correct
12 Correct 1 ms 6488 KB Output is correct
13 Correct 1 ms 6488 KB Output is correct
14 Correct 1 ms 6492 KB Output is correct
15 Correct 1 ms 6492 KB Output is correct
16 Correct 1 ms 6492 KB Output is correct
17 Correct 1 ms 6492 KB Output is correct
18 Correct 1 ms 6492 KB Output is correct
19 Correct 1 ms 6492 KB Output is correct
20 Correct 1 ms 6492 KB Output is correct
21 Correct 1 ms 6488 KB Output is correct
22 Correct 1 ms 6744 KB Output is correct
23 Correct 1 ms 6492 KB Output is correct
24 Correct 1 ms 6492 KB Output is correct
25 Correct 3 ms 9208 KB Output is correct
26 Correct 7 ms 9212 KB Output is correct
27 Correct 8 ms 9420 KB Output is correct
28 Correct 8 ms 9356 KB Output is correct
29 Correct 5 ms 9468 KB Output is correct
30 Correct 6 ms 9212 KB Output is correct
31 Correct 5 ms 9212 KB Output is correct
32 Correct 1 ms 6492 KB Output is correct
33 Correct 355 ms 137868 KB Output is correct
34 Correct 298 ms 130008 KB Output is correct
35 Correct 446 ms 130164 KB Output is correct
36 Correct 721 ms 135856 KB Output is correct
37 Correct 708 ms 135544 KB Output is correct
38 Correct 360 ms 140580 KB Output is correct
39 Correct 343 ms 130056 KB Output is correct
40 Correct 318 ms 130164 KB Output is correct
41 Correct 344 ms 135144 KB Output is correct
42 Correct 1 ms 6488 KB Output is correct
43 Correct 338 ms 137904 KB Output is correct
44 Correct 313 ms 129932 KB Output is correct
45 Correct 509 ms 129924 KB Output is correct
46 Correct 764 ms 136076 KB Output is correct
47 Correct 706 ms 135600 KB Output is correct
48 Correct 367 ms 140660 KB Output is correct
49 Correct 326 ms 129912 KB Output is correct
50 Correct 313 ms 129908 KB Output is correct
51 Correct 373 ms 135240 KB Output is correct
52 Correct 1 ms 6492 KB Output is correct
53 Correct 1 ms 6492 KB Output is correct
54 Correct 1 ms 6492 KB Output is correct
55 Correct 1 ms 6492 KB Output is correct
56 Correct 1 ms 6636 KB Output is correct
57 Correct 1 ms 6492 KB Output is correct
58 Correct 1 ms 6492 KB Output is correct
59 Correct 1 ms 6492 KB Output is correct
60 Correct 1 ms 6492 KB Output is correct
61 Correct 1 ms 6492 KB Output is correct
62 Correct 305 ms 129964 KB Output is correct
63 Correct 748 ms 134068 KB Output is correct
64 Correct 789 ms 136876 KB Output is correct
65 Correct 667 ms 133496 KB Output is correct
66 Correct 694 ms 132236 KB Output is correct
67 Correct 329 ms 129972 KB Output is correct
68 Correct 352 ms 136632 KB Output is correct
69 Correct 1 ms 6492 KB Output is correct
70 Correct 350 ms 137908 KB Output is correct
71 Correct 307 ms 129932 KB Output is correct
72 Correct 482 ms 129976 KB Output is correct
73 Correct 699 ms 135800 KB Output is correct
74 Correct 700 ms 135600 KB Output is correct
75 Correct 388 ms 140660 KB Output is correct
76 Correct 326 ms 130164 KB Output is correct
77 Correct 315 ms 130108 KB Output is correct
78 Correct 351 ms 135288 KB Output is correct
79 Correct 1 ms 6492 KB Output is correct
80 Correct 1 ms 6492 KB Output is correct
81 Correct 1 ms 6492 KB Output is correct
82 Correct 1 ms 6492 KB Output is correct
83 Correct 1 ms 6492 KB Output is correct
84 Correct 1 ms 6492 KB Output is correct
85 Correct 1 ms 6492 KB Output is correct
86 Correct 1 ms 6492 KB Output is correct
87 Correct 1 ms 6492 KB Output is correct
88 Correct 1 ms 6492 KB Output is correct
89 Correct 294 ms 129912 KB Output is correct
90 Correct 725 ms 134068 KB Output is correct
91 Correct 861 ms 136876 KB Output is correct
92 Correct 770 ms 133680 KB Output is correct
93 Correct 798 ms 131980 KB Output is correct
94 Correct 344 ms 130116 KB Output is correct
95 Correct 346 ms 136624 KB Output is correct
96 Correct 3 ms 9212 KB Output is correct
97 Correct 8 ms 9212 KB Output is correct
98 Correct 8 ms 9212 KB Output is correct
99 Correct 11 ms 9432 KB Output is correct
100 Correct 5 ms 9500 KB Output is correct
101 Correct 6 ms 9212 KB Output is correct
102 Correct 6 ms 9248 KB Output is correct
103 Correct 432 ms 129912 KB Output is correct
104 Correct 869 ms 131512 KB Output is correct
105 Correct 752 ms 133296 KB Output is correct
106 Correct 968 ms 134836 KB Output is correct
107 Correct 191 ms 130168 KB Output is correct
108 Correct 555 ms 133452 KB Output is correct
109 Correct 343 ms 142196 KB Output is correct
110 Correct 380 ms 137080 KB Output is correct
111 Correct 188 ms 130164 KB Output is correct
112 Correct 486 ms 136056 KB Output is correct