Submission #917157

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
917157	2024-01-27T10:41:40 Z	GrindMachine	Cats or Dogs (JOI18_catdog)	C++17	100 / 100	563 ms	22352 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	2 ms	6236 KB	Output is correct
2	Correct	2 ms	6336 KB	Output is correct
3	Correct	2 ms	6236 KB	Output is correct
4	Correct	2 ms	6488 KB	Output is correct
5	Correct	3 ms	6236 KB	Output is correct
6	Correct	2 ms	6236 KB	Output is correct
7	Correct	3 ms	6236 KB	Output is correct
8	Correct	2 ms	6236 KB	Output is correct
9	Correct	3 ms	6232 KB	Output is correct
10	Correct	2 ms	6236 KB	Output is correct
11	Correct	2 ms	6232 KB	Output is correct
12	Correct	2 ms	6232 KB	Output is correct
13	Correct	3 ms	6232 KB	Output is correct
14	Correct	2 ms	6236 KB	Output is correct
15	Correct	2 ms	6236 KB	Output is correct
16	Correct	2 ms	6328 KB	Output is correct

Subtask #2
30.0 / 30.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	6236 KB	Output is correct
2	Correct	2 ms	6336 KB	Output is correct
3	Correct	2 ms	6236 KB	Output is correct
4	Correct	2 ms	6488 KB	Output is correct
5	Correct	3 ms	6236 KB	Output is correct
6	Correct	2 ms	6236 KB	Output is correct
7	Correct	3 ms	6236 KB	Output is correct
8	Correct	2 ms	6236 KB	Output is correct
9	Correct	3 ms	6232 KB	Output is correct
10	Correct	2 ms	6236 KB	Output is correct
11	Correct	2 ms	6232 KB	Output is correct
12	Correct	2 ms	6232 KB	Output is correct
13	Correct	3 ms	6232 KB	Output is correct
14	Correct	2 ms	6236 KB	Output is correct
15	Correct	2 ms	6236 KB	Output is correct
16	Correct	2 ms	6328 KB	Output is correct
17	Correct	4 ms	6236 KB	Output is correct
18	Correct	4 ms	6232 KB	Output is correct
19	Correct	3 ms	6236 KB	Output is correct
20	Correct	3 ms	6332 KB	Output is correct
21	Correct	3 ms	6236 KB	Output is correct
22	Correct	3 ms	6232 KB	Output is correct
23	Correct	4 ms	6232 KB	Output is correct
24	Correct	4 ms	6236 KB	Output is correct
25	Correct	4 ms	6340 KB	Output is correct
26	Correct	3 ms	6236 KB	Output is correct
27	Correct	3 ms	6236 KB	Output is correct
28	Correct	3 ms	6236 KB	Output is correct
29	Correct	4 ms	6236 KB	Output is correct
30	Correct	3 ms	6644 KB	Output is correct
31	Correct	3 ms	6236 KB	Output is correct
32	Correct	3 ms	6236 KB	Output is correct

Subtask #3
62.0 / 62.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	6236 KB	Output is correct
2	Correct	2 ms	6336 KB	Output is correct
3	Correct	2 ms	6236 KB	Output is correct
4	Correct	2 ms	6488 KB	Output is correct
5	Correct	3 ms	6236 KB	Output is correct
6	Correct	2 ms	6236 KB	Output is correct
7	Correct	3 ms	6236 KB	Output is correct
8	Correct	2 ms	6236 KB	Output is correct
9	Correct	3 ms	6232 KB	Output is correct
10	Correct	2 ms	6236 KB	Output is correct
11	Correct	2 ms	6232 KB	Output is correct
12	Correct	2 ms	6232 KB	Output is correct
13	Correct	3 ms	6232 KB	Output is correct
14	Correct	2 ms	6236 KB	Output is correct
15	Correct	2 ms	6236 KB	Output is correct
16	Correct	2 ms	6328 KB	Output is correct
17	Correct	4 ms	6236 KB	Output is correct
18	Correct	4 ms	6232 KB	Output is correct
19	Correct	3 ms	6236 KB	Output is correct
20	Correct	3 ms	6332 KB	Output is correct
21	Correct	3 ms	6236 KB	Output is correct
22	Correct	3 ms	6232 KB	Output is correct
23	Correct	4 ms	6232 KB	Output is correct
24	Correct	4 ms	6236 KB	Output is correct
25	Correct	4 ms	6340 KB	Output is correct
26	Correct	3 ms	6236 KB	Output is correct
27	Correct	3 ms	6236 KB	Output is correct
28	Correct	3 ms	6236 KB	Output is correct
29	Correct	4 ms	6236 KB	Output is correct
30	Correct	3 ms	6644 KB	Output is correct
31	Correct	3 ms	6236 KB	Output is correct
32	Correct	3 ms	6236 KB	Output is correct
33	Correct	354 ms	12516 KB	Output is correct
34	Correct	113 ms	12884 KB	Output is correct
35	Correct	307 ms	11080 KB	Output is correct
36	Correct	509 ms	16752 KB	Output is correct
37	Correct	20 ms	9052 KB	Output is correct
38	Correct	552 ms	17804 KB	Output is correct
39	Correct	538 ms	17812 KB	Output is correct
40	Correct	518 ms	17728 KB	Output is correct
41	Correct	563 ms	17988 KB	Output is correct
42	Correct	489 ms	17984 KB	Output is correct
43	Correct	507 ms	17948 KB	Output is correct
44	Correct	541 ms	17728 KB	Output is correct
45	Correct	500 ms	17816 KB	Output is correct
46	Correct	559 ms	17800 KB	Output is correct
47	Correct	503 ms	17684 KB	Output is correct
48	Correct	132 ms	14608 KB	Output is correct
49	Correct	153 ms	16664 KB	Output is correct
50	Correct	53 ms	8600 KB	Output is correct
51	Correct	61 ms	10196 KB	Output is correct
52	Correct	26 ms	8360 KB	Output is correct
53	Correct	241 ms	16724 KB	Output is correct
54	Correct	179 ms	10840 KB	Output is correct
55	Correct	457 ms	14820 KB	Output is correct
56	Correct	312 ms	11680 KB	Output is correct
57	Correct	379 ms	16208 KB	Output is correct
58	Correct	31 ms	10456 KB	Output is correct
59	Correct	61 ms	10064 KB	Output is correct
60	Correct	134 ms	15572 KB	Output is correct
61	Correct	174 ms	16068 KB	Output is correct
62	Correct	89 ms	14036 KB	Output is correct
63	Correct	66 ms	13396 KB	Output is correct
64	Correct	68 ms	14416 KB	Output is correct
65	Correct	86 ms	19252 KB	Output is correct
66	Correct	121 ms	9808 KB	Output is correct
67	Correct	90 ms	15516 KB	Output is correct
68	Correct	197 ms	20052 KB	Output is correct
69	Correct	51 ms	7740 KB	Output is correct
70	Correct	14 ms	6488 KB	Output is correct
71	Correct	92 ms	12376 KB	Output is correct
72	Correct	132 ms	17496 KB	Output is correct
73	Correct	299 ms	22352 KB	Output is correct
74	Correct	308 ms	20040 KB	Output is correct
75	Correct	246 ms	22100 KB	Output is correct
76	Correct	227 ms	21420 KB	Output is correct
77	Correct	322 ms	20304 KB	Output is correct

Submission #917157

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