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Submission #416374

# Submission time Handle Problem Language Result Execution time Memory
416374 2021-06-02T10:40:15 Z model_code Rooted MST (innopolis2021_final_E) C++17
100 / 100
 1313 ms 100572 KB 
#include <bits/stdc++.h>
#define ws weights

using namespace std;

typedef long long ll;


const int N = 3e5 + 10;
const int inf = 1e9 + 20;
const ll infty = (ll) (1e18);

int dsu[N];
vector <int> vs[N], ws[N];

int get(int v) {
    if (v == dsu[v]) return v;
    else return dsu[v] = get(dsu[v]);
}

void uni(int u, int v, int w) {
    u = get(u), v = get(v);
    if (vs[u].size() > vs[v].size()) swap(u, v);
    for (int x : vs[u]) vs[v].push_back(x);
    ws[v].push_back(w);
    for (int x : ws[u]) ws[v].push_back(x);
    dsu[u] = v;
}

int cost[N];
int edge_r[N];
ll t[4 * N][2][2];

void recalc(int v, int l, int r) {
    int m = (l + r) / 2;
    int my_w = edge_r[m - 1];
    for (int i = 0; i < 2; i++) {
        for (int j = 0; j < 2; j++) {
            t[v][i][j] = t[v * 2 + 1][i][1] + t[v * 2 + 2][1][j];
        }
    }
    for (int i = 0; i < 2; i++) {
        for (int j = 0; j < 2; j++) {
            int k = 1 ^ j;
            for (int l = 0; l < 2; l++) {
                t[v][i][l] = min(t[v][i][l], t[v * 2 + 1][i][j] + t[v * 2 + 2][k][l] + my_w);
            }
        }
    }
}

void build_leaf(int v, int i) {
    for (int x = 0; x < 2; x++) {
        for (int y = 0; y < 2; y++) {
            t[v][x][y] = (x && y ? cost[i] : 0);
        }
    }
}

void build(int v, int l, int r) {
    if (r - l == 1) {
        build_leaf(v, l);
    } else {
        int m = (l + r) / 2;
        build(v * 2 + 1, l, m);
        build(v * 2 + 2, m, r);
        recalc(v, l, r);
    }
}

void upd(int v, int l, int r, int i) {
    if (r - l == 1) {
        build_leaf(v, l);
    } else {
        int m = (l + r) / 2;
        if (i < m) {
            upd(v * 2 + 1, l, m, i);
        } else {
            upd(v * 2 + 2, m, r, i);
        }
        recalc(v, l, r);
    }
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n, m;
    cin >> n >> m;
    vector <int> a(n + 1);
    for (int i = 1; i <= n; i++) cin >> a[i];
    vector <pair <int, pair <int, int> > > e;
    auto add_edge = [&] (int a, int b, int w) {
        e.push_back({w, {a, b}});
    };
    for (int i = 2; i <= n; i++) {
        add_edge(i, i - 1, inf);
    }
    for (int i = 0; i < m; i++) {
        int w, u, v;
        cin >> u >> v >> w;
        add_edge(u, v, w);
    }
    sort(e.begin(), e.end());
    for (int i = 1; i <= n; i++) {
        dsu[i] = i;
        vs[i] = {i};
        ws[i] = {};
    }
    for (auto c : e) {
        int u = c.second.first, v = c.second.second;
        if (get(u) != get(v)) {
            uni(u, v, c.first);
        }
    }
    vector <int> perm(n + 1);
    int root = get(1);
    for (int i = 0; i < (int) vs[root].size(); i++) {
        perm[vs[root][i]] = i;
        if (i + 1 < (int) vs[root].size())
            edge_r[i] = ws[root][i];
    }
    for (int i = 1; i <= n; i++) {
        cost[perm[i]] = a[i];
    }
    build(0, 0, n);
    int q;
    cin >> q;
    while (q--) {
        int i, w;
        cin >> i >> w;
        i = perm[i];
        cost[i] = w;
        upd(0, 0, n, i);
        cout << t[0][1][1] << '\n';
    }
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 14412 KB Output is correct
2 Correct 12 ms 14416 KB Output is correct
3 Correct 10 ms 14412 KB Output is correct
4 Correct 13 ms 14516 KB Output is correct
5 Correct 13 ms 14664 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 953 ms 80060 KB Output is correct
2 Correct 835 ms 76520 KB Output is correct
3 Correct 288 ms 20656 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 284 ms 20628 KB Output is correct
2 Correct 249 ms 18480 KB Output is correct
3 Correct 187 ms 16696 KB Output is correct
4 Correct 1074 ms 82808 KB Output is correct
5 Correct 1052 ms 80456 KB Output is correct
6 Correct 929 ms 79084 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 360 ms 74272 KB Output is correct
2 Correct 405 ms 74376 KB Output is correct
3 Correct 398 ms 74652 KB Output is correct
4 Correct 280 ms 21476 KB Output is correct
5 Correct 255 ms 20276 KB Output is correct
6 Correct 173 ms 18784 KB Output is correct
7 Correct 706 ms 82656 KB Output is correct
8 Correct 674 ms 82656 KB Output is correct
9 Correct 699 ms 82808 KB Output is correct
10 Correct 685 ms 82800 KB Output is correct
11 Correct 676 ms 82728 KB Output is correct
12 Correct 686 ms 82648 KB Output is correct
13 Correct 677 ms 82708 KB Output is correct
14 Correct 676 ms 82780 KB Output is correct
15 Correct 823 ms 82704 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 360 ms 74272 KB Output is correct
2 Correct 405 ms 74376 KB Output is correct
3 Correct 398 ms 74652 KB Output is correct
4 Correct 280 ms 21476 KB Output is correct
5 Correct 255 ms 20276 KB Output is correct
6 Correct 173 ms 18784 KB Output is correct
7 Correct 706 ms 82656 KB Output is correct
8 Correct 674 ms 82656 KB Output is correct
9 Correct 699 ms 82808 KB Output is correct
10 Correct 685 ms 82800 KB Output is correct
11 Correct 676 ms 82728 KB Output is correct
12 Correct 686 ms 82648 KB Output is correct
13 Correct 677 ms 82708 KB Output is correct
14 Correct 676 ms 82780 KB Output is correct
15 Correct 823 ms 82704 KB Output is correct
16 Correct 387 ms 74200 KB Output is correct
17 Correct 405 ms 74504 KB Output is correct
18 Correct 421 ms 74592 KB Output is correct
19 Correct 286 ms 21404 KB Output is correct
20 Correct 266 ms 20264 KB Output is correct
21 Correct 178 ms 18800 KB Output is correct
22 Correct 670 ms 82748 KB Output is correct
23 Correct 670 ms 82728 KB Output is correct
24 Correct 724 ms 82736 KB Output is correct
25 Correct 732 ms 82640 KB Output is correct
26 Correct 663 ms 82700 KB Output is correct
27 Correct 766 ms 82748 KB Output is correct
28 Correct 721 ms 82948 KB Output is correct
29 Correct 628 ms 82708 KB Output is correct
30 Correct 731 ms 82684 KB Output is correct

Subtask #6
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1147 ms 100572 KB Output is correct
2 Correct 1259 ms 99656 KB Output is correct
3 Correct 1272 ms 100152 KB Output is correct
4 Correct 1313 ms 99692 KB Output is correct
5 Correct 1176 ms 99092 KB Output is correct
6 Correct 1197 ms 99372 KB Output is correct
7 Correct 1176 ms 100548 KB Output is correct
8 Correct 1186 ms 99612 KB Output is correct
9 Correct 1124 ms 100196 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 14412 KB Output is correct
2 Correct 12 ms 14416 KB Output is correct
3 Correct 10 ms 14412 KB Output is correct
4 Correct 13 ms 14516 KB Output is correct
5 Correct 13 ms 14664 KB Output is correct
6 Correct 295 ms 44496 KB Output is correct
7 Correct 380 ms 44616 KB Output is correct
8 Correct 305 ms 44852 KB Output is correct
9 Correct 478 ms 48560 KB Output is correct
10 Correct 156 ms 18048 KB Output is correct
11 Correct 140 ms 17520 KB Output is correct
12 Correct 115 ms 16956 KB Output is correct

Subtask #8
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 14412 KB Output is correct
2 Correct 12 ms 14416 KB Output is correct
3 Correct 10 ms 14412 KB Output is correct
4 Correct 13 ms 14516 KB Output is correct
5 Correct 13 ms 14664 KB Output is correct
6 Correct 953 ms 80060 KB Output is correct
7 Correct 835 ms 76520 KB Output is correct
8 Correct 288 ms 20656 KB Output is correct
9 Correct 284 ms 20628 KB Output is correct
10 Correct 249 ms 18480 KB Output is correct
11 Correct 187 ms 16696 KB Output is correct
12 Correct 1074 ms 82808 KB Output is correct
13 Correct 1052 ms 80456 KB Output is correct
14 Correct 929 ms 79084 KB Output is correct
15 Correct 360 ms 74272 KB Output is correct
16 Correct 405 ms 74376 KB Output is correct
17 Correct 398 ms 74652 KB Output is correct
18 Correct 280 ms 21476 KB Output is correct
19 Correct 255 ms 20276 KB Output is correct
20 Correct 173 ms 18784 KB Output is correct
21 Correct 706 ms 82656 KB Output is correct
22 Correct 674 ms 82656 KB Output is correct
23 Correct 699 ms 82808 KB Output is correct
24 Correct 685 ms 82800 KB Output is correct
25 Correct 676 ms 82728 KB Output is correct
26 Correct 686 ms 82648 KB Output is correct
27 Correct 677 ms 82708 KB Output is correct
28 Correct 676 ms 82780 KB Output is correct
29 Correct 823 ms 82704 KB Output is correct
30 Correct 387 ms 74200 KB Output is correct
31 Correct 405 ms 74504 KB Output is correct
32 Correct 421 ms 74592 KB Output is correct
33 Correct 286 ms 21404 KB Output is correct
34 Correct 266 ms 20264 KB Output is correct
35 Correct 178 ms 18800 KB Output is correct
36 Correct 670 ms 82748 KB Output is correct
37 Correct 670 ms 82728 KB Output is correct
38 Correct 724 ms 82736 KB Output is correct
39 Correct 732 ms 82640 KB Output is correct
40 Correct 663 ms 82700 KB Output is correct
41 Correct 766 ms 82748 KB Output is correct
42 Correct 721 ms 82948 KB Output is correct
43 Correct 628 ms 82708 KB Output is correct
44 Correct 731 ms 82684 KB Output is correct
45 Correct 1147 ms 100572 KB Output is correct
46 Correct 1259 ms 99656 KB Output is correct
47 Correct 1272 ms 100152 KB Output is correct
48 Correct 1313 ms 99692 KB Output is correct
49 Correct 1176 ms 99092 KB Output is correct
50 Correct 1197 ms 99372 KB Output is correct
51 Correct 1176 ms 100548 KB Output is correct
52 Correct 1186 ms 99612 KB Output is correct
53 Correct 1124 ms 100196 KB Output is correct
54 Correct 295 ms 44496 KB Output is correct
55 Correct 380 ms 44616 KB Output is correct
56 Correct 305 ms 44852 KB Output is correct
57 Correct 478 ms 48560 KB Output is correct
58 Correct 156 ms 18048 KB Output is correct
59 Correct 140 ms 17520 KB Output is correct
60 Correct 115 ms 16956 KB Output is correct
61 Correct 12 ms 14412 KB Output is correct
62 Correct 757 ms 74376 KB Output is correct
63 Correct 752 ms 74456 KB Output is correct
64 Correct 705 ms 74688 KB Output is correct
65 Correct 363 ms 21488 KB Output is correct
66 Correct 263 ms 20272 KB Output is correct
67 Correct 215 ms 18760 KB Output is correct
68 Correct 1080 ms 82784 KB Output is correct