Submission #737589

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
737589	2023-05-07T11:57:52 Z	GrindMachine	Bubble Sort 2 (JOI18_bubblesort2)	C++17	100 / 100	3736 ms	43704 KB

bubblesort2

// 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:
edi: http://s3-ap-northeast-1.amazonaws.com/data.cms.ioi-jp.org/open-2018/2018-open-bubblesort2-sol-en.pdf
https://codeforces.com/blog/entry/61340?#comment-452982
(read edi of linked usaco problem, it contains the proof for the approach mentioned in the joi edi)

let's rewrite every index of a as (ai,i)
so that all guys are unique

let bi = final pos of guy i in sorted a[]

key obs:
in one pass of bubblesort, a guy may move how many ever places to the right
but it can move at most 1 place to the left

so for every guy, lower bound on #of ops = i-b[i]

how to find ans using the lower bounds?
in fact, ans = max(all lower bounds)
i.e ans = max(i-b[i]) for all i

for a guy with positive i-b[i], he either moves left (i-b[i] is positive cuz someone bigger than a[i] is there to the left, so when this bigger guy moves to the right, this guy would move one step to the left)
for a guy with i-b[i] = 0, he never moves right (may move left tho)

so max(i-b[i]) dec by 1 in every op until it becomes 0
proof complete

queries can be handled efficiently using lazysegtree + fenwick tree

*/

#include "bubblesort2.h"

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 fenwick {
    int siz;
    vector<T> tree;

    fenwick(int n) {
        siz = n;
        tree = vector<T>(n + 1);
    }

    int lsb(int x) {
        return x & -x;
    }

    void build(vector<T> &a, int n) {
        for (int i = 1; i <= n; ++i) {
            int par = i + lsb(i);
            tree[i] += a[i];

            if (par <= siz) {
                tree[par] += tree[i];
            }
        }
    }

    void pupd(int i, T v) {
        i++;

        while (i <= siz) {
            tree[i] += v;
            i += lsb(i);
        }
    }

    T sum(int i) {
        i++;

        T res = 0;

        while (i) {
            res += tree[i];
            i -= lsb(i);
        }

        return res;
    }

    T query(int l, int r) {
        if (l > r) return 0;
        T res = sum(r) - sum(l - 1);
        return res;
    }
};

template<typename T>
struct lazysegtree {
    /*=======================================================*/

    struct data {
        int a;
    };

    struct lazy {
        int a;
    };

    data d_neutral = { -inf1};
    lazy l_neutral = {0};

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

    void create(int x, int lx, int rx, T v) {
        tr[x].a = v;
    }

    void modify(int x, int lx, int rx, T v) {
        if (v.ff == 1) {
            // set
            tr[x].a = v.ss;
        }
        else {
            // add
            lz[x].a = v.ss;
        }
    }

    void propagate(int x, int lx, int rx) {
        ll v = lz[x].a;
        if (!v) return;

        tr[x].a += 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);
    }
};

vector<int> countScans(vector<int> a, vector<int> qx, vector<int> qv) {
    int n = sz(a);
    int q = sz(qx);

    vector<pii> b;
    rep(i, n) {
        b.pb({a[i], i});
    }
    rep(i, q) {
        b.pb({qv[i], qx[i]});
    }

    sort(all(b));
    b.resize(unique(all(b)) - b.begin());
    int siz = sz(b);

    auto get_ind = [&](pii p) {
        return lower_bound(all(b), p) - b.begin();
    };

    lazysegtree<pii> st(siz + 5);
    fenwick<int> fenw(siz + 5);

    rep(i, n) {
        int ind = get_ind({a[i], i});
        st.rupd(ind, ind, {1, i});
        fenw.pupd(ind, 1);
    }

    rep(i, n) {
        int ind = get_ind({a[i], i});
        st.rupd(ind + 1, siz, {2, -1});
    }

    vector<int> ans(q);

    rep(id, q) {
        int i = qx[id];
        int v = qv[id];

        int ind1 = get_ind({a[i], i});
        st.rupd(ind1, ind1, {1, -inf1});
        st.rupd(ind1, siz, {2, 1});
        fenw.pupd(ind1, -1);

        a[i] = v;

        int ind2 = get_ind({a[i], i});
        int smaller = fenw.query(0, ind2 - 1);
        st.rupd(ind2, ind2, {1, i - smaller});
        st.rupd(ind2 + 1, siz, {2, -1});
        fenw.pupd(ind2, 1);

        ans[id] = st.query(0, siz).a;
    }

    return ans;
}

Subtask #1

17.0 / 17.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	340 KB	Output is correct
2	Correct	3 ms	340 KB	Output is correct
3	Correct	7 ms	440 KB	Output is correct
4	Correct	7 ms	440 KB	Output is correct
5	Correct	7 ms	468 KB	Output is correct
6	Correct	6 ms	520 KB	Output is correct
7	Correct	7 ms	516 KB	Output is correct
8	Correct	6 ms	468 KB	Output is correct
9	Correct	6 ms	440 KB	Output is correct
10	Correct	6 ms	440 KB	Output is correct
11	Correct	6 ms	436 KB	Output is correct
12	Correct	6 ms	468 KB	Output is correct
13	Correct	6 ms	568 KB	Output is correct
14	Correct	6 ms	468 KB	Output is correct
15	Correct	6 ms	512 KB	Output is correct
16	Correct	6 ms	472 KB	Output is correct
17	Correct	6 ms	512 KB	Output is correct
18	Correct	6 ms	440 KB	Output is correct

Subtask #2

21.0 / 21.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	340 KB	Output is correct
2	Correct	3 ms	340 KB	Output is correct
3	Correct	7 ms	440 KB	Output is correct
4	Correct	7 ms	440 KB	Output is correct
5	Correct	7 ms	468 KB	Output is correct
6	Correct	6 ms	520 KB	Output is correct
7	Correct	7 ms	516 KB	Output is correct
8	Correct	6 ms	468 KB	Output is correct
9	Correct	6 ms	440 KB	Output is correct
10	Correct	6 ms	440 KB	Output is correct
11	Correct	6 ms	436 KB	Output is correct
12	Correct	6 ms	468 KB	Output is correct
13	Correct	6 ms	568 KB	Output is correct
14	Correct	6 ms	468 KB	Output is correct
15	Correct	6 ms	512 KB	Output is correct
16	Correct	6 ms	472 KB	Output is correct
17	Correct	6 ms	512 KB	Output is correct
18	Correct	6 ms	440 KB	Output is correct
19	Correct	21 ms	980 KB	Output is correct
20	Correct	28 ms	1064 KB	Output is correct
21	Correct	25 ms	1028 KB	Output is correct
22	Correct	26 ms	1076 KB	Output is correct
23	Correct	25 ms	1100 KB	Output is correct
24	Correct	25 ms	980 KB	Output is correct
25	Correct	30 ms	1080 KB	Output is correct
26	Correct	27 ms	980 KB	Output is correct
27	Correct	23 ms	1072 KB	Output is correct
28	Correct	24 ms	1080 KB	Output is correct

Subtask #3

22.0 / 22.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	36 ms	1512 KB	Output is correct
2	Correct	110 ms	2900 KB	Output is correct
3	Correct	195 ms	5088 KB	Output is correct
4	Correct	202 ms	5032 KB	Output is correct
5	Correct	195 ms	5016 KB	Output is correct
6	Correct	196 ms	4928 KB	Output is correct
7	Correct	201 ms	5020 KB	Output is correct
8	Correct	189 ms	5020 KB	Output is correct
9	Correct	180 ms	5020 KB	Output is correct
10	Correct	157 ms	3748 KB	Output is correct
11	Correct	160 ms	3752 KB	Output is correct
12	Correct	160 ms	3752 KB	Output is correct
13	Correct	176 ms	3804 KB	Output is correct
14	Correct	158 ms	3748 KB	Output is correct
15	Correct	159 ms	3720 KB	Output is correct
16	Correct	150 ms	3700 KB	Output is correct
17	Correct	150 ms	3756 KB	Output is correct
18	Correct	142 ms	3780 KB	Output is correct

Subtask #4

40.0 / 40.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	340 KB	Output is correct
2	Correct	3 ms	340 KB	Output is correct
3	Correct	7 ms	440 KB	Output is correct
4	Correct	7 ms	440 KB	Output is correct
5	Correct	7 ms	468 KB	Output is correct
6	Correct	6 ms	520 KB	Output is correct
7	Correct	7 ms	516 KB	Output is correct
8	Correct	6 ms	468 KB	Output is correct
9	Correct	6 ms	440 KB	Output is correct
10	Correct	6 ms	440 KB	Output is correct
11	Correct	6 ms	436 KB	Output is correct
12	Correct	6 ms	468 KB	Output is correct
13	Correct	6 ms	568 KB	Output is correct
14	Correct	6 ms	468 KB	Output is correct
15	Correct	6 ms	512 KB	Output is correct
16	Correct	6 ms	472 KB	Output is correct
17	Correct	6 ms	512 KB	Output is correct
18	Correct	6 ms	440 KB	Output is correct
19	Correct	21 ms	980 KB	Output is correct
20	Correct	28 ms	1064 KB	Output is correct
21	Correct	25 ms	1028 KB	Output is correct
22	Correct	26 ms	1076 KB	Output is correct
23	Correct	25 ms	1100 KB	Output is correct
24	Correct	25 ms	980 KB	Output is correct
25	Correct	30 ms	1080 KB	Output is correct
26	Correct	27 ms	980 KB	Output is correct
27	Correct	23 ms	1072 KB	Output is correct
28	Correct	24 ms	1080 KB	Output is correct
29	Correct	36 ms	1512 KB	Output is correct
30	Correct	110 ms	2900 KB	Output is correct
31	Correct	195 ms	5088 KB	Output is correct
32	Correct	202 ms	5032 KB	Output is correct
33	Correct	195 ms	5016 KB	Output is correct
34	Correct	196 ms	4928 KB	Output is correct
35	Correct	201 ms	5020 KB	Output is correct
36	Correct	189 ms	5020 KB	Output is correct
37	Correct	180 ms	5020 KB	Output is correct
38	Correct	157 ms	3748 KB	Output is correct
39	Correct	160 ms	3752 KB	Output is correct
40	Correct	160 ms	3752 KB	Output is correct
41	Correct	176 ms	3804 KB	Output is correct
42	Correct	158 ms	3748 KB	Output is correct
43	Correct	159 ms	3720 KB	Output is correct
44	Correct	150 ms	3700 KB	Output is correct
45	Correct	150 ms	3756 KB	Output is correct
46	Correct	142 ms	3780 KB	Output is correct
47	Correct	739 ms	16200 KB	Output is correct
48	Correct	3038 ms	41000 KB	Output is correct
49	Correct	3136 ms	42960 KB	Output is correct
50	Correct	3136 ms	42852 KB	Output is correct
51	Correct	3286 ms	42864 KB	Output is correct
52	Correct	3224 ms	42856 KB	Output is correct
53	Correct	3551 ms	42852 KB	Output is correct
54	Correct	3462 ms	43112 KB	Output is correct
55	Correct	3736 ms	43324 KB	Output is correct
56	Correct	3299 ms	43688 KB	Output is correct
57	Correct	3351 ms	43612 KB	Output is correct
58	Correct	3010 ms	43704 KB	Output is correct
59	Correct	2699 ms	43204 KB	Output is correct
60	Correct	2581 ms	43320 KB	Output is correct
61	Correct	2650 ms	43152 KB	Output is correct
62	Correct	2557 ms	42968 KB	Output is correct
63	Correct	2519 ms	42872 KB	Output is correct
64	Correct	2624 ms	42876 KB	Output is correct
65	Correct	2581 ms	42640 KB	Output is correct
66	Correct	2391 ms	42628 KB	Output is correct
67	Correct	2370 ms	42600 KB	Output is correct