oj.uz

Submission #747413

# Submission time Handle Problem Language Result Execution time Memory
747413 2023-05-24T07:06:09 Z GrindMachine Hedgehog Daniyar and Algorithms (IZhO19_sortbooks) C++17
100 / 100
 991 ms 110132 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

/*

guy j has to cross guy i (i < j) if:
a[j] < a[i]

for all guys that must cross each other, find if a[i]+a[j] <= k

rewriting the problem:
for given (l,r), find the max val of a[i] + a[j], s.t:
i < j and a[i] > a[j]

i.e find max sum inversion pair in range

we can try to use sweepline

sweep over r, maintaining the max ans for all l
so when answering a query, we can just find the max sum over all l in range [l,r] and check if it's > k

what changes when we move from r-1 to r

a[r] forms an inversion pair only with a[i] > a[r], i < r
let the indices of all guys < r with val > a[r] in descending order of indices be:
i1 > i2 > ... > ik

(i1,r) forms an inversion pair, so we can upd the val at i1 to a[i1] + a[r]

(i2,r) also forms an inversion pair

there are 2 cases to consider for i2:
1) a[i2] <= a[i1]: (i1,r) gives better result than (i2,r), so no need to update
2) a[i2] > a[i1]: (i2,i1) gives better result than (i2,r), so no need to update

similar arguments apply for i3,i4,...,ik

so we just have to upd the val at i1
i1 = next greater value to the left of a[r]
which can be found using a stack

updates and range max queries can be handled with a segtree

*/

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 a;
    };

    data neutral = {-inf2};

    data merge(data &left, data &right) {
        data curr;
        curr.a = max(left.a, right.a);
        return curr;
    }

    void create(int i, T v) {

    }

    void modify(int i, T v) {
        amax(tr[i].a, v);
    }

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

    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,m; cin >> n >> m;
    vector<ll> a(n+5);
    rep1(i,n) cin >> a[i];

    stack<ll> st;
    vector<ll> nge(n+5,-1);

    rev(i,n,1){
        while(!st.empty() and a[i] > a[st.top()]){
            nge[st.top()] = i;
            st.pop();
        }
        st.push(i);
    }

    vector<array<ll,3>> queries[n+5];

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

    segtree<ll> seg(n+5);
    vector<ll> ans(m+5);

    rep1(r,n){
        ll j = nge[r];
        if(j != -1){
            seg.pupd(j, a[r] + a[j]);            
        }

        for(auto [l,k,id] : queries[r]){
            ll mx = seg.query(l,r).a;
            if(mx > k) ans[id] = 0;
            else ans[id] = 1;
        }
    }

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

int main()
{
    fastio;

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

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

    return 0;
}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 320 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 328 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 324 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct

Subtask #2
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 320 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 328 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 324 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 2 ms 596 KB Output is correct
12 Correct 3 ms 724 KB Output is correct
13 Correct 3 ms 716 KB Output is correct
14 Correct 4 ms 852 KB Output is correct
15 Correct 4 ms 876 KB Output is correct
16 Correct 4 ms 836 KB Output is correct
17 Correct 3 ms 852 KB Output is correct
18 Correct 3 ms 816 KB Output is correct

Subtask #3
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 960 ms 100888 KB Output is correct
2 Correct 991 ms 100724 KB Output is correct
3 Correct 979 ms 100232 KB Output is correct
4 Correct 973 ms 100604 KB Output is correct
5 Correct 949 ms 110132 KB Output is correct

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 67 ms 11948 KB Output is correct
2 Correct 58 ms 12104 KB Output is correct
3 Correct 61 ms 12876 KB Output is correct
4 Correct 65 ms 12824 KB Output is correct
5 Correct 59 ms 12796 KB Output is correct
6 Correct 47 ms 12668 KB Output is correct
7 Correct 47 ms 12748 KB Output is correct
8 Correct 59 ms 11592 KB Output is correct
9 Correct 30 ms 5568 KB Output is correct
10 Correct 61 ms 11684 KB Output is correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 320 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 328 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 324 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 2 ms 596 KB Output is correct
12 Correct 3 ms 724 KB Output is correct
13 Correct 3 ms 716 KB Output is correct
14 Correct 4 ms 852 KB Output is correct
15 Correct 4 ms 876 KB Output is correct
16 Correct 4 ms 836 KB Output is correct
17 Correct 3 ms 852 KB Output is correct
18 Correct 3 ms 816 KB Output is correct
19 Correct 157 ms 22344 KB Output is correct
20 Correct 155 ms 22352 KB Output is correct
21 Correct 139 ms 25644 KB Output is correct
22 Correct 138 ms 24652 KB Output is correct
23 Correct 149 ms 24784 KB Output is correct
24 Correct 133 ms 26528 KB Output is correct
25 Correct 123 ms 26404 KB Output is correct
26 Correct 150 ms 26060 KB Output is correct
27 Correct 149 ms 26068 KB Output is correct
28 Correct 153 ms 25880 KB Output is correct
29 Correct 158 ms 25680 KB Output is correct
30 Correct 175 ms 25800 KB Output is correct
31 Correct 163 ms 25704 KB Output is correct
32 Correct 175 ms 25688 KB Output is correct
33 Correct 165 ms 25768 KB Output is correct
34 Correct 119 ms 25812 KB Output is correct
35 Correct 116 ms 25904 KB Output is correct
36 Correct 114 ms 25824 KB Output is correct
37 Correct 107 ms 25876 KB Output is correct
38 Correct 127 ms 25932 KB Output is correct
39 Correct 143 ms 24828 KB Output is correct
40 Correct 114 ms 20148 KB Output is correct
41 Correct 135 ms 24080 KB Output is correct

Subtask #6
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 320 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 328 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 324 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 2 ms 596 KB Output is correct
12 Correct 3 ms 724 KB Output is correct
13 Correct 3 ms 716 KB Output is correct
14 Correct 4 ms 852 KB Output is correct
15 Correct 4 ms 876 KB Output is correct
16 Correct 4 ms 836 KB Output is correct
17 Correct 3 ms 852 KB Output is correct
18 Correct 3 ms 816 KB Output is correct
19 Correct 960 ms 100888 KB Output is correct
20 Correct 991 ms 100724 KB Output is correct
21 Correct 979 ms 100232 KB Output is correct
22 Correct 973 ms 100604 KB Output is correct
23 Correct 949 ms 110132 KB Output is correct
24 Correct 67 ms 11948 KB Output is correct
25 Correct 58 ms 12104 KB Output is correct
26 Correct 61 ms 12876 KB Output is correct
27 Correct 65 ms 12824 KB Output is correct
28 Correct 59 ms 12796 KB Output is correct
29 Correct 47 ms 12668 KB Output is correct
30 Correct 47 ms 12748 KB Output is correct
31 Correct 59 ms 11592 KB Output is correct
32 Correct 30 ms 5568 KB Output is correct
33 Correct 61 ms 11684 KB Output is correct
34 Correct 157 ms 22344 KB Output is correct
35 Correct 155 ms 22352 KB Output is correct
36 Correct 139 ms 25644 KB Output is correct
37 Correct 138 ms 24652 KB Output is correct
38 Correct 149 ms 24784 KB Output is correct
39 Correct 133 ms 26528 KB Output is correct
40 Correct 123 ms 26404 KB Output is correct
41 Correct 150 ms 26060 KB Output is correct
42 Correct 149 ms 26068 KB Output is correct
43 Correct 153 ms 25880 KB Output is correct
44 Correct 158 ms 25680 KB Output is correct
45 Correct 175 ms 25800 KB Output is correct
46 Correct 163 ms 25704 KB Output is correct
47 Correct 175 ms 25688 KB Output is correct
48 Correct 165 ms 25768 KB Output is correct
49 Correct 119 ms 25812 KB Output is correct
50 Correct 116 ms 25904 KB Output is correct
51 Correct 114 ms 25824 KB Output is correct
52 Correct 107 ms 25876 KB Output is correct
53 Correct 127 ms 25932 KB Output is correct
54 Correct 143 ms 24828 KB Output is correct
55 Correct 114 ms 20148 KB Output is correct
56 Correct 135 ms 24080 KB Output is correct
57 Correct 932 ms 97948 KB Output is correct
58 Correct 925 ms 97868 KB Output is correct
59 Correct 894 ms 98788 KB Output is correct
60 Correct 895 ms 98688 KB Output is correct
61 Correct 918 ms 98604 KB Output is correct
62 Correct 888 ms 98892 KB Output is correct
63 Correct 563 ms 108660 KB Output is correct
64 Correct 570 ms 108764 KB Output is correct
65 Correct 855 ms 107116 KB Output is correct
66 Correct 848 ms 106940 KB Output is correct
67 Correct 870 ms 106944 KB Output is correct
68 Correct 946 ms 106076 KB Output is correct
69 Correct 922 ms 106076 KB Output is correct
70 Correct 920 ms 106148 KB Output is correct
71 Correct 934 ms 106220 KB Output is correct
72 Correct 947 ms 106048 KB Output is correct
73 Correct 501 ms 104028 KB Output is correct
74 Correct 538 ms 104436 KB Output is correct
75 Correct 518 ms 104028 KB Output is correct
76 Correct 506 ms 104208 KB Output is correct
77 Correct 496 ms 104120 KB Output is correct
78 Correct 807 ms 100648 KB Output is correct
79 Correct 614 ms 70100 KB Output is correct
80 Correct 806 ms 96668 KB Output is correct