oj.uz

Submission #897758

# Submission time Handle Problem Language Result Execution time Memory
897758 2024-01-03T16:08:03 Z GrindMachine The short shank; Redemption (BOI21_prison) C++17
70 / 100
 2000 ms 145580 KB 
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a,b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a,b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif

/*

read somewhere that aliens trick can be used in this problem

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

template<typename T>
struct lazysegtree {
    /*=======================================================*/
 
    struct data {
        ll mn,ind;
    };
 
    struct lazy {
        ll a;
    };
 
    data d_neutral = {inf2,-1};
    lazy l_neutral = {0};
 
    void merge(data &curr, data &left, data &right) {
        if(left.mn <= right.mn) curr = left;
        else curr = right;
    }
 
    void create(int x, int lx, int rx, T v) {
        tr[x].mn = 0;
        tr[x].ind = lx;
    }
 
    void modify(int x, int lx, int rx, T v) {
        lz[x].a = v;
    }
 
    void propagate(int x, int lx, int rx) {
        ll v = lz[x].a;
        if(!v) return;
 
        tr[x].mn += v;
        
        if(rx - lx > 1){
            lz[2*x+1].a += v;
            lz[2*x+2].a += v;
        }
 
        lz[x] = l_neutral;
    }
 
    /*=======================================================*/
 
    int siz = 1;
    vector<data> tr;
    vector<lazy> lz;
 
    lazysegtree() {
 
    }
 
    lazysegtree(int n) {
        while (siz < n) siz *= 2;
        tr.assign(2 * siz, d_neutral);
        lz.assign(2 * siz, l_neutral);
    }
 
    void build(vector<T> &a, int n, int x, int lx, int rx) {
        if (rx - lx == 1) {
            if (lx < n) {
                create(x, lx, rx, a[lx]);
            }
 
            return;
        }
 
        int mid = (lx + rx) / 2;
 
        build(a, n, 2 * x + 1, lx, mid);
        build(a, n, 2 * x + 2, mid, rx);
 
        merge(tr[x], tr[2 * x + 1], tr[2 * x + 2]);
    }
 
    void build(vector<T> &a, int n) {
        build(a, n, 0, 0, siz);
    }
 
    void rupd(int l, int r, T v, int x, int lx, int rx) {
        propagate(x, lx, rx);
 
        if (lx >= r or rx <= l) return;
        if (lx >= l and rx <= r) {
            modify(x, lx, rx, v);
            propagate(x, lx, rx);
            return;
        }
 
        int mid = (lx + rx) / 2;
 
        rupd(l, r, v, 2 * x + 1, lx, mid);
        rupd(l, r, v, 2 * x + 2, mid, rx);
 
        merge(tr[x], tr[2 * x + 1], tr[2 * x + 2]);
    }
 
    void rupd(int l, int r, T v) {
        rupd(l, r + 1, v, 0, 0, siz);
    }
 
    data query(int l, int r, int x, int lx, int rx) {
        propagate(x, lx, rx);
 
        if (lx >= r or rx <= l) return d_neutral;
        if (lx >= l and rx <= r) return tr[x];
 
        int mid = (lx + rx) / 2;
 
        data curr;
        data left = query(l, r, 2 * x + 1, lx, mid);
        data right = query(l, r, 2 * x + 2, mid, rx);
 
        merge(curr, left, right);
        return curr;
    }
 
    data query(int l, int r) {
        return query(l, r + 1, 0, 0, siz);
    }
};
 
template<typename T>
struct sparse_table {
    /*============================*/
 
    T merge(T a, T b) {
        return min(a,b);
    }
 
    /*============================*/
 
    vector<vector<T>> table;
    vector<int> bin_log;
    int LOG = 0;
 
    sparse_table() {
 
    }
 
    sparse_table(vector<T> &a, int n) {
        while ((1 << LOG) <= n) LOG++;
 
        table = vector<vector<T>>(n, vector<T>(LOG));
        bin_log = vector<int>(n + 1);
 
        rep(i, n) table[i][0] = a[i];
 
        rep1(j, LOG - 1) {
            rep(i, n) {
                int jump = 1 << (j - 1);
                if (i + jump >= n) {
                    break;
                }
 
                table[i][j] = merge(table[i][j - 1], table[i + jump][j - 1]);
            }
        }
 
        bin_log[1] = 0;
        for (int i = 2; i <= n; ++i) {
            bin_log[i] = bin_log[i / 2] + 1;
        }
    }
 
    T query(int l, int r) {
        int len = r - l + 1;
        int k = bin_log[len];
 
        T val1 = table[l][k];
        T val2 = table[r - (1 << k) + 1][k];
 
        return merge(val1, val2);
    }
};
 
void solve(int test_case)
{
    ll n,d,t; cin >> n >> d >> t;
    d++; // we need d+1 segs
    vector<ll> a(n+5);
    rep1(i,n) cin >> a[i];
 
    vector<ll> b(n+5);
    rep1(i,n) b[i] = a[i] - i;
 
    sparse_table<ll> sparse(b,n+1);
    vector<ll> lx(n+5); // lx[i] = first pos to the left of i s.t if we start making ops from this pos, a[i] <= t
 
    rep1(i,n){
        // a[j] + (i-j) = (a[j]-j) + i
        ll l = 1, r = i;
        while(l <= r){
            ll mid = (l+r) >> 1;
            if(sparse.query(mid,i) + i <= t){
                lx[i] = mid;
                l = mid + 1;
            }
            else{
                r = mid - 1;
            }
        }
    }

    vector<ll> dp(n+5), cnt(n+5);
        
    auto go = [&](ll lambda){
        fill(all(dp),0);
        fill(all(cnt),0);
        lazysegtree<ll> st(n+5);
        vector<ll> dummy(n+5);
        st.build(dummy,n+1);

        rep1(i,n){
            // range add
            st.rupd(0,lx[i]-1,1);
 
            // range min
            auto [mn,ind] = st.query(0,i-1);
            dp[i] = mn+lambda;
            cnt[i] = cnt[ind]+1;
            st.rupd(i,i,dp[i]);
        }
    };

    ll l = -inf1, r = inf1;
    ll lambda = inf2;

    while(l <= r){
        ll mid = (l+r) >> 1;
        go(mid);
        if(cnt[n] <= d){
            r = mid-1;
            lambda = mid;
        }
        else{
            l = mid+1;
        }
    }

    assert(lambda != inf2);

    go(lambda);
    ll ans = dp[n]-d*lambda;
    cout << ans << endl;
}

int main()
{
    fastio;

    int t = 1;
    // cin >> t;

    rep1(i, t) {
        solve(i);
    }

    return 0;
}

Subtask #1
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 4 ms 344 KB Output is correct
3 Correct 4 ms 348 KB Output is correct
4 Correct 4 ms 348 KB Output is correct
5 Correct 4 ms 560 KB Output is correct
6 Correct 4 ms 348 KB Output is correct
7 Correct 4 ms 348 KB Output is correct
8 Correct 4 ms 352 KB Output is correct
9 Correct 5 ms 564 KB Output is correct
10 Correct 4 ms 344 KB Output is correct
11 Correct 4 ms 564 KB Output is correct

Subtask #2
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Execution timed out 2075 ms 145580 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 4 ms 344 KB Output is correct
3 Correct 4 ms 348 KB Output is correct
4 Correct 4 ms 348 KB Output is correct
5 Correct 4 ms 560 KB Output is correct
6 Correct 4 ms 348 KB Output is correct
7 Correct 4 ms 348 KB Output is correct
8 Correct 4 ms 352 KB Output is correct
9 Correct 5 ms 564 KB Output is correct
10 Correct 4 ms 344 KB Output is correct
11 Correct 4 ms 564 KB Output is correct
12 Correct 1 ms 504 KB Output is correct
13 Correct 4 ms 348 KB Output is correct
14 Correct 4 ms 348 KB Output is correct
15 Correct 4 ms 460 KB Output is correct
16 Correct 4 ms 348 KB Output is correct
17 Correct 5 ms 348 KB Output is correct
18 Correct 4 ms 348 KB Output is correct
19 Correct 4 ms 564 KB Output is correct
20 Correct 4 ms 348 KB Output is correct
21 Correct 4 ms 348 KB Output is correct
22 Correct 4 ms 564 KB Output is correct
23 Correct 49 ms 1396 KB Output is correct
24 Correct 53 ms 1396 KB Output is correct
25 Correct 55 ms 1524 KB Output is correct
26 Correct 46 ms 1404 KB Output is correct
27 Correct 46 ms 1404 KB Output is correct
28 Correct 46 ms 1404 KB Output is correct
29 Correct 57 ms 1400 KB Output is correct
30 Correct 44 ms 1400 KB Output is correct
31 Correct 43 ms 1412 KB Output is correct
32 Correct 47 ms 1604 KB Output is correct
33 Correct 42 ms 1464 KB Output is correct
34 Correct 49 ms 1376 KB Output is correct
35 Correct 46 ms 1368 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 600 KB Output is correct
2 Correct 1132 ms 23436 KB Output is correct
3 Correct 1144 ms 23544 KB Output is correct
4 Correct 1125 ms 23216 KB Output is correct
5 Correct 1082 ms 23512 KB Output is correct
6 Correct 1111 ms 23516 KB Output is correct
7 Correct 1026 ms 23276 KB Output is correct
8 Correct 943 ms 23448 KB Output is correct
9 Correct 995 ms 23288 KB Output is correct
10 Correct 1051 ms 23276 KB Output is correct

Subtask #5
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 4 ms 344 KB Output is correct
3 Correct 4 ms 348 KB Output is correct
4 Correct 4 ms 348 KB Output is correct
5 Correct 4 ms 560 KB Output is correct
6 Correct 4 ms 348 KB Output is correct
7 Correct 4 ms 348 KB Output is correct
8 Correct 4 ms 352 KB Output is correct
9 Correct 5 ms 564 KB Output is correct
10 Correct 4 ms 344 KB Output is correct
11 Correct 4 ms 564 KB Output is correct
12 Correct 1 ms 504 KB Output is correct
13 Correct 4 ms 348 KB Output is correct
14 Correct 4 ms 348 KB Output is correct
15 Correct 4 ms 460 KB Output is correct
16 Correct 4 ms 348 KB Output is correct
17 Correct 5 ms 348 KB Output is correct
18 Correct 4 ms 348 KB Output is correct
19 Correct 4 ms 564 KB Output is correct
20 Correct 4 ms 348 KB Output is correct
21 Correct 4 ms 348 KB Output is correct
22 Correct 4 ms 564 KB Output is correct
23 Correct 49 ms 1396 KB Output is correct
24 Correct 53 ms 1396 KB Output is correct
25 Correct 55 ms 1524 KB Output is correct
26 Correct 46 ms 1404 KB Output is correct
27 Correct 46 ms 1404 KB Output is correct
28 Correct 46 ms 1404 KB Output is correct
29 Correct 57 ms 1400 KB Output is correct
30 Correct 44 ms 1400 KB Output is correct
31 Correct 43 ms 1412 KB Output is correct
32 Correct 47 ms 1604 KB Output is correct
33 Correct 42 ms 1464 KB Output is correct
34 Correct 49 ms 1376 KB Output is correct
35 Correct 46 ms 1368 KB Output is correct
36 Correct 0 ms 600 KB Output is correct
37 Correct 1132 ms 23436 KB Output is correct
38 Correct 1144 ms 23544 KB Output is correct
39 Correct 1125 ms 23216 KB Output is correct
40 Correct 1082 ms 23512 KB Output is correct
41 Correct 1111 ms 23516 KB Output is correct
42 Correct 1026 ms 23276 KB Output is correct
43 Correct 943 ms 23448 KB Output is correct
44 Correct 995 ms 23288 KB Output is correct
45 Correct 1051 ms 23276 KB Output is correct
46 Correct 0 ms 344 KB Output is correct
47 Correct 4 ms 344 KB Output is correct
48 Correct 6 ms 348 KB Output is correct
49 Correct 5 ms 348 KB Output is correct
50 Correct 4 ms 564 KB Output is correct
51 Correct 4 ms 348 KB Output is correct
52 Correct 4 ms 556 KB Output is correct
53 Correct 4 ms 348 KB Output is correct
54 Correct 4 ms 348 KB Output is correct
55 Correct 4 ms 396 KB Output is correct
56 Correct 4 ms 348 KB Output is correct
57 Correct 50 ms 1424 KB Output is correct
58 Correct 47 ms 1404 KB Output is correct
59 Correct 47 ms 1472 KB Output is correct
60 Correct 47 ms 1404 KB Output is correct
61 Correct 51 ms 1424 KB Output is correct
62 Correct 46 ms 1404 KB Output is correct
63 Correct 46 ms 1400 KB Output is correct
64 Correct 41 ms 1488 KB Output is correct
65 Correct 42 ms 1404 KB Output is correct
66 Correct 45 ms 1372 KB Output is correct
67 Correct 43 ms 1404 KB Output is correct
68 Correct 48 ms 1372 KB Output is correct
69 Correct 44 ms 1400 KB Output is correct
70 Correct 0 ms 348 KB Output is correct
71 Correct 1125 ms 23688 KB Output is correct
72 Correct 1132 ms 23388 KB Output is correct
73 Correct 1090 ms 23276 KB Output is correct
74 Correct 1105 ms 23516 KB Output is correct
75 Correct 1081 ms 23504 KB Output is correct
76 Correct 970 ms 23292 KB Output is correct
77 Correct 931 ms 23284 KB Output is correct
78 Correct 1010 ms 23636 KB Output is correct
79 Correct 1086 ms 23284 KB Output is correct
80 Correct 1154 ms 23508 KB Output is correct
81 Correct 1126 ms 23484 KB Output is correct
82 Correct 1091 ms 23380 KB Output is correct
83 Correct 1151 ms 23292 KB Output is correct
84 Correct 1150 ms 22972 KB Output is correct
85 Correct 1082 ms 23512 KB Output is correct
86 Correct 1048 ms 23312 KB Output is correct
87 Correct 947 ms 23472 KB Output is correct
88 Correct 1018 ms 23288 KB Output is correct
89 Correct 1060 ms 23280 KB Output is correct
90 Correct 1075 ms 23300 KB Output is correct

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 4 ms 344 KB Output is correct
3 Correct 4 ms 348 KB Output is correct
4 Correct 4 ms 348 KB Output is correct
5 Correct 4 ms 560 KB Output is correct
6 Correct 4 ms 348 KB Output is correct
7 Correct 4 ms 348 KB Output is correct
8 Correct 4 ms 352 KB Output is correct
9 Correct 5 ms 564 KB Output is correct
10 Correct 4 ms 344 KB Output is correct
11 Correct 4 ms 564 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Execution timed out 2075 ms 145580 KB Time limit exceeded
14 Halted 0 ms 0 KB -