CSES - NOI 2024

Submission details
Task:	Thin Ice
Sender:	Veikko Heikkinen
Submission time:	2024-03-06 16:19:11 +0200
Language:	C++ (C++20)
Status:	READY
Result:	100

Feedback
group	verdict	score
#1	ACCEPTED	17
#2	ACCEPTED	12
#3	ACCEPTED	11
#4	ACCEPTED	19
#5	ACCEPTED	14
#6	ACCEPTED	27

Test results
test	verdict	time	group
#1	ACCEPTED	0.01 s	1, 5, 6	details
#2	ACCEPTED	0.01 s	1, 5, 6	details
#3	ACCEPTED	0.01 s	1, 5, 6	details
#4	ACCEPTED	0.01 s	1, 5, 6	details
#5	ACCEPTED	0.01 s	1, 5, 6	details
#6	ACCEPTED	0.01 s	1, 5, 6	details
#7	ACCEPTED	0.01 s	1, 5, 6	details
#8	ACCEPTED	0.01 s	1, 5, 6	details
#9	ACCEPTED	0.01 s	1, 2, 5, 6	details
#10	ACCEPTED	0.15 s	2, 6	details
#11	ACCEPTED	0.13 s	2, 6	details
#12	ACCEPTED	0.14 s	2, 6	details
#13	ACCEPTED	0.13 s	2, 6	details
#14	ACCEPTED	0.13 s	2, 6	details
#15	ACCEPTED	0.14 s	2, 6	details
#16	ACCEPTED	0.14 s	2, 6	details
#17	ACCEPTED	0.14 s	2, 6	details
#18	ACCEPTED	0.14 s	2, 6	details
#19	ACCEPTED	0.13 s	2, 6	details
#20	ACCEPTED	0.13 s	2, 6	details
#21	ACCEPTED	0.12 s	2, 6	details
#22	ACCEPTED	0.01 s	3, 4, 5, 6	details
#23	ACCEPTED	0.01 s	3, 4, 5, 6	details
#24	ACCEPTED	0.01 s	3, 4, 5, 6	details
#25	ACCEPTED	0.01 s	3, 4, 5, 6	details
#26	ACCEPTED	0.01 s	3, 4, 5, 6	details
#27	ACCEPTED	0.01 s	3, 4, 5, 6	details
#28	ACCEPTED	0.18 s	4, 6	details
#29	ACCEPTED	0.14 s	4, 6	details
#30	ACCEPTED	0.14 s	4, 6	details
#31	ACCEPTED	0.16 s	4, 6	details
#32	ACCEPTED	0.12 s	4, 6	details
#33	ACCEPTED	0.10 s	4, 6	details
#34	ACCEPTED	0.17 s	4, 6	details
#35	ACCEPTED	0.01 s	5, 6	details
#36	ACCEPTED	0.01 s	5, 6	details
#37	ACCEPTED	0.01 s	5, 6	details
#38	ACCEPTED	0.01 s	5, 6	details
#39	ACCEPTED	0.01 s	5, 6	details
#40	ACCEPTED	0.01 s	5, 6	details
#41	ACCEPTED	0.01 s	5, 6	details
#42	ACCEPTED	0.17 s	6	details
#43	ACCEPTED	0.17 s	6	details
#44	ACCEPTED	0.12 s	6	details
#45	ACCEPTED	0.18 s	6	details
#46	ACCEPTED	0.13 s	6	details
#47	ACCEPTED	0.12 s	6	details
#48	ACCEPTED	0.16 s	6	details

Code

#include <bits/stdc++.h>

#define debug(x) cout << #x << ": " << x << endl
#define all(x) begin(x),end(x)
#define rall(x) rbegin(x),rend(x)
#define fi first
#define se second

using namespace std;
using ll = long long;
using pii = pair<int, int>;

struct dsu {
    vector<int> p, sz, con;
    vector<vector<int>> ch;
    set<int> upd;
    
    dsu() {}
    dsu(int n) {
        p.resize(n);
        iota(all(p), 0);
        sz.resize(n, 1);
        con.resize(n, 0);
        ch.resize(n);
    }
    
    int fs(int u) {
        return u == p[u] ? u : p[u] = fs(p[u]);
    }
    
    void us(int a, int b) {
        a = fs(a);
        b = fs(b);
        if (a == b) return;
        if (sz[a] < sz[b]) swap(a, b);
        if (ch[a].size() < ch[b].size()) swap(ch[a], ch[b]);
        for (int i : ch[b]) ch[a].push_back(i);
        ch[b].clear();
        sz[a] += sz[b];
        con[a] |= con[b];
        p[b] = a;
        upd.insert(a);
    }
};

const int N = 400400;

vector<int> ch[N];
int sz[N], val[N];
bool con[N];

const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

int dfs(int u, int cnt) {
    int ans = min(val[u], cnt + sz[u]);
    for (int v : ch[u]) if (con[v]) {
        ans = max(ans, dfs(v, min(val[u], cnt + sz[u] - sz[v])));
    }
    return ans;
}

void solve() {
    int n, m;
    cin >> n >> m;
    
    auto ind = [&n, &m](int i, int j) {
        return m * i + j;
    };
    
    vector<vector<int>> a(n, vector<int>(m));
    vector<array<int, 3>> v(n*m);
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
            int d;
            cin >> d;
            a[i][j] = d;
            v[ind(i, j)] = {d, i, j};
        }
    }
    
    dsu dsu(n*m);
    for (int i = 0; i < n; ++i) {
        dsu.con[ind(i, 0)] = 1;
        dsu.con[ind(i, m-1)] = 1;
    }
    for (int j = 0; j < m; ++j) {
        dsu.con[ind(0, j)] = 1;
        dsu.con[ind(n-1, j)] = 1;
    }
    
    int w = 0;
    
    sort(rall(v));
    int k = 0;
    for (int d = 2e5; d > 0; --d) {
        int j = k;
        while (j < n*m && v[j][0] == d) {
            for (int i = 0; i < 4; ++i) {
                int x = v[j][1] + dx[i];
                int y = v[j][2] + dy[i];
                if (x >= 0 && x < n && y >= 0 && y < m && a[x][y] >= v[j][0]) {
                    dsu.us(ind(x, y), ind(v[j][1], v[j][2]));
                }
            }
            ++j;
        }
        j = k;
        while (j < n*m && v[j][0] == d) {
            dsu.upd.insert(ind(v[j][1], v[j][2]));
            ++j;
        }
        k = j;
        
        for (int u : dsu.upd) if (u == dsu.fs(u)) {
            sz[w] = dsu.sz[u];
            con[w] = dsu.con[u];
            val[w] = d;
            for (int v : dsu.ch[u]) {
                ch[w].push_back(v);
            }
            dsu.ch[u] = {w};
            ++w;
        }
        dsu.upd.clear();
    }
    
    cout << dfs(w-1, 0) << '\n';
}

int main() {
    cin.tie(0) -> sync_with_stdio(0);
    
    solve();
    
    return 0;
}

Test details

Test 1

Group: 1, 5, 6

Verdict: ACCEPTED

input
`4 4 9 11 5 7 7 9 14 3 1 3 2 3 11 4 14 8` view save

correct output
`10` view save

user output
`10` view save

Test 2

Group: 1, 5, 6

Verdict: ACCEPTED

input
`5 3 10 7 11 8 5 5 12 9 10 3 13 9 ...` view save

correct output
`10` view save

user output
`10` view save

Test 3

Group: 1, 5, 6

Verdict: ACCEPTED

input
`4 4 3 2 2 2 5 1 1 1 8 4 1 1 7 6 2 1` view save

correct output
`8` view save

user output
`8` view save

Test 4

Group: 1, 5, 6

Verdict: ACCEPTED

input
`3 5 1 11 1 3 5 4 12 7 8 7 13 14 14 9 4` view save

correct output
`14` view save

user output
`14` view save

Test 5

Group: 1, 5, 6

Verdict: ACCEPTED

input
`5 3 11 8 12 11 11 12 6 2 3 11 8 13 ...` view save

correct output
`12` view save

user output
`12` view save

Test 6

Group: 1, 5, 6

Verdict: ACCEPTED

input
`3 5 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14` view save

correct output
`14` view save

user output
`14` view save

Test 7

Group: 1, 5, 6

Verdict: ACCEPTED

input
`4 4 12 8 6 5 12 9 6 1 10 1 3 2 8 1 1 1` view save

correct output
`12` view save

user output
`12` view save

Test 8

Group: 1, 5, 6

Verdict: ACCEPTED

input
`4 4 8 3 15 14 10 12 2 4 5 16 9 6 7 13 1 11` view save

correct output
`13` view save

user output
`13` view save

Test 9

Group: 1, 2, 5, 6

Verdict: ACCEPTED

input
`4 4 4 1 1 2 3 5 4 2 2 2 1 2 1 4 3 4` view save

correct output
`4` view save

user output
`4` view save

Test 10

Group: 2, 6

Verdict: ACCEPTED

input
`10 20000 5 3 2 1 3 2 3 3 4 5 1 1 2 3 5 ...` view save

correct output
`5` view save

user output
`5` view save

Test 11

Group: 2, 6

Verdict: ACCEPTED

input
`10 20000 1 2 1 2 1 2 1 2 1 1 1 1 2 1 1 ...` view save

correct output
`3` view save

user output
`3` view save

Test 12

Group: 2, 6

Verdict: ACCEPTED

input
`10 20000 3 2 2 3 1 2 1 4 4 3 1 4 3 2 4 ...` view save

correct output
`5` view save

user output
`5` view save

Test 13

Group: 2, 6

Verdict: ACCEPTED

input
`20000 10 1 1 3 1 2 1 1 1 1 1 1 2 2 1 1 1 1 2 1 1 2 1 1 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 ...` view save

correct output
`4` view save

user output
`4` view save

Test 14

Group: 2, 6

Verdict: ACCEPTED

input
`10 20000 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...` view save

correct output
`3` view save

user output
`3` view save

Test 15

Group: 2, 6

Verdict: ACCEPTED

input
`10 20000 3 1 3 1 2 1 2 3 2 2 1 2 1 1 2 ...` view save

correct output
`3` view save

user output
`3` view save

Test 16

Group: 2, 6

Verdict: ACCEPTED

input
`10 20000 1 2 2 2 1 2 3 1 2 2 2 1 2 2 2 ...` view save

correct output
`4` view save

user output
`4` view save

Test 17

Group: 2, 6

Verdict: ACCEPTED

input
`10 20000 3 3 2 3 2 3 2 2 2 2 2 1 3 2 1 ...` view save

correct output
`4` view save

user output
`4` view save

Test 18

Group: 2, 6

Verdict: ACCEPTED

input
`10 20000 1 3 3 1 1 4 3 3 3 1 2 2 1 3 1 ...` view save

correct output
`5` view save

user output
`5` view save

Test 19

Group: 2, 6

Verdict: ACCEPTED

input
`7 28571 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ...` view save

correct output
`3` view save

user output
`3` view save

Test 20

Group: 2, 6

Verdict: ACCEPTED

input
`28571 7 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ...` view save

correct output
`5` view save

user output
`5` view save

Test 21

Group: 2, 6

Verdict: ACCEPTED

input
`447 447 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ...` view save

correct output
`3` view save

user output
`3` view save

Test 22

Group: 3, 4, 5, 6

Verdict: ACCEPTED

input
`1 100 46 23 23 55 37 17 30 32 25 71 ...` view save

correct output
`30` view save

user output
`30` view save

Test 23

Group: 3, 4, 5, 6

Verdict: ACCEPTED

input
`1 100 8 13 12 11 15 15 15 19 18 21 2...` view save

correct output
`76` view save

user output
`76` view save

Test 24

Group: 3, 4, 5, 6

Verdict: ACCEPTED

input
`1 100 94 94 94 95 95 91 97 100 92 98...` view save

correct output
`95` view save

user output
`95` view save

Test 25

Group: 3, 4, 5, 6

Verdict: ACCEPTED

input
`1 100 83 83 83 83 83 83 83 83 83 83 ...` view save

correct output
`83` view save

user output
`83` view save

Test 26

Group: 3, 4, 5, 6

Verdict: ACCEPTED

input
`1 100 33 34 35 38 38 40 41 42 42 45 ...` view save

correct output
`95` view save

user output
`95` view save

Test 27

Group: 3, 4, 5, 6

Verdict: ACCEPTED

input
`1 100 57 1 80 39 18 63 30 86 85 55 8...` view save

correct output
`29` view save

user output
`29` view save

Test 28

Group: 4, 6

Verdict: ACCEPTED

input
`1 200000 138736 14949 12344 104147 1333...` view save

correct output
`1806` view save

user output
`1806` view save

Test 29

Group: 4, 6

Verdict: ACCEPTED

input
`1 200000 141245 141090 141163 141286 14...` view save

correct output
`155109` view save

user output
`155109` view save

Test 30

Group: 4, 6

Verdict: ACCEPTED

input
`1 200000 102358 102469 102440 102402 10...` view save

correct output
`152388` view save

user output
`152388` view save

Test 31

Group: 4, 6

Verdict: ACCEPTED

input
`1 200000 180410 160820 160820 180614 18...` view save

correct output
`160832` view save

user output
`160832` view save

Test 32

Group: 4, 6

Verdict: ACCEPTED

input
`1 200000 198270 198270 198270 198270 19...` view save

correct output
`198270` view save

user output
`198270` view save

Test 33

Group: 4, 6

Verdict: ACCEPTED

input
`1 200000 1 1 3 2 1 1 2 3 6 6 6 7 8 9 10...` view save

correct output
`199995` view save

user output
`199995` view save

Test 34

Group: 4, 6

Verdict: ACCEPTED

input
`1 200000 14737 162555 44228 170991 1340...` view save

correct output
`1902` view save

user output
`1902` view save

Test 35

Group: 5, 6

Verdict: ACCEPTED

input
`31 32 669 792 226 189 860 737 291 83...` view save

correct output
`565` view save

user output
`565` view save

Test 36

Group: 5, 6

Verdict: ACCEPTED

input
`10 100 730 698 339 743 536 702 94 556...` view save

correct output
`529` view save

user output
`529` view save

Test 37

Group: 5, 6

Verdict: ACCEPTED

input
`32 31 633 613 618 605 635 638 668 67...` view save

correct output
`678` view save

user output
`678` view save

Test 38

Group: 5, 6

Verdict: ACCEPTED

input
`142 7 983 930 963 926 979 962 962 966 930 963 924 928 928 926 926 929 929 922 931 931 978 929 929 929 922 959 928 964 ...` view save

correct output
`934` view save

user output
`934` view save

Test 39

Group: 5, 6

Verdict: ACCEPTED

input
`31 32 977 977 977 977 977 977 977 97...` view save

correct output
`977` view save

user output
`977` view save

Test 40

Group: 5, 6

Verdict: ACCEPTED

input
`50 20 1 27 14 23 38 48 56 3 12 9 6 2...` view save

correct output
`997` view save

user output
`997` view save

Test 41

Group: 5, 6

Verdict: ACCEPTED

input
`20 50 481 532 624 290 965 58 448 872...` view save

correct output
`504` view save

user output
`504` view save

Test 42

Group: 6

Verdict: ACCEPTED

input
`447 447 6474 27185 108482 124481 16058...` view save

correct output
`88202` view save

user output
`88202` view save

Test 43

Group: 6

Verdict: ACCEPTED

input
`1000 200 27722 57131 197677 184858 9285...` view save

correct output
`89324` view save

user output
`89324` view save

Test 44

Group: 6

Verdict: ACCEPTED

input
`447 447 70928 73154 72640 74764 75237 ...` view save

correct output
`181096` view save

user output
`181096` view save

Test 45

Group: 6

Verdict: ACCEPTED

input
`7 28571 193031 185883 171670 185794 17...` view save

correct output
`171680` view save

user output
`171680` view save

Test 46

Group: 6

Verdict: ACCEPTED

input
`10 20000 191628 191628 191628 191628 19...` view save

correct output
`191628` view save

user output
`191628` view save

Test 47

Group: 6

Verdict: ACCEPTED

input
`200 1000 3550 2640 3791 4248 4257 4504 ...` view save

correct output
`199997` view save

user output
`199997` view save

Test 48

Group: 6

Verdict: ACCEPTED

input
`1000 200 198379 62425 88013 50967 49098...` view save

correct output
`89131` view save

user output
`89131` view save

NOI 2024

Thin Ice

Code

Test details

Test 1

Test 2

Test 3

Test 4

Test 5

Test 6

Test 7

Test 8

Test 9

Test 10

Test 11

Test 12

Test 13

Test 14

Test 15

Test 16

Test 17

Test 18

Test 19

Test 20

Test 21

Test 22

Test 23

Test 24

Test 25

Test 26

Test 27

Test 28

Test 29

Test 30

Test 31

Test 32

Test 33

Test 34

Test 35

Test 36

Test 37

Test 38

Test 39

Test 40

Test 41

Test 42

Test 43

Test 44

Test 45

Test 46

Test 47

Test 48

Tasks

Submissions (Veikko Heikkinen)