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Submission #971060

# Submission time Handle Problem Language Result Execution time Memory
971060 2024-04-27T21:38:44 Z vladilius The short shank; Redemption (BOI21_prison) C++17
70 / 100
 1588 ms 18712 KB 
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = double;
using pll = pair<ld, int>;
using pii = pair<int, int>;
#define f first
#define s second
const int inf = 1e9;
 
struct ST{
    vector<ld> t, p;
    vector<int> k;
    int n;
    void build(int v, int tl, int tr){
        if (tl == tr){
            k[v] = tl;
            return;
        }
        int tm = (tl + tr) / 2, vv = 2 * v;
        build(vv, tl, tm);
        build(vv + 1, tm + 1, tr);
        t[v] = tl;
    }
    ST(int ns){
        n = ns;
        t.resize(4 * n);
        p.resize(4 * n);
        k.resize(4 * n);
        build(1, 1, n);
    }
    void push(int& v, int& vv){
        if (!p[v]) return;
        p[vv] += p[v]; t[vv] += p[v];
        p[vv + 1] += p[v]; t[vv + 1] += p[v];
        p[v] = 0;
    }
    void add(int v, int tl, int tr, int& l, int& r, ld& x){
        if (l > tr || r < tl) return;
        if (l <= tl && tr <= r){
            t[v] += x;
            p[v] += x;
            return;
        }
        int tm = (tl + tr) / 2, vv = 2 * v;
        push(v, vv);
        add(vv, tl, tm, l, r, x);
        add(vv + 1, tm + 1, tr, l, r, x);
        if (t[vv] > t[vv + 1]){
            t[v] = t[vv + 1];
            k[v] = k[vv + 1];
        }
        else {
            t[v] = t[vv];
            k[v] = k[vv];
        }
        t[v] = min(t[vv], t[vv + 1]);
    }
    void add(int l, int r, ld x){
        if (l > r) return;
        add(1, 1, n, l, r, x);
    }
    pll get(int v, int tl, int tr, int& l, int& r){
        if (l > tr || r < tl) return {inf, 0};
        if (l <= tl && tr <= r){
            return {t[v], k[v]};
        }
        int tm = (tl + tr) / 2, vv = 2 * v;
        push(v, vv);
        return min(get(vv, tl, tm, l, r), get(vv + 1, tm + 1, tr, l, r));
    }
    pll get(int l, int r){
        return get(1, 1, n, l, r);
    }
};
 
int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    
    int n, d, t; cin>>n>>d>>t;
    vector<int> a(n + 1);
    for (int i = 1; i <= n; i++){
        cin>>a[i];
    }
    
    vector<int> h(n + 1);
    int mx = 0, cnt = 0;
    for (int j = 1; j <= n; j++){
        if (a[j] <= t){
            int m = t - a[j];
            mx = max(mx, j + m);
        }
        cnt += (j <= mx);
        h[j] = cnt;
    }
    
    if (d == 1){
        vector<int> hr(n + 1);
        reverse(a.begin() + 1, a.end());
        int mx = 0, cnt = 0;
        for (int j = 1; j <= n; j++){
            if (a[j] <= t){
                int m = t - a[j];
                mx = max(mx, j + m);
            }
            cnt += (j <= mx);
            hr[j] = cnt;
        }
        
        int out = n;
        for (int i = 1; i <= n; i++){
            out = min(out, h[i] + hr[n - i]);
        }
        cout<<out<<"\n";
        return 0;
    }
    
    vector<int> r(n + 1);
    for (int i = 1; i <= n; i++){
        if (a[i] > t) continue;
        int m = t - a[i];
        r[i] = i + m;
    }
    
    const int lg = ceil(log2(n));
    vector<vector<int>> sp(n + 1, vector<int>(lg));
    for (int i = 1; i <= n; i++){
        sp[i][0] = r[i];
    }
    for (int j = 1; j < lg; j++){
        for (int i = 1; i + (1 << j) <= n + 1; i++){
            sp[i][j] = max(sp[i][j - 1], sp[i + (1 << (j - 1))][j - 1]);
        }
    }
    vector<int> log(n + 1);
    for (int i = 2; i <= n; i++){
        log[i] = log[i / 2] + 1;
    }
    
    auto check = [&](int x, int y){
        int k = log[y - x + 1];
        return max(sp[x][k], sp[y - (1 << k) + 1][k]) >= y;
    };
 
    vector<int> f(n);
    for (int i = 1; i < n; i++){
        auto good = [&](int m){
            return check(m, i + 1);
        };
        int l = 0, r = i + 1;
        while (l + 1 < r){
            int m = (l + r) / 2;
            if (good(m)){
                l = m;
            }
            else {
                r = m - 1;
            }
        }
        if (good(r)) l = r;
        f[i] = l;
    }
    
    auto solve = [&](ld m){
        pll dp[n + 1];
        ST T(n);
        for (int i = 1; i <= n; i++){
            dp[i] = {h[i], 0};
            T.add(1, f[i - 1] - 1, 1);
            auto [v, j] = T.get(1, i - 1);
            dp[i] = min(dp[i], {v + m, dp[j].s + 1});
            T.add(i, i, dp[i].f);
        }
        return dp[n];
    };
    
    ld lb = 0, rb = n;
    int tt = 40;
    while (tt--){
        ld m = (lb + rb) / 2;
        auto [v, k] = solve(m);
        if (k > d){
            lb = m;
        }
        else {
            rb = m;
        }
    }
    
    auto [v, k] = solve(lb);
    cout<<round(v - lb * d)<<"\n";
}

Subtask #1
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 600 KB Output is correct
2 Correct 5 ms 344 KB Output is correct
3 Correct 5 ms 348 KB Output is correct
4 Correct 6 ms 540 KB Output is correct
5 Correct 6 ms 348 KB Output is correct
6 Correct 6 ms 540 KB Output is correct
7 Correct 6 ms 348 KB Output is correct
8 Correct 6 ms 348 KB Output is correct
9 Correct 6 ms 348 KB Output is correct
10 Correct 6 ms 348 KB Output is correct
11 Correct 6 ms 548 KB Output is correct

Subtask #2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Incorrect 45 ms 6228 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 600 KB Output is correct
2 Correct 5 ms 344 KB Output is correct
3 Correct 5 ms 348 KB Output is correct
4 Correct 6 ms 540 KB Output is correct
5 Correct 6 ms 348 KB Output is correct
6 Correct 6 ms 540 KB Output is correct
7 Correct 6 ms 348 KB Output is correct
8 Correct 6 ms 348 KB Output is correct
9 Correct 6 ms 348 KB Output is correct
10 Correct 6 ms 348 KB Output is correct
11 Correct 6 ms 548 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 5 ms 348 KB Output is correct
14 Correct 5 ms 528 KB Output is correct
15 Correct 6 ms 348 KB Output is correct
16 Correct 7 ms 348 KB Output is correct
17 Correct 6 ms 348 KB Output is correct
18 Correct 6 ms 348 KB Output is correct
19 Correct 6 ms 344 KB Output is correct
20 Correct 6 ms 600 KB Output is correct
21 Correct 6 ms 348 KB Output is correct
22 Correct 6 ms 496 KB Output is correct
23 Correct 66 ms 1228 KB Output is correct
24 Correct 66 ms 1220 KB Output is correct
25 Correct 66 ms 1252 KB Output is correct
26 Correct 67 ms 1224 KB Output is correct
27 Correct 64 ms 1244 KB Output is correct
28 Correct 66 ms 1248 KB Output is correct
29 Correct 66 ms 1224 KB Output is correct
30 Correct 59 ms 1220 KB Output is correct
31 Correct 59 ms 1248 KB Output is correct
32 Correct 62 ms 1244 KB Output is correct
33 Correct 61 ms 1224 KB Output is correct
34 Correct 68 ms 1252 KB Output is correct
35 Correct 65 ms 1252 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1588 ms 16792 KB Output is correct
3 Correct 1572 ms 16772 KB Output is correct
4 Correct 1484 ms 16816 KB Output is correct
5 Correct 1458 ms 16684 KB Output is correct
6 Correct 1493 ms 16672 KB Output is correct
7 Correct 1358 ms 16676 KB Output is correct
8 Correct 1309 ms 16940 KB Output is correct
9 Correct 1447 ms 16716 KB Output is correct
10 Correct 1470 ms 16752 KB Output is correct

Subtask #5
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 600 KB Output is correct
2 Correct 5 ms 344 KB Output is correct
3 Correct 5 ms 348 KB Output is correct
4 Correct 6 ms 540 KB Output is correct
5 Correct 6 ms 348 KB Output is correct
6 Correct 6 ms 540 KB Output is correct
7 Correct 6 ms 348 KB Output is correct
8 Correct 6 ms 348 KB Output is correct
9 Correct 6 ms 348 KB Output is correct
10 Correct 6 ms 348 KB Output is correct
11 Correct 6 ms 548 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 5 ms 348 KB Output is correct
14 Correct 5 ms 528 KB Output is correct
15 Correct 6 ms 348 KB Output is correct
16 Correct 7 ms 348 KB Output is correct
17 Correct 6 ms 348 KB Output is correct
18 Correct 6 ms 348 KB Output is correct
19 Correct 6 ms 344 KB Output is correct
20 Correct 6 ms 600 KB Output is correct
21 Correct 6 ms 348 KB Output is correct
22 Correct 6 ms 496 KB Output is correct
23 Correct 66 ms 1228 KB Output is correct
24 Correct 66 ms 1220 KB Output is correct
25 Correct 66 ms 1252 KB Output is correct
26 Correct 67 ms 1224 KB Output is correct
27 Correct 64 ms 1244 KB Output is correct
28 Correct 66 ms 1248 KB Output is correct
29 Correct 66 ms 1224 KB Output is correct
30 Correct 59 ms 1220 KB Output is correct
31 Correct 59 ms 1248 KB Output is correct
32 Correct 62 ms 1244 KB Output is correct
33 Correct 61 ms 1224 KB Output is correct
34 Correct 68 ms 1252 KB Output is correct
35 Correct 65 ms 1252 KB Output is correct
36 Correct 0 ms 348 KB Output is correct
37 Correct 1588 ms 16792 KB Output is correct
38 Correct 1572 ms 16772 KB Output is correct
39 Correct 1484 ms 16816 KB Output is correct
40 Correct 1458 ms 16684 KB Output is correct
41 Correct 1493 ms 16672 KB Output is correct
42 Correct 1358 ms 16676 KB Output is correct
43 Correct 1309 ms 16940 KB Output is correct
44 Correct 1447 ms 16716 KB Output is correct
45 Correct 1470 ms 16752 KB Output is correct
46 Correct 0 ms 348 KB Output is correct
47 Correct 5 ms 528 KB Output is correct
48 Correct 5 ms 348 KB Output is correct
49 Correct 6 ms 548 KB Output is correct
50 Correct 6 ms 348 KB Output is correct
51 Correct 6 ms 540 KB Output is correct
52 Correct 6 ms 348 KB Output is correct
53 Correct 6 ms 348 KB Output is correct
54 Correct 6 ms 344 KB Output is correct
55 Correct 6 ms 344 KB Output is correct
56 Correct 6 ms 344 KB Output is correct
57 Correct 65 ms 1216 KB Output is correct
58 Correct 66 ms 1252 KB Output is correct
59 Correct 68 ms 1472 KB Output is correct
60 Correct 65 ms 1244 KB Output is correct
61 Correct 67 ms 1224 KB Output is correct
62 Correct 66 ms 1252 KB Output is correct
63 Correct 66 ms 1252 KB Output is correct
64 Correct 59 ms 1244 KB Output is correct
65 Correct 60 ms 1252 KB Output is correct
66 Correct 61 ms 1252 KB Output is correct
67 Correct 61 ms 1252 KB Output is correct
68 Correct 68 ms 1532 KB Output is correct
69 Correct 64 ms 1248 KB Output is correct
70 Correct 0 ms 348 KB Output is correct
71 Correct 1559 ms 16800 KB Output is correct
72 Correct 1565 ms 16804 KB Output is correct
73 Correct 1531 ms 16720 KB Output is correct
74 Correct 1481 ms 16800 KB Output is correct
75 Correct 1464 ms 16628 KB Output is correct
76 Correct 1324 ms 18580 KB Output is correct
77 Correct 1307 ms 18712 KB Output is correct
78 Correct 1450 ms 16600 KB Output is correct
79 Correct 1461 ms 16676 KB Output is correct
80 Correct 1516 ms 16912 KB Output is correct
81 Correct 1522 ms 16652 KB Output is correct
82 Correct 1513 ms 16684 KB Output is correct
83 Correct 1561 ms 16608 KB Output is correct
84 Correct 1512 ms 16832 KB Output is correct
85 Correct 1488 ms 16860 KB Output is correct
86 Correct 1449 ms 16732 KB Output is correct
87 Correct 1333 ms 16604 KB Output is correct
88 Correct 1377 ms 16984 KB Output is correct
89 Correct 1020 ms 18624 KB Output is correct
90 Correct 1184 ms 16740 KB Output is correct

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 600 KB Output is correct
2 Correct 5 ms 344 KB Output is correct
3 Correct 5 ms 348 KB Output is correct
4 Correct 6 ms 540 KB Output is correct
5 Correct 6 ms 348 KB Output is correct
6 Correct 6 ms 540 KB Output is correct
7 Correct 6 ms 348 KB Output is correct
8 Correct 6 ms 348 KB Output is correct
9 Correct 6 ms 348 KB Output is correct
10 Correct 6 ms 348 KB Output is correct
11 Correct 6 ms 548 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Incorrect 45 ms 6228 KB Output isn't correct
14 Halted 0 ms 0 KB -