oj.uz

Submission #970746

# Submission time Handle Problem Language Result Execution time Memory
970746 2024-04-27T08:00:07 Z GrindMachine Split the Attractions (IOI19_split) C++17
100 / 100
 83 ms 29508 KB 
#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) (int)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:
https://codeforces.com/blog/entry/68940?#comment-532790
https://codeforces.com/blog/entry/68940?#comment-532806

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

#include "split.h"

vector<int> adj1[N], adj2[N], adj3[N];
vector<bool> vis(N);

void dfs1(int u){
    vis[u] = 1;
    trav(v,adj1[u]){
        if(vis[v]) conts;
        adj2[u].pb(v), adj2[v].pb(u);
        dfs1(v);
    }
}

vector<int> subsiz(N);

void dfs2(int u, int p){
    subsiz[u] = 1;
    trav(v,adj2[u]){
        if(v == p) conts;
        dfs2(v,u);
        subsiz[u] += subsiz[v];
    }
}

int dfs3(int u, int p){
    trav(v,adj2[u]){
        if(v == p) conts;
        if(subsiz[v] > subsiz[0]/2){
            return dfs3(v,u);
        }
    }

    return u;
}

vector<int> nodes[N];
vector<int> subr(N);

void dfs4(int u, int p, int r){
    nodes[r].pb(u);
    subr[u] = r;
    trav(v,adj2[u]){
        if(v == p) conts;
        dfs4(v,u,r);
    }
}

vector<int> ans;
int to_col;

void dfs5(int u, int p){
    if(to_col){
        ans[u] = 1;
        to_col--;
    }

    trav(v,adj2[u]){
        if(v == p) conts;
        if(ans[v] != -1) conts;
        dfs5(v,u);
    }
}

vector<int> ord;

void dfs6(int u){
    vis[u] = 1;
    ord.pb(u);
    trav(v,adj3[u]){
        if(vis[v]) conts;
        dfs6(v);
    }
}

vector<int> find_split(int n, int A, int B, int C, vector<int> U, vector<int> V) {
    rep(i,sz(U)){
        int u = U[i], v = V[i];
        adj1[u].pb(v), adj1[v].pb(u);
    }

    // find arbitrary spanning tree
    dfs1(0);

    // find centroid of spanning tree
    dfs2(0,-1);
    int c = dfs3(0,-1);
        
    // root @centroid
    // wlog, A <= B <= C
    // if any of the subtrees have size >= A, done
    // we can find a cc of size A in that subtree and this may waste at most n/2 nodes (cuz rooted @centroid)
    // B <= n/2, so we can find a cc of size B in the rest of the tree
    vector<int> subs;
    trav(v,adj2[c]){
        subs.pb(v);
        dfs4(v,c,v);
    }

    vector<pii> col_ord = {{A,0},{B,1},{C,2}};
    sort(all(col_ord));
    A = col_ord[0].ff, B = col_ord[1].ff, C = col_ord[2].ff;
    ans = vector<int>(n,-1);

    trav(v,subs){
        if(sz(nodes[v]) < A) conts;
        rep(j,A){
            ans[nodes[v][j]] = 0;
        }

        to_col = B;
        dfs5(c,-1);
        rep(i,n) if(ans[i] == -1) ans[i] = 2;

        rep(i,n) ans[i] = col_ord[ans[i]].ss+1;
        return ans;
    }

    // if no solution found, it means that all subtrees have size < A
    // consider edges that go between subtrees
    // each subtree compressed into a single node with weight = size of subtree
    // add edge between 2 nodes if the corresponding subtrees are connected by an edge
    // find a connected subgraph of the nodes with sum of weights >= A
    // found using a dfs, stop at the first time when size >= A
    // at most 2A nodes wasted after this (because all have weight < A)
    // A+B+C = n, A <= C, so 2A+B <= n
    // so we will be able to find a connected subgraph of size B in the remaining graph
    // if no connected subgraph has sum of weights >= A, then no solution exists
    rep(u,n){
        trav(v,adj1[u]){
            if(u == c or v == c) conts;
            if(subr[u] != subr[v]){
                adj3[subr[u]].pb(subr[v]);
            }
        }
    }

    fill(all(vis),0);

    trav(u,subs){
        if(vis[u]) conts;
        ord.clear();
        dfs6(u);
        int sum = 0;
        trav(v,ord) sum += sz(nodes[v]);
        if(sum < A) conts;
        sum = 0;

        trav(v,ord){
            auto &curr = nodes[v];
            rep(j,sz(curr)){
                if(sum == A) break;
                ans[curr[j]] = 0;
                sum++;
            }
        }

        assert(sum == A);

        to_col = B;
        dfs5(c,-1);
        rep(i,n) if(ans[i] == -1) ans[i] = 2;

        rep(i,n) ans[i] = col_ord[ans[i]].ss+1;
        return ans;
    }

    fill(all(ans),0);
    return ans;
}

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10588 KB ok, correct split
2 Correct 3 ms 10648 KB ok, correct split
3 Correct 2 ms 10588 KB ok, correct split
4 Correct 3 ms 10588 KB ok, correct split
5 Correct 3 ms 10588 KB ok, correct split
6 Correct 3 ms 10588 KB ok, correct split
7 Correct 57 ms 24140 KB ok, correct split
8 Correct 59 ms 22760 KB ok, correct split
9 Correct 62 ms 22860 KB ok, correct split
10 Correct 55 ms 24396 KB ok, correct split
11 Correct 58 ms 24304 KB ok, correct split

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10588 KB ok, correct split
2 Correct 3 ms 10584 KB ok, correct split
3 Correct 3 ms 10588 KB ok, correct split
4 Correct 72 ms 22828 KB ok, correct split
5 Correct 52 ms 19796 KB ok, correct split
6 Correct 56 ms 24416 KB ok, correct split
7 Correct 58 ms 22848 KB ok, correct split
8 Correct 78 ms 21600 KB ok, correct split
9 Correct 51 ms 19600 KB ok, correct split
10 Correct 52 ms 23500 KB ok, correct split
11 Correct 52 ms 23340 KB ok, correct split
12 Correct 50 ms 23496 KB ok, correct split

Subtask #3
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10588 KB ok, correct split
2 Correct 57 ms 19868 KB ok, correct split
3 Correct 21 ms 14172 KB ok, correct split
4 Correct 3 ms 10588 KB ok, correct split
5 Correct 55 ms 21588 KB ok, correct split
6 Correct 59 ms 21632 KB ok, correct split
7 Correct 53 ms 21588 KB ok, correct split
8 Correct 56 ms 21840 KB ok, correct split
9 Correct 54 ms 21592 KB ok, correct split
10 Correct 19 ms 13660 KB ok, no valid answer
11 Correct 26 ms 15192 KB ok, no valid answer
12 Correct 56 ms 21968 KB ok, no valid answer
13 Correct 65 ms 20200 KB ok, no valid answer
14 Correct 54 ms 23496 KB ok, no valid answer

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 10584 KB ok, correct split
2 Correct 3 ms 10588 KB ok, no valid answer
3 Correct 4 ms 10584 KB ok, correct split
4 Correct 3 ms 10588 KB ok, correct split
5 Correct 3 ms 10588 KB ok, correct split
6 Correct 3 ms 10588 KB ok, correct split
7 Correct 3 ms 10540 KB ok, correct split
8 Correct 3 ms 10588 KB ok, correct split
9 Correct 4 ms 10844 KB ok, correct split
10 Correct 4 ms 10844 KB ok, correct split
11 Correct 3 ms 10588 KB ok, correct split
12 Correct 4 ms 10844 KB ok, correct split
13 Correct 3 ms 10588 KB ok, correct split
14 Correct 2 ms 10588 KB ok, correct split
15 Correct 3 ms 10588 KB ok, correct split
16 Correct 3 ms 10588 KB ok, correct split
17 Correct 3 ms 10588 KB ok, correct split
18 Correct 3 ms 10588 KB ok, correct split
19 Correct 3 ms 10584 KB ok, correct split
20 Correct 3 ms 10584 KB ok, correct split
21 Correct 4 ms 10844 KB ok, correct split
22 Correct 4 ms 10844 KB ok, correct split
23 Correct 4 ms 10844 KB ok, correct split
24 Correct 4 ms 10844 KB ok, correct split
25 Correct 4 ms 10844 KB ok, correct split
26 Correct 4 ms 11100 KB ok, correct split
27 Correct 4 ms 11100 KB ok, correct split
28 Correct 5 ms 10844 KB ok, correct split
29 Correct 3 ms 10588 KB ok, correct split
30 Correct 4 ms 10844 KB ok, correct split
31 Correct 3 ms 10588 KB ok, correct split
32 Correct 3 ms 10588 KB ok, correct split
33 Correct 3 ms 10588 KB ok, correct split
34 Correct 4 ms 10844 KB ok, correct split
35 Correct 4 ms 10844 KB ok, correct split
36 Correct 4 ms 10844 KB ok, correct split
37 Correct 4 ms 10844 KB ok, correct split
38 Correct 4 ms 10844 KB ok, correct split
39 Correct 4 ms 10844 KB ok, correct split
40 Correct 4 ms 10844 KB ok, correct split
41 Correct 5 ms 10660 KB ok, correct split
42 Correct 3 ms 10588 KB ok, correct split
43 Correct 4 ms 10844 KB ok, correct split
44 Correct 4 ms 10844 KB ok, correct split
45 Correct 5 ms 10844 KB ok, correct split
46 Correct 4 ms 10744 KB ok, correct split
47 Correct 4 ms 10844 KB ok, no valid answer
48 Correct 3 ms 10844 KB ok, correct split
49 Correct 4 ms 10844 KB ok, correct split
50 Correct 3 ms 10584 KB ok, no valid answer
51 Correct 3 ms 10584 KB ok, no valid answer
52 Correct 4 ms 10844 KB ok, no valid answer
53 Correct 4 ms 10844 KB ok, no valid answer
54 Correct 4 ms 10844 KB ok, no valid answer
55 Correct 4 ms 10844 KB ok, no valid answer
56 Correct 4 ms 10840 KB ok, no valid answer

Subtask #5
36.0 / 36.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10588 KB ok, correct split
2 Correct 3 ms 10648 KB ok, correct split
3 Correct 2 ms 10588 KB ok, correct split
4 Correct 3 ms 10588 KB ok, correct split
5 Correct 3 ms 10588 KB ok, correct split
6 Correct 3 ms 10588 KB ok, correct split
7 Correct 57 ms 24140 KB ok, correct split
8 Correct 59 ms 22760 KB ok, correct split
9 Correct 62 ms 22860 KB ok, correct split
10 Correct 55 ms 24396 KB ok, correct split
11 Correct 58 ms 24304 KB ok, correct split
12 Correct 3 ms 10588 KB ok, correct split
13 Correct 3 ms 10584 KB ok, correct split
14 Correct 3 ms 10588 KB ok, correct split
15 Correct 72 ms 22828 KB ok, correct split
16 Correct 52 ms 19796 KB ok, correct split
17 Correct 56 ms 24416 KB ok, correct split
18 Correct 58 ms 22848 KB ok, correct split
19 Correct 78 ms 21600 KB ok, correct split
20 Correct 51 ms 19600 KB ok, correct split
21 Correct 52 ms 23500 KB ok, correct split
22 Correct 52 ms 23340 KB ok, correct split
23 Correct 50 ms 23496 KB ok, correct split
24 Correct 3 ms 10588 KB ok, correct split
25 Correct 57 ms 19868 KB ok, correct split
26 Correct 21 ms 14172 KB ok, correct split
27 Correct 3 ms 10588 KB ok, correct split
28 Correct 55 ms 21588 KB ok, correct split
29 Correct 59 ms 21632 KB ok, correct split
30 Correct 53 ms 21588 KB ok, correct split
31 Correct 56 ms 21840 KB ok, correct split
32 Correct 54 ms 21592 KB ok, correct split
33 Correct 19 ms 13660 KB ok, no valid answer
34 Correct 26 ms 15192 KB ok, no valid answer
35 Correct 56 ms 21968 KB ok, no valid answer
36 Correct 65 ms 20200 KB ok, no valid answer
37 Correct 54 ms 23496 KB ok, no valid answer
38 Correct 2 ms 10584 KB ok, correct split
39 Correct 3 ms 10588 KB ok, no valid answer
40 Correct 4 ms 10584 KB ok, correct split
41 Correct 3 ms 10588 KB ok, correct split
42 Correct 3 ms 10588 KB ok, correct split
43 Correct 3 ms 10588 KB ok, correct split
44 Correct 3 ms 10540 KB ok, correct split
45 Correct 3 ms 10588 KB ok, correct split
46 Correct 4 ms 10844 KB ok, correct split
47 Correct 4 ms 10844 KB ok, correct split
48 Correct 3 ms 10588 KB ok, correct split
49 Correct 4 ms 10844 KB ok, correct split
50 Correct 3 ms 10588 KB ok, correct split
51 Correct 2 ms 10588 KB ok, correct split
52 Correct 3 ms 10588 KB ok, correct split
53 Correct 3 ms 10588 KB ok, correct split
54 Correct 3 ms 10588 KB ok, correct split
55 Correct 3 ms 10588 KB ok, correct split
56 Correct 3 ms 10584 KB ok, correct split
57 Correct 3 ms 10584 KB ok, correct split
58 Correct 4 ms 10844 KB ok, correct split
59 Correct 4 ms 10844 KB ok, correct split
60 Correct 4 ms 10844 KB ok, correct split
61 Correct 4 ms 10844 KB ok, correct split
62 Correct 4 ms 10844 KB ok, correct split
63 Correct 4 ms 11100 KB ok, correct split
64 Correct 4 ms 11100 KB ok, correct split
65 Correct 5 ms 10844 KB ok, correct split
66 Correct 3 ms 10588 KB ok, correct split
67 Correct 4 ms 10844 KB ok, correct split
68 Correct 3 ms 10588 KB ok, correct split
69 Correct 3 ms 10588 KB ok, correct split
70 Correct 3 ms 10588 KB ok, correct split
71 Correct 4 ms 10844 KB ok, correct split
72 Correct 4 ms 10844 KB ok, correct split
73 Correct 4 ms 10844 KB ok, correct split
74 Correct 4 ms 10844 KB ok, correct split
75 Correct 4 ms 10844 KB ok, correct split
76 Correct 4 ms 10844 KB ok, correct split
77 Correct 4 ms 10844 KB ok, correct split
78 Correct 5 ms 10660 KB ok, correct split
79 Correct 3 ms 10588 KB ok, correct split
80 Correct 4 ms 10844 KB ok, correct split
81 Correct 4 ms 10844 KB ok, correct split
82 Correct 5 ms 10844 KB ok, correct split
83 Correct 4 ms 10744 KB ok, correct split
84 Correct 4 ms 10844 KB ok, no valid answer
85 Correct 3 ms 10844 KB ok, correct split
86 Correct 4 ms 10844 KB ok, correct split
87 Correct 3 ms 10584 KB ok, no valid answer
88 Correct 3 ms 10584 KB ok, no valid answer
89 Correct 4 ms 10844 KB ok, no valid answer
90 Correct 4 ms 10844 KB ok, no valid answer
91 Correct 4 ms 10844 KB ok, no valid answer
92 Correct 4 ms 10844 KB ok, no valid answer
93 Correct 4 ms 10840 KB ok, no valid answer
94 Correct 65 ms 21584 KB ok, correct split
95 Correct 80 ms 24740 KB ok, correct split
96 Correct 74 ms 23632 KB ok, correct split
97 Correct 22 ms 14172 KB ok, correct split
98 Correct 23 ms 14428 KB ok, correct split
99 Correct 31 ms 15452 KB ok, correct split
100 Correct 76 ms 22092 KB ok, correct split
101 Correct 71 ms 21332 KB ok, correct split
102 Correct 69 ms 21960 KB ok, correct split
103 Correct 66 ms 21964 KB ok, correct split
104 Correct 64 ms 22536 KB ok, correct split
105 Correct 36 ms 16676 KB ok, correct split
106 Correct 83 ms 29508 KB ok, correct split
107 Correct 55 ms 19936 KB ok, correct split
108 Correct 52 ms 19804 KB ok, correct split
109 Correct 77 ms 21588 KB ok, correct split
110 Correct 78 ms 22516 KB ok, correct split
111 Correct 76 ms 22352 KB ok, correct split
112 Correct 78 ms 22860 KB ok, correct split
113 Correct 82 ms 22864 KB ok, correct split
114 Correct 10 ms 11868 KB ok, correct split
115 Correct 9 ms 11912 KB ok, correct split
116 Correct 76 ms 22604 KB ok, correct split
117 Correct 74 ms 22368 KB ok, correct split
118 Correct 55 ms 19916 KB ok, correct split
119 Correct 52 ms 19652 KB ok, correct split
120 Correct 56 ms 22152 KB ok, correct split
121 Correct 53 ms 19792 KB ok, no valid answer
122 Correct 54 ms 20564 KB ok, no valid answer
123 Correct 76 ms 22044 KB ok, no valid answer
124 Correct 79 ms 22100 KB ok, no valid answer
125 Correct 64 ms 22984 KB ok, no valid answer
126 Correct 53 ms 22220 KB ok, no valid answer
127 Correct 65 ms 22128 KB ok, no valid answer