oj.uz

Submission #916874

# Submission time Handle Problem Language Result Execution time Memory
916874 2024-01-26T16:25:59 Z GrindMachine Unique Cities (JOI19_ho_t5) C++17
100 / 100
 587 ms 100564 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:
edi
https://codeforces.com/blog/entry/65042?#comment-491880

key idea:
for a node u, let d = arbitrary node with farthest dis from u
all good nodes lie on the path from u to d

proof:
consider the tree rooted at the path (u,d)
anybody in a branching subtree cant be good
why? because there exists another node on the path (u,d) with the same distance
if there exists a good guy in the subtree, then it contradicts the definition of d (d should have been somewhere in the subtree)

(s,t) = endpoints of diameter
farthest node from u = s or t

run dfs from s and t, calculate answers

when we go into a subtree, find the deepest in the other subtree and remove the respective nodes from consideration 
(look at the pictures in the edi for better understanding)

in order to find #of good nodes, maintain a lazy segtree with range add updates and min, no.of min queries
when going into a subtree, add 1 to all bad nodes that are caused by the deepest in the other subtree
we need #of 0s
we know that min_val >= 0, so just get min and #of min

how to count #of distinct guys?

similar idea to ceoi harbingers
maintain a stack of all the "unique nodes" (i.e nodes with colors that are not present before its position in the stack) when doing the dfs
when we want to add a new node, add him only if the color is not present in the stack
keep an additional variable called "siz" which maintains the size of the active part of the stack
when we want to remove multiple nodes, just change the value of siz
rollback the changes after dfs

*/

const int MOD = 1e9 + 7;
const int N = 2e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

vector<ll> adj[N];
vector<ll> a(N);
pll diam = {-1,-1};

void dfs1(ll u, ll p, ll d){
    pll px = {d,u};
    amax(diam,px);
    trav(v,adj[u]){
        if(v == p) conts;
        dfs1(v,u,d+1);
    }
}

ll dis[N][2];
ll deepest[N][2];

void dfs2(ll u, ll p, ll t){
    trav(v,adj[u]){
        if(v == p) conts;
        dis[v][t] = dis[u][t]+1;
        dfs2(v,u,t);
        amax(deepest[u][t],deepest[v][t]+1);
    }
}

vector<ll> ans(N);
vector<ll> mx_without(N);
vector<ll> first_occ(N,inf2);
vector<pll> active(N);
ll siz = 0;

void dfs3(ll u, ll p, ll d, ll t){
    ll mx = deepest[u][t];
    ll cnt = upper_bound(active.begin(),active.begin()+siz,make_pair(d-mx,-1ll))-active.begin();
    if(dis[u][t] >= dis[u][t^1]){
        ans[u] = cnt;
    }

    mx = 0;
 
    trav(v,adj[u]){
        if(v == p) conts;
        mx_without[v] = mx;
        amax(mx,deepest[v][t]+1);
    }
 
    mx = 0;
    reverse(all(adj[u]));
 
    trav(v,adj[u]){
        if(v == p) conts;
        amax(mx_without[v],mx);
        amax(mx,deepest[v][t]+1);
    }
 
    reverse(all(adj[u]));
    
    trav(v,adj[u]){
        if(v == p) conts;

        vector<array<ll,4>> history;

        mx = mx_without[v];
        ll new_siz = upper_bound(active.begin(),active.begin()+siz,make_pair(d-mx,-1ll))-active.begin();
        ll old_siz = siz;
        history.pb({3,siz,-1,-1});
        siz = new_siz;

        ll x = a[u];

        if(first_occ[x] >= siz){
            history.pb({1,siz,active[siz].ff,active[siz].ss});
            history.pb({2,x,first_occ[x],-1});
            history.pb({3,siz,-1,-1});

            ll w = active[siz].ss;
            if(first_occ[a[w]] == siz){            
                history.pb({2,a[w],first_occ[a[w]],-1});
                first_occ[a[w]] = inf2;
            }

            active[siz] = {d,u};
            first_occ[x] = siz;
            siz++;
        }

        dfs3(v,u,d+1,t);

        reverse(all(history));

        trav(ar,history){
            auto [t,ind,val1,val2] = ar;
            if(t == 1){
                active[ind] = {val1,val2};
            }
            else if(t == 2){
                first_occ[ind] = val1;
            }
            else{
                siz = ind;
            }
        }
    }
}

void solve(int test_case)
{
    ll n,m; cin >> n >> m;
    rep1(i,n-1){
        ll u,v; cin >> u >> v;
        adj[u].pb(v), adj[v].pb(u);
    }
    rep1(i,n) cin >> a[i];

    dfs1(1,-1,0);
    ll s = diam.ss;
    diam = {-1,-1};
    dfs1(s,-1,0);
    ll t = diam.ss;

    dfs2(s,-1,0);
    dfs2(t,-1,1);

    dfs3(s,-1,0,0);
    dfs3(t,-1,0,1);

    rep1(i,n){
        cout << ans[i] << endl;
    }
}

int main()
{
    fastio;

    int t = 1;
    // cin >> t;

    rep1(i, t) {
        solve(i);
    }

    return 0;
}

Compilation message

joi2019_ho_t5.cpp: In function 'void dfs3(ll, ll, ll, ll)':
joi2019_ho_t5.cpp:158:12: warning: unused variable 'old_siz' [-Wunused-variable]
  158 |         ll old_siz = siz;
      |            ^~~~~~~

Subtask #1
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 16472 KB Output is correct
2 Correct 7 ms 16732 KB Output is correct
3 Correct 6 ms 16844 KB Output is correct
4 Correct 7 ms 16988 KB Output is correct
5 Correct 7 ms 16732 KB Output is correct
6 Correct 7 ms 16988 KB Output is correct
7 Correct 7 ms 16732 KB Output is correct
8 Correct 7 ms 16476 KB Output is correct
9 Correct 8 ms 16732 KB Output is correct
10 Correct 7 ms 16732 KB Output is correct
11 Correct 7 ms 16732 KB Output is correct
12 Correct 7 ms 16476 KB Output is correct
13 Correct 7 ms 16988 KB Output is correct
14 Correct 7 ms 16728 KB Output is correct
15 Correct 7 ms 16732 KB Output is correct
16 Correct 7 ms 16472 KB Output is correct
17 Correct 8 ms 17032 KB Output is correct
18 Correct 7 ms 16732 KB Output is correct
19 Correct 8 ms 16732 KB Output is correct
20 Correct 8 ms 17340 KB Output is correct
21 Correct 7 ms 16988 KB Output is correct
22 Correct 7 ms 16476 KB Output is correct
23 Correct 7 ms 16808 KB Output is correct
24 Correct 7 ms 16732 KB Output is correct
25 Correct 7 ms 16984 KB Output is correct
26 Correct 7 ms 16476 KB Output is correct
27 Correct 7 ms 17240 KB Output is correct
28 Correct 7 ms 16988 KB Output is correct
29 Correct 8 ms 16988 KB Output is correct
30 Correct 7 ms 16564 KB Output is correct
31 Correct 7 ms 16988 KB Output is correct
32 Correct 7 ms 16988 KB Output is correct

Subtask #2
32.0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 114 ms 24056 KB Output is correct
2 Correct 188 ms 53872 KB Output is correct
3 Correct 26 ms 22104 KB Output is correct
4 Correct 265 ms 28448 KB Output is correct
5 Correct 420 ms 80552 KB Output is correct
6 Correct 419 ms 54212 KB Output is correct
7 Correct 262 ms 28356 KB Output is correct
8 Correct 321 ms 33592 KB Output is correct
9 Correct 305 ms 32324 KB Output is correct
10 Correct 323 ms 31976 KB Output is correct
11 Correct 189 ms 28812 KB Output is correct
12 Correct 407 ms 61520 KB Output is correct
13 Correct 356 ms 53964 KB Output is correct
14 Correct 382 ms 52264 KB Output is correct
15 Correct 141 ms 26584 KB Output is correct
16 Correct 350 ms 63432 KB Output is correct
17 Correct 447 ms 54480 KB Output is correct

Subtask #3
32.0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 228 ms 26964 KB Output is correct
2 Correct 584 ms 96820 KB Output is correct
3 Correct 40 ms 25228 KB Output is correct
4 Correct 370 ms 28672 KB Output is correct
5 Correct 573 ms 100564 KB Output is correct
6 Correct 552 ms 70368 KB Output is correct
7 Correct 347 ms 28368 KB Output is correct
8 Correct 439 ms 47444 KB Output is correct
9 Correct 408 ms 40792 KB Output is correct
10 Correct 452 ms 35828 KB Output is correct
11 Correct 324 ms 28432 KB Output is correct
12 Correct 587 ms 90716 KB Output is correct
13 Correct 470 ms 63304 KB Output is correct
14 Correct 515 ms 65740 KB Output is correct
15 Correct 151 ms 27016 KB Output is correct
16 Correct 457 ms 75460 KB Output is correct
17 Correct 499 ms 70348 KB Output is correct

Subtask #4
32.0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 16472 KB Output is correct
2 Correct 7 ms 16732 KB Output is correct
3 Correct 6 ms 16844 KB Output is correct
4 Correct 7 ms 16988 KB Output is correct
5 Correct 7 ms 16732 KB Output is correct
6 Correct 7 ms 16988 KB Output is correct
7 Correct 7 ms 16732 KB Output is correct
8 Correct 7 ms 16476 KB Output is correct
9 Correct 8 ms 16732 KB Output is correct
10 Correct 7 ms 16732 KB Output is correct
11 Correct 7 ms 16732 KB Output is correct
12 Correct 7 ms 16476 KB Output is correct
13 Correct 7 ms 16988 KB Output is correct
14 Correct 7 ms 16728 KB Output is correct
15 Correct 7 ms 16732 KB Output is correct
16 Correct 7 ms 16472 KB Output is correct
17 Correct 8 ms 17032 KB Output is correct
18 Correct 7 ms 16732 KB Output is correct
19 Correct 8 ms 16732 KB Output is correct
20 Correct 8 ms 17340 KB Output is correct
21 Correct 7 ms 16988 KB Output is correct
22 Correct 7 ms 16476 KB Output is correct
23 Correct 7 ms 16808 KB Output is correct
24 Correct 7 ms 16732 KB Output is correct
25 Correct 7 ms 16984 KB Output is correct
26 Correct 7 ms 16476 KB Output is correct
27 Correct 7 ms 17240 KB Output is correct
28 Correct 7 ms 16988 KB Output is correct
29 Correct 8 ms 16988 KB Output is correct
30 Correct 7 ms 16564 KB Output is correct
31 Correct 7 ms 16988 KB Output is correct
32 Correct 7 ms 16988 KB Output is correct
33 Correct 114 ms 24056 KB Output is correct
34 Correct 188 ms 53872 KB Output is correct
35 Correct 26 ms 22104 KB Output is correct
36 Correct 265 ms 28448 KB Output is correct
37 Correct 420 ms 80552 KB Output is correct
38 Correct 419 ms 54212 KB Output is correct
39 Correct 262 ms 28356 KB Output is correct
40 Correct 321 ms 33592 KB Output is correct
41 Correct 305 ms 32324 KB Output is correct
42 Correct 323 ms 31976 KB Output is correct
43 Correct 189 ms 28812 KB Output is correct
44 Correct 407 ms 61520 KB Output is correct
45 Correct 356 ms 53964 KB Output is correct
46 Correct 382 ms 52264 KB Output is correct
47 Correct 141 ms 26584 KB Output is correct
48 Correct 350 ms 63432 KB Output is correct
49 Correct 447 ms 54480 KB Output is correct
50 Correct 228 ms 26964 KB Output is correct
51 Correct 584 ms 96820 KB Output is correct
52 Correct 40 ms 25228 KB Output is correct
53 Correct 370 ms 28672 KB Output is correct
54 Correct 573 ms 100564 KB Output is correct
55 Correct 552 ms 70368 KB Output is correct
56 Correct 347 ms 28368 KB Output is correct
57 Correct 439 ms 47444 KB Output is correct
58 Correct 408 ms 40792 KB Output is correct
59 Correct 452 ms 35828 KB Output is correct
60 Correct 324 ms 28432 KB Output is correct
61 Correct 587 ms 90716 KB Output is correct
62 Correct 470 ms 63304 KB Output is correct
63 Correct 515 ms 65740 KB Output is correct
64 Correct 151 ms 27016 KB Output is correct
65 Correct 457 ms 75460 KB Output is correct
66 Correct 499 ms 70348 KB Output is correct
67 Correct 27 ms 18512 KB Output is correct
68 Correct 144 ms 47860 KB Output is correct
69 Correct 239 ms 45648 KB Output is correct
70 Correct 319 ms 28496 KB Output is correct
71 Correct 432 ms 80976 KB Output is correct
72 Correct 396 ms 54120 KB Output is correct
73 Correct 311 ms 28364 KB Output is correct
74 Correct 323 ms 38736 KB Output is correct
75 Correct 334 ms 33316 KB Output is correct
76 Correct 349 ms 32532 KB Output is correct
77 Correct 275 ms 28476 KB Output is correct
78 Correct 474 ms 67072 KB Output is correct
79 Correct 386 ms 59980 KB Output is correct
80 Correct 384 ms 49356 KB Output is correct
81 Correct 159 ms 26580 KB Output is correct
82 Correct 353 ms 63340 KB Output is correct
83 Correct 366 ms 54404 KB Output is correct
84 Correct 309 ms 28600 KB Output is correct
85 Correct 466 ms 81084 KB Output is correct
86 Correct 397 ms 54544 KB Output is correct
87 Correct 299 ms 28364 KB Output is correct
88 Correct 341 ms 39756 KB Output is correct
89 Correct 348 ms 36176 KB Output is correct
90 Correct 342 ms 34644 KB Output is correct
91 Correct 250 ms 28356 KB Output is correct
92 Correct 420 ms 79188 KB Output is correct
93 Correct 362 ms 46536 KB Output is correct
94 Correct 364 ms 42380 KB Output is correct
95 Correct 139 ms 25768 KB Output is correct
96 Correct 369 ms 63604 KB Output is correct
97 Correct 361 ms 54672 KB Output is correct
98 Correct 350 ms 28496 KB Output is correct
99 Correct 445 ms 81488 KB Output is correct
100 Correct 522 ms 66788 KB Output is correct
101 Correct 313 ms 28424 KB Output is correct
102 Correct 404 ms 43160 KB Output is correct
103 Correct 365 ms 37472 KB Output is correct
104 Correct 366 ms 36072 KB Output is correct
105 Correct 267 ms 28616 KB Output is correct
106 Correct 539 ms 71232 KB Output is correct
107 Correct 406 ms 61040 KB Output is correct
108 Correct 536 ms 54748 KB Output is correct
109 Correct 153 ms 25792 KB Output is correct
110 Correct 445 ms 66664 KB Output is correct
111 Correct 512 ms 65488 KB Output is correct