Submission #917158

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
917158	2024-01-27T10:42:48 Z	GrindMachine	Cats or Dogs (JOI18_catdog)	C++17	100 / 100	551 ms	20308 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 {
        int dp[2][2];
        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();
}

Compilation message

catdog.cpp: In function 'int get_ans()':
catdog.cpp:254:17: warning: '<anonymous>[0]' is used uninitialized in this function [-Wuninitialized]
  254 |             amin(ans,dp[i][j]);
      |             ~~~~^~~~~~~~~~~~~~
catdog.cpp:254:17: warning: '<anonymous>[1]' is used uninitialized in this function [-Wuninitialized]
catdog.cpp:254:17: warning: '*((void*)(&<anonymous>)+8)[0]' is used uninitialized in this function [-Wuninitialized]
catdog.cpp:254:17: warning: '*((void*)(&<anonymous>)+8)[1]' is used uninitialized in this function [-Wuninitialized]

Subtask #1
8.0 / 8.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	6232 KB	Output is correct
2	Correct	3 ms	6236 KB	Output is correct
3	Correct	2 ms	6236 KB	Output is correct
4	Correct	3 ms	6232 KB	Output is correct
5	Correct	3 ms	6236 KB	Output is correct
6	Correct	3 ms	6236 KB	Output is correct
7	Correct	2 ms	6236 KB	Output is correct
8	Correct	3 ms	6232 KB	Output is correct
9	Correct	3 ms	6236 KB	Output is correct
10	Correct	3 ms	6236 KB	Output is correct
11	Correct	3 ms	6236 KB	Output is correct
12	Correct	3 ms	6232 KB	Output is correct
13	Correct	3 ms	6236 KB	Output is correct
14	Correct	3 ms	6236 KB	Output is correct
15	Correct	3 ms	6228 KB	Output is correct
16	Correct	3 ms	6236 KB	Output is correct

Subtask #2
30.0 / 30.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	2 ms	6232 KB	Output is correct
2	Correct	3 ms	6236 KB	Output is correct
3	Correct	2 ms	6236 KB	Output is correct
4	Correct	3 ms	6232 KB	Output is correct
5	Correct	3 ms	6236 KB	Output is correct
6	Correct	3 ms	6236 KB	Output is correct
7	Correct	2 ms	6236 KB	Output is correct
8	Correct	3 ms	6232 KB	Output is correct
9	Correct	3 ms	6236 KB	Output is correct
10	Correct	3 ms	6236 KB	Output is correct
11	Correct	3 ms	6236 KB	Output is correct
12	Correct	3 ms	6232 KB	Output is correct
13	Correct	3 ms	6236 KB	Output is correct
14	Correct	3 ms	6236 KB	Output is correct
15	Correct	3 ms	6228 KB	Output is correct
16	Correct	3 ms	6236 KB	Output is correct
17	Correct	4 ms	6236 KB	Output is correct
18	Correct	6 ms	6236 KB	Output is correct
19	Correct	3 ms	6236 KB	Output is correct
20	Correct	2 ms	6236 KB	Output is correct
21	Correct	3 ms	6232 KB	Output is correct
22	Correct	3 ms	6316 KB	Output is correct
23	Correct	4 ms	6236 KB	Output is correct
24	Correct	4 ms	6236 KB	Output is correct
25	Correct	4 ms	6236 KB	Output is correct
26	Correct	4 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	6236 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	6232 KB	Output is correct
2	Correct	3 ms	6236 KB	Output is correct
3	Correct	2 ms	6236 KB	Output is correct
4	Correct	3 ms	6232 KB	Output is correct
5	Correct	3 ms	6236 KB	Output is correct
6	Correct	3 ms	6236 KB	Output is correct
7	Correct	2 ms	6236 KB	Output is correct
8	Correct	3 ms	6232 KB	Output is correct
9	Correct	3 ms	6236 KB	Output is correct
10	Correct	3 ms	6236 KB	Output is correct
11	Correct	3 ms	6236 KB	Output is correct
12	Correct	3 ms	6232 KB	Output is correct
13	Correct	3 ms	6236 KB	Output is correct
14	Correct	3 ms	6236 KB	Output is correct
15	Correct	3 ms	6228 KB	Output is correct
16	Correct	3 ms	6236 KB	Output is correct
17	Correct	4 ms	6236 KB	Output is correct
18	Correct	6 ms	6236 KB	Output is correct
19	Correct	3 ms	6236 KB	Output is correct
20	Correct	2 ms	6236 KB	Output is correct
21	Correct	3 ms	6232 KB	Output is correct
22	Correct	3 ms	6316 KB	Output is correct
23	Correct	4 ms	6236 KB	Output is correct
24	Correct	4 ms	6236 KB	Output is correct
25	Correct	4 ms	6236 KB	Output is correct
26	Correct	4 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	6236 KB	Output is correct
31	Correct	3 ms	6236 KB	Output is correct
32	Correct	3 ms	6236 KB	Output is correct
33	Correct	313 ms	11392 KB	Output is correct
34	Correct	107 ms	11856 KB	Output is correct
35	Correct	292 ms	10148 KB	Output is correct
36	Correct	473 ms	15004 KB	Output is correct
37	Correct	20 ms	8792 KB	Output is correct
38	Correct	551 ms	16000 KB	Output is correct
39	Correct	508 ms	15936 KB	Output is correct
40	Correct	484 ms	15936 KB	Output is correct
41	Correct	512 ms	15888 KB	Output is correct
42	Correct	495 ms	16060 KB	Output is correct
43	Correct	483 ms	15936 KB	Output is correct
44	Correct	480 ms	16068 KB	Output is correct
45	Correct	478 ms	15952 KB	Output is correct
46	Correct	489 ms	15768 KB	Output is correct
47	Correct	487 ms	15760 KB	Output is correct
48	Correct	129 ms	13260 KB	Output is correct
49	Correct	142 ms	15048 KB	Output is correct
50	Correct	50 ms	8272 KB	Output is correct
51	Correct	57 ms	9688 KB	Output is correct
52	Correct	25 ms	8028 KB	Output is correct
53	Correct	215 ms	15068 KB	Output is correct
54	Correct	170 ms	10076 KB	Output is correct
55	Correct	423 ms	13132 KB	Output is correct
56	Correct	261 ms	10652 KB	Output is correct
57	Correct	352 ms	14420 KB	Output is correct
58	Correct	30 ms	9948 KB	Output is correct
59	Correct	58 ms	9304 KB	Output is correct
60	Correct	129 ms	14116 KB	Output is correct
61	Correct	143 ms	14516 KB	Output is correct
62	Correct	91 ms	12660 KB	Output is correct
63	Correct	64 ms	12656 KB	Output is correct
64	Correct	68 ms	13660 KB	Output is correct
65	Correct	86 ms	18104 KB	Output is correct
66	Correct	97 ms	9316 KB	Output is correct
67	Correct	89 ms	14772 KB	Output is correct
68	Correct	190 ms	18416 KB	Output is correct
69	Correct	46 ms	7504 KB	Output is correct
70	Correct	11 ms	6516 KB	Output is correct
71	Correct	87 ms	11652 KB	Output is correct
72	Correct	132 ms	16412 KB	Output is correct
73	Correct	281 ms	20308 KB	Output is correct
74	Correct	301 ms	18008 KB	Output is correct
75	Correct	233 ms	20208 KB	Output is correct
76	Correct	216 ms	19472 KB	Output is correct
77	Correct	302 ms	18632 KB	Output is correct

Submission #917158

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