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답안 #1069604

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
1069604 2024-08-22T06:51:16 Z caterpillow Mizuyokan 2 (JOI23_mizuyokan2) C++17
28 / 100
 4000 ms 19140 KB 
#include <bits/stdc++.h>

using namespace std;

using ll = long long;
#define vt vector
#define f first
#define s second
#define pb push_back
#define all(x) x.begin(), x.end()
#define size(x) ((int) (x).size())
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define ROF(i, a, b) for (int i = (b) - 1; i >= (a); i--)
#define F0R(i, b) FOR (i, 0, b)
#define endl '\n'

/*

constraints suggest a sqrt solution
note that we can account for the high-low case by simply starting at a 0 before the query start

it is never optimal to make a "low" point involve multiple segments
we can consider low points as points, and edges as ranges such that the sum is greater than the node on either side
valid edges make a dag, and we can do a simple dp to solve subtasks 1 and 2

observations:

    say we are trying to find valid v for some current node u
    find the closest range such that the sum is greater than u
    then, there will be at most log A_max nodes after this who are invalid transitions
    this is because each time we reach an invalid node, our total range sum at least doubles

    also, we can rephrase validity as pfx[v - 1] - pfx[u] > a[v], or pfx[v - 1] - a[v] > pfx[u]

using the first observation, we can calculate dp[u] in reverse, with each state taking log n * log A_max time

 */

const ll inf = 1e18;
struct Seg1 {
    int n;
    vt<ll> seg;
    void init(int _n) {
        for (n = 1; n < _n; n *= 2);
        seg.resize(2 * n, inf);
    }
    ll query(int l, int r) {
        ll res = inf;
        for (l += n, r += n + 1; l < r; l /= 2, r /= 2) {
            if (l & 1) res = min(res, seg[l++]);
            if (r & 1) res = min(seg[--r], res);
        }
        return res;
    }
    void upd(int i, ll v) {
        seg[i += n] = v;
        while (i /= 2) seg[i] = min(seg[2 * i], seg[2 * i + 1]);
    }
    int walk(ll x, int i) {
        if (i >= n) return i - n;
        if (seg[2 * i + 1] <= x) return walk(x, 2 * i + 1);
        else return walk(x, 2 * i);
    }

    vt<int> lhs, rhs;
    // find the last element in [l, r] such that a[i] <= x
    int walk_range(ll x, int l, int r) {
        lhs.clear();
        rhs.clear();
        int ol = l;
        for (l += n, r += n + 1; l < r; l /= 2, r /= 2) {
            if (l & 1) lhs.pb(l++);
            if (r & 1) rhs.pb(--r);
        }
        for (int i : rhs) if (seg[i] <= x) return walk(x, i);
        reverse(all(lhs));
        for (int i : lhs) if (seg[i] <= x) return walk(x, i);
        return ol - 1;
    }
};

struct Seg2 {
    int n;
    vt<ll> seg;
    void init(int _n) {
        for (n = 1; n < _n; n *= 2);
        seg.resize(2 * n, -inf);
    }
    ll query(int l, int r) {
        ll res = -inf;
        for (l += n, r += n + 1; l < r; l /= 2, r /= 2) {
            if (l & 1) res = max(res, seg[l++]);
            if (r & 1) res = max(seg[--r], res);
        }
        return res;
    }
    void upd(int i, ll v) {
        seg[i += n] = v;
        while (i /= 2) seg[i] = max(seg[2 * i], seg[2 * i + 1]);
    }
};

int solve(vt<ll> a) {
    int n = size(a);
    vt<ll> pfx(n + 1); // 1 - indexed
    F0R (i, n) pfx[i + 1] = pfx[i] + a[i];
    Seg1 seg;
    Seg2 dp;
    seg.init(n), dp.init(n);
    F0R (i, n) seg.upd(i, pfx[i] - a[i]);

    ROF (i, 0, n) {
        // find minimum j such that the sum from i + 1 to j is > a[i]
        ll cur = (i == n - 1); // special case for last guy

        int j = upper_bound(all(pfx), a[i] + pfx[i + 1]) - pfx.begin();
        j--;
        if (j == n) {
            dp.upd(i, cur);
            continue;
        }
        cur = 2; // we can at least end with a high

        int last = n;
        while (true) {
            int nxt = seg.walk_range(pfx[i + 1], j + 1, last - 1);

            cur = max(cur, dp.query(nxt + 1, last - 1) + 2);

            if (nxt == j) break;
            last = nxt;
        }

        dp.upd(i, cur);
    }

    ll ans = max(1ll, dp.query(0, 0));

    // special case for starting on a big guy
    int last = n;
    while (true) {
        int nxt = seg.walk_range(0, 0, last - 1);
        ans = max(ans, 1 + dp.query(nxt + 1, last - 1));

        if (nxt == -1) break;
        last = nxt;
    }

    return ans;
}

main() {
    cin.tie(0)->sync_with_stdio(0);

    int n; cin >> n;
    vt<ll> a(n); F0R (i, n) cin >> a[i];
    int q; cin >> q;
    F0R (i, q) {
        ll j, v; cin >> j >> v; j--;
        a[j] = v;
        int l, r; cin >> l >> r;
        vt<ll> tmp;
        FOR (j, l, r) {
            tmp.pb(a[j]);
        }
        cout << solve(tmp) << endl;
    }
}

Compilation message

mizuyokan2.cpp:152:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
  152 | main() {
      | ^~~~

Subtask #1
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 456 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 456 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 604 KB Output is correct
21 Correct 0 ms 348 KB Output is correct

Subtask #2
9.0 / 9.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 456 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 456 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 604 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 1 ms 348 KB Output is correct
26 Correct 3 ms 604 KB Output is correct
27 Correct 2 ms 604 KB Output is correct
28 Correct 3 ms 620 KB Output is correct
29 Correct 3 ms 616 KB Output is correct
30 Correct 2 ms 348 KB Output is correct
31 Correct 2 ms 348 KB Output is correct
32 Correct 2 ms 344 KB Output is correct
33 Correct 1 ms 604 KB Output is correct
34 Correct 2 ms 348 KB Output is correct
35 Correct 2 ms 604 KB Output is correct
36 Correct 3 ms 348 KB Output is correct
37 Correct 2 ms 604 KB Output is correct
38 Correct 2 ms 344 KB Output is correct
39 Correct 1 ms 348 KB Output is correct
40 Correct 1 ms 348 KB Output is correct

Subtask #3
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 456 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 456 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 604 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 1 ms 348 KB Output is correct
26 Correct 3 ms 604 KB Output is correct
27 Correct 2 ms 604 KB Output is correct
28 Correct 3 ms 620 KB Output is correct
29 Correct 3 ms 616 KB Output is correct
30 Correct 2 ms 348 KB Output is correct
31 Correct 2 ms 348 KB Output is correct
32 Correct 2 ms 344 KB Output is correct
33 Correct 1 ms 604 KB Output is correct
34 Correct 2 ms 348 KB Output is correct
35 Correct 2 ms 604 KB Output is correct
36 Correct 3 ms 348 KB Output is correct
37 Correct 2 ms 604 KB Output is correct
38 Correct 2 ms 344 KB Output is correct
39 Correct 1 ms 348 KB Output is correct
40 Correct 1 ms 348 KB Output is correct
41 Correct 23 ms 3932 KB Output is correct
42 Correct 17 ms 4576 KB Output is correct
43 Correct 23 ms 4572 KB Output is correct
44 Correct 17 ms 4844 KB Output is correct
45 Correct 83 ms 11472 KB Output is correct
46 Correct 352 ms 17864 KB Output is correct
47 Correct 214 ms 16076 KB Output is correct
48 Correct 370 ms 18336 KB Output is correct
49 Correct 492 ms 18124 KB Output is correct
50 Correct 389 ms 17428 KB Output is correct
51 Correct 320 ms 17732 KB Output is correct
52 Correct 141 ms 17172 KB Output is correct
53 Correct 312 ms 19140 KB Output is correct
54 Correct 356 ms 17196 KB Output is correct
55 Correct 261 ms 17820 KB Output is correct
56 Correct 370 ms 17284 KB Output is correct
57 Correct 157 ms 10368 KB Output is correct
58 Correct 317 ms 17612 KB Output is correct
59 Correct 77 ms 16360 KB Output is correct
60 Correct 101 ms 11384 KB Output is correct

Subtask #4
0 / 32.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 453 ms 5092 KB Output is correct
3 Correct 2853 ms 6068 KB Output is correct
4 Execution timed out 4010 ms 5264 KB Time limit exceeded
5 Halted 0 ms 0 KB -

Subtask #5
0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 456 KB Output is correct
3 Correct 420 ms 4780 KB Output is correct
4 Correct 2813 ms 4944 KB Output is correct
5 Execution timed out 4049 ms 17788 KB Time limit exceeded
6 Halted 0 ms 0 KB -

Subtask #6
0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 456 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 456 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 604 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 1 ms 348 KB Output is correct
26 Correct 3 ms 604 KB Output is correct
27 Correct 2 ms 604 KB Output is correct
28 Correct 3 ms 620 KB Output is correct
29 Correct 3 ms 616 KB Output is correct
30 Correct 2 ms 348 KB Output is correct
31 Correct 2 ms 348 KB Output is correct
32 Correct 2 ms 344 KB Output is correct
33 Correct 1 ms 604 KB Output is correct
34 Correct 2 ms 348 KB Output is correct
35 Correct 2 ms 604 KB Output is correct
36 Correct 3 ms 348 KB Output is correct
37 Correct 2 ms 604 KB Output is correct
38 Correct 2 ms 344 KB Output is correct
39 Correct 1 ms 348 KB Output is correct
40 Correct 1 ms 348 KB Output is correct
41 Correct 23 ms 3932 KB Output is correct
42 Correct 17 ms 4576 KB Output is correct
43 Correct 23 ms 4572 KB Output is correct
44 Correct 17 ms 4844 KB Output is correct
45 Correct 83 ms 11472 KB Output is correct
46 Correct 352 ms 17864 KB Output is correct
47 Correct 214 ms 16076 KB Output is correct
48 Correct 370 ms 18336 KB Output is correct
49 Correct 492 ms 18124 KB Output is correct
50 Correct 389 ms 17428 KB Output is correct
51 Correct 320 ms 17732 KB Output is correct
52 Correct 141 ms 17172 KB Output is correct
53 Correct 312 ms 19140 KB Output is correct
54 Correct 356 ms 17196 KB Output is correct
55 Correct 261 ms 17820 KB Output is correct
56 Correct 370 ms 17284 KB Output is correct
57 Correct 157 ms 10368 KB Output is correct
58 Correct 317 ms 17612 KB Output is correct
59 Correct 77 ms 16360 KB Output is correct
60 Correct 101 ms 11384 KB Output is correct
61 Correct 0 ms 344 KB Output is correct
62 Correct 453 ms 5092 KB Output is correct
63 Correct 2853 ms 6068 KB Output is correct
64 Execution timed out 4010 ms 5264 KB Time limit exceeded
65 Halted 0 ms 0 KB -