oj.uz

Submission #746507

# Submission time Handle Problem Language Result Execution time Memory
746507 2023-05-22T15:18:04 Z GrindMachine Triple Jump (JOI19_jumps) C++17
100 / 100
 690 ms 121636 KB 
// Om Namah Shivaya

#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) 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

/*

refs:
https://codeforces.com/blog/entry/68269?#comment-527139
edi


choose l <= a < b < c <= r s.t:
b-a <= c-b
arr[a]+arr[b]+arr[c] is max

let's say we fix (a,b)
when can we consider (a,b) as an option
if there is a guy in between with a higher val, then we dont have to consider pair (a,b)

if there exists k s.t a < k < b with arr[k] >= arr[a] or arr[k] >= arr[b], then we can do this:
arr[k] >= arr[a]: set a = k
arr[k] >= arr[b]: set b = k

by doing this, we reduce the jump distance from a to b
so we have more options for c

in short, consider pair (a,b) only if there is nobody in between with a higher or equal value

how many such pairs are there?

iterate over b from 1 to n and find all valid a

maintain all valid a values when increasing b
once some a becomes bad (some >= guy appears in between), he never becomes good for bigger b

we want to find all a for whom nobody >= them has appeared in [a,b] so far

when moving to a new b, we can make pairs (a,b) for all active a
then we will remove all a values for which arr[a] <= arr[b]

(yet to complete explanation)

*/

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 segtree {
    // https://codeforces.com/blog/entry/18051

    /*=======================================================*/

    struct data {
        ll mx1, mx2, res;
    };

    data neutral = {-inf2, -inf2, -inf2};

    data merge(data &left, data &right) {
        data curr;
        
        curr.mx1 = max(left.mx1,right.mx1);
        curr.mx2 = max(left.mx2,right.mx2);
        curr.res = max({left.res, right.res, left.mx2 + right.mx1});
        
        return curr;
    }

    void create(int i, T v) {
        tr[i].mx1 = v;
    }

    void modify(int i, T v) {
        amax(tr[i].mx2, v);
        tr[i].res = tr[i].mx1 + tr[i].mx2;
    }

    /*=======================================================*/

    int n;
    vector<data> tr;

    segtree() {

    }

    segtree(int siz) {
        init(siz);
    }

    void init(int siz) {
        n = siz;
        tr.assign(2 * n, neutral);
    }

    void build(vector<T> &a, int siz) {
        rep(i, siz) create(i + n, a[i]);
        rev(i, n - 1, 1) tr[i] = merge(tr[i << 1], tr[i << 1 | 1]);
    }

    void pupd(int i, T v) {
        modify(i + n, v);
        for (i = (i + n) >> 1; i; i >>= 1) tr[i] = merge(tr[i << 1], tr[i << 1 | 1]);
    }

    data query(int l, int r) {
        data resl = neutral, resr = neutral;

        for (l += n, r += n; l <= r; l >>= 1, r >>= 1) {
            if (l & 1) resl = merge(resl, tr[l++]);
            if (!(r & 1)) resr = merge(tr[r--], resr);
        }

        return merge(resl, resr);
    }
};

void solve(int test_case)
{
    ll n; cin >> n;
    vector<ll> arr(n+5);
    rep1(i,n) cin >> arr[i];

    vector<ll> good;
    vector<pll> pairs;

    rep1(b,n){
        while(!good.empty() and arr[b] >= arr[good.back()]){
            pairs.pb({good.back(), b});
            good.pop_back();
        }

        if(!good.empty()){
            pairs.pb({good.back(), b});
        }

        good.pb(b);
    }

    // for(auto [a, b] : pairs){
    //     if(a < 3) conts;
    //     ll dis = b - a;
    //     ll min_c = b + dis;
    //     ll val = 0;

    //     for(int c = min_c; c <= 12; ++c){
    //         amax(val, arr[a]+arr[b]+arr[c]);
    //     }

    //     pll px = {a, b};
    //     debug(px);
    //     debug(val);
    //     cout << endl;
    // }

    vector<ll> enter[n+5];
    for(auto [a,b] : pairs){
        enter[a].pb(b);
    }

    ll q; cin >> q;
    vector<pll> queries[n+5];

    rep1(i,q){
        ll l,r; cin >> l >> r;
        queries[l].pb({r, i});
    }

    vector<ll> ans(q+5);
    segtree<ll> st(n+5);
    st.build(arr,n+1);

    rev(l,n,1){
        trav(b,enter[l]){
            ll dis = b - l;
            ll c = b + dis;
            if(c <= n){
                st.pupd(c, arr[l] + arr[b]);
            }
        }

        for(auto [r, id] : queries[l]){
            ans[id] = st.query(l,r).res;
        }
    }

    rep1(i,q) cout << ans[i] << endl;
}

int main()
{
    fastio;

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

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

    return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 320 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 320 KB Output is correct

Subtask #2
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 320 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 320 KB Output is correct
11 Correct 171 ms 28328 KB Output is correct
12 Correct 161 ms 27968 KB Output is correct
13 Correct 172 ms 28108 KB Output is correct
14 Correct 173 ms 28148 KB Output is correct
15 Correct 180 ms 28232 KB Output is correct
16 Correct 178 ms 27456 KB Output is correct
17 Correct 174 ms 27612 KB Output is correct
18 Correct 179 ms 27368 KB Output is correct
19 Correct 168 ms 27964 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 94 ms 34360 KB Output is correct
2 Correct 58 ms 30040 KB Output is correct
3 Correct 61 ms 31620 KB Output is correct
4 Correct 94 ms 34396 KB Output is correct
5 Correct 91 ms 34356 KB Output is correct
6 Correct 91 ms 34348 KB Output is correct
7 Correct 98 ms 34392 KB Output is correct
8 Correct 94 ms 34356 KB Output is correct
9 Correct 88 ms 34420 KB Output is correct

Subtask #4
54.0 / 54.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 320 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 320 KB Output is correct
11 Correct 171 ms 28328 KB Output is correct
12 Correct 161 ms 27968 KB Output is correct
13 Correct 172 ms 28108 KB Output is correct
14 Correct 173 ms 28148 KB Output is correct
15 Correct 180 ms 28232 KB Output is correct
16 Correct 178 ms 27456 KB Output is correct
17 Correct 174 ms 27612 KB Output is correct
18 Correct 179 ms 27368 KB Output is correct
19 Correct 168 ms 27964 KB Output is correct
20 Correct 94 ms 34360 KB Output is correct
21 Correct 58 ms 30040 KB Output is correct
22 Correct 61 ms 31620 KB Output is correct
23 Correct 94 ms 34396 KB Output is correct
24 Correct 91 ms 34356 KB Output is correct
25 Correct 91 ms 34348 KB Output is correct
26 Correct 98 ms 34392 KB Output is correct
27 Correct 94 ms 34356 KB Output is correct
28 Correct 88 ms 34420 KB Output is correct
29 Correct 650 ms 118532 KB Output is correct
30 Correct 542 ms 107520 KB Output is correct
31 Correct 577 ms 111552 KB Output is correct
32 Correct 657 ms 118524 KB Output is correct
33 Correct 623 ms 118536 KB Output is correct
34 Correct 669 ms 116248 KB Output is correct
35 Correct 690 ms 115972 KB Output is correct
36 Correct 602 ms 115876 KB Output is correct
37 Correct 647 ms 117424 KB Output is correct
38 Correct 438 ms 121120 KB Output is correct
39 Correct 429 ms 121064 KB Output is correct
40 Correct 396 ms 117856 KB Output is correct
41 Correct 382 ms 117280 KB Output is correct
42 Correct 415 ms 117332 KB Output is correct
43 Correct 413 ms 119036 KB Output is correct
44 Correct 439 ms 121412 KB Output is correct
45 Correct 437 ms 121484 KB Output is correct
46 Correct 421 ms 118252 KB Output is correct
47 Correct 426 ms 117868 KB Output is correct
48 Correct 403 ms 117864 KB Output is correct
49 Correct 415 ms 119908 KB Output is correct
50 Correct 474 ms 121576 KB Output is correct
51 Correct 492 ms 121636 KB Output is correct
52 Correct 489 ms 119348 KB Output is correct
53 Correct 465 ms 118936 KB Output is correct
54 Correct 488 ms 118784 KB Output is correct
55 Correct 480 ms 120524 KB Output is correct