Submission #917162

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
917162	2024-01-27T10:44:49 Z	GrindMachine	Cats or Dogs (JOI18_catdog)	C++17	100 / 100	670 ms	21564 KB

catdog

#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://oj.uz/submission/374896

tree dp for 38 points:
r[u] = sum(min(r[v],b[v]+1))
b[u] = sum(min(r[v]+1,b[v]))

key idea:
when a node is changed, only the dp values of its parents are affected
only update parents
=> hld

if the problem was on a line, we could use a segtree
each node [l,r] contains dp[x][y], which denotes the min cost to achieve comp[l] = x and comp[r] = y
can be merged easily

how to extend this idea to a tree?

each node belongs to exactly 1 chain in the hld
when processing a chain, only dp values in the chain will change
some nodes on the chain may have children that belong to other chains
for such children, their values wont change, so their contribution to dp[u][0/1] is fixed
because these values dont change, we can put them in the segtree leaf that denotes u
i.e for the segtree leaf that denotes u,
dp[0][0] = sum(min(r[v],b[v]+1)), v doesnt belong to the same chain as u
dp[1][1] = sum(min(r[v]+1,b[v])), v doesnt belong to the same chain as u
dp[0][1] = dp[1][0] = inf (range only contains 1 node, so starting comp = ending comp)

with all these values in the segtree, find the value at the root of the chain
now when we move up, we move to another chain
so we have to update the new dp values of the parent of the current chain (which may or may not be the root of the new chain)
tnis can be done by adding/subtracting some value from the dp values of the parent and then doing a point update on the segtree
repeat the same process for all chains
at the end of the process, we would have updated the dp chain that contains the root of the tree (which is 1)
when we want to get the answer, just find the dp of the chain that contains the root and return the min value of dp[x][y]

*/

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

template<typename T>
struct segtree {
    // https://codeforces.com/blog/entry/18051

    /*=======================================================*/

    struct data {
        array<array<int,2>,2> dp;
        bool active;

        data(){
            rep(i,2){
                rep(j,2){
                    dp[i][j] = inf1;
                }
            }
            active = false;
        }
    };

    data neutral = data();

    data merge(data &left, data &right) {
        if(!left.active and !right.active) return left;
        if(!right.active) return left;
        if(!left.active) return right;
        
        data curr;
        curr.active = true;

        rep(i,2){
            rep(j,2){
                rep(k,2){
                    rep(l,2){
                        amin(curr.dp[i][l],left.dp[i][j]+right.dp[k][l]+(j!=k));
                    }
                }
            }
        }

        return curr;
    }

    void create(int i, T v) {

    }

    void modify(int i, T v) {
        tr[i] = neutral;
        tr[i].dp[0][0] = v.ff;
        tr[i].dp[1][1] = v.ss;
        tr[i].active = true;
    }

    /*=======================================================*/

    int n;
    vector<data> tr;

    segtree() {

    }

    segtree(int siz) {
        init(siz);
    }

    void init(int siz) {
        n = siz;
        tr.assign(2 * n, neutral);
    }

    void build(vector<T> &a, int siz) {
        rep(i, siz) create(i + n, a[i]);
        rev(i, n - 1, 1) tr[i] = merge(tr[i << 1], tr[i << 1 | 1]);
    }

    void pupd(int i, T v) {
        modify(i + n, v);
        for (i = (i + n) >> 1; i; i >>= 1) tr[i] = merge(tr[i << 1], tr[i << 1 | 1]);
    }

    data query(int l, int r) {
        data resl = neutral, resr = neutral;

        for (l += n, r += n; l <= r; l >>= 1, r >>= 1) {
            if (l & 1) resl = merge(resl, tr[l++]);
            if (!(r & 1)) resr = merge(tr[r--], resr);
        }

        return merge(resl, resr);
    }
};

vector<int> adj[N];
vector<int> a(N); // 0 = none, 1 = cat, 2 = dog
vector<int> subsiz(N);
vector<int> depth(N), par(N);

void dfs1(int u, int p){
    subsiz[u] = 1;
    if(p != -1) par[u] = p;
    trav(v,adj[u]){
        if(v == p) conts;
        depth[v] = depth[u]+1;
        dfs1(v,u);
        subsiz[u] += subsiz[v];
    }
}

vector<int> pos(N), head(N), chain_siz(N);
int timer = 1;

void dfs2(int u, int p, int h){
    pos[u] = timer++;
    head[u] = h;
    chain_siz[h]++;

    pii mx = {-inf1,-1};
    trav(v,adj[u]){
        if(v == p) conts;
        pii px = {subsiz[v],v};
        amax(mx,px);
    }

    int heavy = mx.ss;
    if(heavy != -1){
        dfs2(heavy,u,h);
    }

    trav(v,adj[u]){
        if(v == p or v == heavy) conts;
        dfs2(v,u,v);
    }
}

segtree<pii> st;

void initialize(int n, std::vector<int> A, std::vector<int> B) {
    rep(i,n-1){
        int u = A[i], v = B[i];
        adj[u].pb(v), adj[v].pb(u);
    }

    dfs1(1,-1);
    dfs2(1,-1,1);
    st = segtree<pii>(n+5);
    rep1(i,n) st.pupd(i,{0,0});
}

vector<int> sum1(N), sum2(N);

int get_ans(){
    auto dp = st.query(pos[1],pos[1]+chain_siz[1]-1).dp;

    int ans = inf1;

    rep(i,2){
        rep(j,2){
            amin(ans,dp[i][j]);
        }
    }

    return ans;
}

void rem(int u){
    while(u){
        if(u == head[u]){
            auto dp = st.query(pos[u],pos[u]+chain_siz[u]-1).dp;
            int cat = min(dp[0][0],dp[0][1]);
            int dog = min(dp[1][0],dp[1][1]);
            sum1[par[u]] -= min(cat,dog+1);
            sum2[par[u]] -= min(cat+1,dog);
            u = par[u];
        }
        else{
            u = head[u];
        }
    }
}

void add(int u){
    while(u){
        {
            pii px = {sum1[u],sum2[u]};

            if(a[u] == 1){
                px.ss = inf1;
            }
            else if(a[u] == 2){
                px.ff = inf1;
            }

            st.pupd(pos[u],px);
        }

        if(u == head[u]){
            auto dp = st.query(pos[u],pos[u]+chain_siz[u]-1).dp;
            int cat = min(dp[0][0],dp[0][1]);
            int dog = min(dp[1][0],dp[1][1]);
            sum1[par[u]] += min(cat,dog+1);
            sum2[par[u]] += min(cat+1,dog);
            u = par[u];
        }
        else{
            u = head[u];
        }
    }
}

void change_state(int u, int val){
    rem(u);
    a[u] = val;
    add(u);
}
 
int cat(int v) {
    change_state(v,1);
    return get_ans();
}
 
int dog(int v) {
    change_state(v,2);
    return get_ans();
}
 
int neighbor(int v) {
    change_state(v,0);
    return get_ans();
}

Subtask #1
8.0 / 8.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	3 ms	6236 KB	Output is correct
2	Correct	3 ms	6236 KB	Output is correct
3	Correct	2 ms	6236 KB	Output is correct
4	Correct	2 ms	6236 KB	Output is correct
5	Correct	2 ms	6236 KB	Output is correct
6	Correct	3 ms	6236 KB	Output is correct
7	Correct	2 ms	6256 KB	Output is correct
8	Correct	3 ms	6236 KB	Output is correct
9	Correct	2 ms	6236 KB	Output is correct
10	Correct	2 ms	6236 KB	Output is correct
11	Correct	3 ms	6236 KB	Output is correct
12	Correct	3 ms	6236 KB	Output is correct
13	Correct	2 ms	6236 KB	Output is correct
14	Correct	3 ms	6236 KB	Output is correct
15	Correct	3 ms	6236 KB	Output is correct
16	Correct	2 ms	6236 KB	Output is correct

Subtask #2
30.0 / 30.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	3 ms	6236 KB	Output is correct
2	Correct	3 ms	6236 KB	Output is correct
3	Correct	2 ms	6236 KB	Output is correct
4	Correct	2 ms	6236 KB	Output is correct
5	Correct	2 ms	6236 KB	Output is correct
6	Correct	3 ms	6236 KB	Output is correct
7	Correct	2 ms	6256 KB	Output is correct
8	Correct	3 ms	6236 KB	Output is correct
9	Correct	2 ms	6236 KB	Output is correct
10	Correct	2 ms	6236 KB	Output is correct
11	Correct	3 ms	6236 KB	Output is correct
12	Correct	3 ms	6236 KB	Output is correct
13	Correct	2 ms	6236 KB	Output is correct
14	Correct	3 ms	6236 KB	Output is correct
15	Correct	3 ms	6236 KB	Output is correct
16	Correct	2 ms	6236 KB	Output is correct
17	Correct	5 ms	6236 KB	Output is correct
18	Correct	4 ms	6236 KB	Output is correct
19	Correct	3 ms	6236 KB	Output is correct
20	Correct	3 ms	6236 KB	Output is correct
21	Correct	3 ms	6236 KB	Output is correct
22	Correct	3 ms	6236 KB	Output is correct
23	Correct	6 ms	6236 KB	Output is correct
24	Correct	4 ms	6236 KB	Output is correct
25	Correct	4 ms	6312 KB	Output is correct
26	Correct	3 ms	6240 KB	Output is correct
27	Correct	3 ms	6236 KB	Output is correct
28	Correct	3 ms	6240 KB	Output is correct
29	Correct	4 ms	6244 KB	Output is correct
30	Correct	3 ms	6236 KB	Output is correct
31	Correct	3 ms	6244 KB	Output is correct
32	Correct	4 ms	6236 KB	Output is correct

Subtask #3
62.0 / 62.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	3 ms	6236 KB	Output is correct
2	Correct	3 ms	6236 KB	Output is correct
3	Correct	2 ms	6236 KB	Output is correct
4	Correct	2 ms	6236 KB	Output is correct
5	Correct	2 ms	6236 KB	Output is correct
6	Correct	3 ms	6236 KB	Output is correct
7	Correct	2 ms	6256 KB	Output is correct
8	Correct	3 ms	6236 KB	Output is correct
9	Correct	2 ms	6236 KB	Output is correct
10	Correct	2 ms	6236 KB	Output is correct
11	Correct	3 ms	6236 KB	Output is correct
12	Correct	3 ms	6236 KB	Output is correct
13	Correct	2 ms	6236 KB	Output is correct
14	Correct	3 ms	6236 KB	Output is correct
15	Correct	3 ms	6236 KB	Output is correct
16	Correct	2 ms	6236 KB	Output is correct
17	Correct	5 ms	6236 KB	Output is correct
18	Correct	4 ms	6236 KB	Output is correct
19	Correct	3 ms	6236 KB	Output is correct
20	Correct	3 ms	6236 KB	Output is correct
21	Correct	3 ms	6236 KB	Output is correct
22	Correct	3 ms	6236 KB	Output is correct
23	Correct	6 ms	6236 KB	Output is correct
24	Correct	4 ms	6236 KB	Output is correct
25	Correct	4 ms	6312 KB	Output is correct
26	Correct	3 ms	6240 KB	Output is correct
27	Correct	3 ms	6236 KB	Output is correct
28	Correct	3 ms	6240 KB	Output is correct
29	Correct	4 ms	6244 KB	Output is correct
30	Correct	3 ms	6236 KB	Output is correct
31	Correct	3 ms	6244 KB	Output is correct
32	Correct	4 ms	6236 KB	Output is correct
33	Correct	363 ms	11396 KB	Output is correct
34	Correct	122 ms	12068 KB	Output is correct
35	Correct	339 ms	10148 KB	Output is correct
36	Correct	593 ms	14980 KB	Output is correct
37	Correct	21 ms	9052 KB	Output is correct
38	Correct	666 ms	17156 KB	Output is correct
39	Correct	670 ms	17164 KB	Output is correct
40	Correct	608 ms	17172 KB	Output is correct
41	Correct	616 ms	17164 KB	Output is correct
42	Correct	564 ms	17216 KB	Output is correct
43	Correct	637 ms	17164 KB	Output is correct
44	Correct	584 ms	17168 KB	Output is correct
45	Correct	598 ms	17192 KB	Output is correct
46	Correct	612 ms	17216 KB	Output is correct
47	Correct	643 ms	17180 KB	Output is correct
48	Correct	173 ms	14252 KB	Output is correct
49	Correct	177 ms	15940 KB	Output is correct
50	Correct	57 ms	8600 KB	Output is correct
51	Correct	64 ms	10452 KB	Output is correct
52	Correct	27 ms	8280 KB	Output is correct
53	Correct	316 ms	16212 KB	Output is correct
54	Correct	201 ms	10584 KB	Output is correct
55	Correct	521 ms	14120 KB	Output is correct
56	Correct	298 ms	11560 KB	Output is correct
57	Correct	410 ms	15516 KB	Output is correct
58	Correct	39 ms	10708 KB	Output is correct
59	Correct	75 ms	9960 KB	Output is correct
60	Correct	155 ms	15060 KB	Output is correct
61	Correct	174 ms	15324 KB	Output is correct
62	Correct	112 ms	13460 KB	Output is correct
63	Correct	75 ms	12996 KB	Output is correct
64	Correct	76 ms	14584 KB	Output is correct
65	Correct	115 ms	18936 KB	Output is correct
66	Correct	109 ms	9820 KB	Output is correct
67	Correct	94 ms	15444 KB	Output is correct
68	Correct	242 ms	19380 KB	Output is correct
69	Correct	49 ms	7764 KB	Output is correct
70	Correct	12 ms	6488 KB	Output is correct
71	Correct	97 ms	12152 KB	Output is correct
72	Correct	133 ms	16980 KB	Output is correct
73	Correct	305 ms	21460 KB	Output is correct
74	Correct	321 ms	19284 KB	Output is correct
75	Correct	256 ms	21564 KB	Output is correct
76	Correct	227 ms	20684 KB	Output is correct
77	Correct	317 ms	19696 KB	Output is correct

Submission #917162

Compilation message

Subtask #1 8.0 / 8.0

Subtask #2 30.0 / 30.0

Subtask #3 62.0 / 62.0

Subtask #1
8.0 / 8.0

Subtask #2
30.0 / 30.0

Subtask #3
62.0 / 62.0