oj.uz

Submission #748486

# Submission time Handle Problem Language Result Execution time Memory
748486 2023-05-26T10:56:08 Z GrindMachine Abduction 2 (JOI17_abduction2) C++17
100 / 100
 2439 ms 331592 KB 
// Om Namah Shivaya

#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) 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

write O(nm) dp and optimize

how to optimize?
we may try to reduce the #of vis states

compress straight chains into single jumps
this reduces the #of vis states
so we can memoize the dp in a map

just apply these optimizations and pray that it passes

*/

const int MOD = 1e9 + 7;
const int N = 5e4 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

template<typename T>
struct sparse_table {
    /*============================*/

    T merge(T a, T b) {
        return max(a, b);
    }

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

    vector<vector<T>> table;
    vector<int> bin_log;
    int LOG = 0;

    sparse_table() {

    }

    sparse_table(vector<T> &a, int n) {
        while ((1 << LOG) <= n) LOG++;

        table = vector<vector<T>>(n, vector<T>(LOG));
        bin_log = vector<int>(n + 1);

        rep(i, n) table[i][0] = a[i];

        rep1(j, LOG - 1) {
            rep(i, n) {
                int jump = 1 << (j - 1);
                if (i + jump >= n) {
                    break;
                }

                table[i][j] = merge(table[i][j - 1], table[i + jump][j - 1]);
            }
        }

        bin_log[1] = 0;
        for (int i = 2; i <= n; ++i) {
            bin_log[i] = bin_log[i / 2] + 1;
        }
    }

    T query(int l, int r) {
        int len = r - l + 1;
        int k = bin_log[len];

        T val1 = table[l][k];
        T val2 = table[r - (1 << k) + 1][k];

        return merge(val1, val2);
    }
};

ll n,m,q;
vector<ll> a(N), b(N);
map<array<ll,3>, ll> dp;
sparse_table<ll> st1, st2;

ll first_left(sparse_table<ll> &st, ll i, ll v){
    ll l = 0, r = i;
    ll ans = -1;
    
    while(l <= r){
        ll mid = (l + r) >> 1;
        if(st.query(mid,i) > v){
            ans = mid;
            l = mid + 1;
        }
        else{
            r = mid - 1;
        }
    } 

    return ans;
}

ll first_right(sparse_table<ll> &st, ll i, ll v){
    ll l = i, r = sz(st.table)-1;
    ll ans = -1;
    
    while(l <= r){
        ll mid = (l + r) >> 1;
        if(st.query(i,mid) > v){
            ans = mid;
            r = mid - 1;
        }
        else{
            l = mid + 1;
        }
    } 

    return ans;
}

ll go(ll i, ll j, ll d){
    if(i < 1 or i > n or j < 1 or j > m) return -1;
    array<ll,3> key = {i,j,d};
    if(dp.count(key)) return dp[key];

    ll ans = 0;

    if(d <= 1){
        if(b[j] > a[i]){
            amax(ans, 1 + go(i-1,j,2));
            amax(ans, 1 + go(i+1,j,3));
        }
        else{
            // find first pos where dir changes
            // use sparse table to optimize
            if(d == 0){
                ll p = first_left(st2,j,a[i]);
                amax(ans, abs(j-p) + go(i,p,d));
            }
            else{
                ll p = first_right(st2,j,a[i]);
                amax(ans, abs(j-p) + go(i,p,d));
            }
        }
    }
    else{
        if(a[i] > b[j]){
            amax(ans, 1 + go(i,j-1,0));
            amax(ans, 1 + go(i,j+1,1));       
        }
        else{
            if(d == 2){
                ll p = first_left(st1,i,b[j]);
                amax(ans, abs(i-p) + go(p,j,d));
            }
            else{                
                ll p = first_right(st1,i,b[j]);
                amax(ans, abs(i-p) + go(p,j,d));
            }
        }
    }

    return dp[key] = ans;
}

void solve(int test_case)
{
    cin >> n >> m >> q;
    rep1(i,n) cin >> a[i];
    rep1(i,m) cin >> b[i];

    a[0] = inf2, a[n+1] = inf2;
    b[0] = inf2, b[m+1] = inf2;

    st1 = sparse_table<ll>(a,n+2);
    st2 = sparse_table<ll>(b,m+2);

    while(q--){
        ll i,j; cin >> i >> j;
        ll ans = 1 + max({go(i,j-1,0), go(i,j+1,1), go(i-1,j,2), go(i+1,j,3)});
        cout << ans << endl;
    }
}

int main()
{
    fastio;

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

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

    return 0;
}

Subtask #1
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1108 KB Output is correct
2 Correct 1 ms 1108 KB Output is correct
3 Correct 1 ms 1108 KB Output is correct
4 Correct 1 ms 1108 KB Output is correct
5 Correct 1 ms 1112 KB Output is correct
6 Correct 1 ms 1108 KB Output is correct
7 Correct 1 ms 1108 KB Output is correct
8 Correct 1 ms 1108 KB Output is correct
9 Correct 1 ms 1108 KB Output is correct
10 Correct 1 ms 1108 KB Output is correct
11 Correct 1 ms 1108 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1108 KB Output is correct
2 Correct 1 ms 1108 KB Output is correct
3 Correct 1 ms 1108 KB Output is correct
4 Correct 1 ms 1108 KB Output is correct
5 Correct 1 ms 1112 KB Output is correct
6 Correct 1 ms 1108 KB Output is correct
7 Correct 1 ms 1108 KB Output is correct
8 Correct 1 ms 1108 KB Output is correct
9 Correct 1 ms 1108 KB Output is correct
10 Correct 1 ms 1108 KB Output is correct
11 Correct 1 ms 1108 KB Output is correct
12 Correct 2 ms 1620 KB Output is correct
13 Correct 2 ms 1620 KB Output is correct
14 Correct 2 ms 1620 KB Output is correct
15 Correct 2 ms 1620 KB Output is correct
16 Correct 3 ms 1620 KB Output is correct
17 Correct 2 ms 1620 KB Output is correct
18 Correct 2 ms 1620 KB Output is correct
19 Correct 4 ms 2184 KB Output is correct
20 Correct 6 ms 2388 KB Output is correct
21 Correct 5 ms 2260 KB Output is correct
22 Correct 6 ms 2592 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1108 KB Output is correct
2 Correct 1 ms 1108 KB Output is correct
3 Correct 1 ms 1108 KB Output is correct
4 Correct 1 ms 1108 KB Output is correct
5 Correct 1 ms 1112 KB Output is correct
6 Correct 1 ms 1108 KB Output is correct
7 Correct 1 ms 1108 KB Output is correct
8 Correct 1 ms 1108 KB Output is correct
9 Correct 1 ms 1108 KB Output is correct
10 Correct 1 ms 1108 KB Output is correct
11 Correct 1 ms 1108 KB Output is correct
12 Correct 2 ms 1620 KB Output is correct
13 Correct 2 ms 1620 KB Output is correct
14 Correct 2 ms 1620 KB Output is correct
15 Correct 2 ms 1620 KB Output is correct
16 Correct 3 ms 1620 KB Output is correct
17 Correct 2 ms 1620 KB Output is correct
18 Correct 2 ms 1620 KB Output is correct
19 Correct 4 ms 2184 KB Output is correct
20 Correct 6 ms 2388 KB Output is correct
21 Correct 5 ms 2260 KB Output is correct
22 Correct 6 ms 2592 KB Output is correct
23 Correct 33 ms 18788 KB Output is correct
24 Correct 31 ms 18796 KB Output is correct
25 Correct 30 ms 18888 KB Output is correct
26 Correct 31 ms 18816 KB Output is correct
27 Correct 32 ms 18892 KB Output is correct
28 Correct 76 ms 30636 KB Output is correct
29 Correct 40 ms 20480 KB Output is correct
30 Correct 143 ms 35520 KB Output is correct
31 Correct 161 ms 40220 KB Output is correct
32 Correct 38 ms 19524 KB Output is correct
33 Correct 60 ms 23052 KB Output is correct

Subtask #4
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 2132 KB Output is correct
2 Correct 6 ms 2132 KB Output is correct
3 Correct 5 ms 2132 KB Output is correct
4 Correct 5 ms 2132 KB Output is correct
5 Correct 6 ms 2148 KB Output is correct
6 Correct 4 ms 2260 KB Output is correct
7 Correct 3 ms 2132 KB Output is correct
8 Correct 9 ms 2824 KB Output is correct
9 Correct 8 ms 2924 KB Output is correct
10 Correct 10 ms 2716 KB Output is correct
11 Correct 8 ms 2900 KB Output is correct

Subtask #5
56.0 / 56.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1108 KB Output is correct
2 Correct 1 ms 1108 KB Output is correct
3 Correct 1 ms 1108 KB Output is correct
4 Correct 1 ms 1108 KB Output is correct
5 Correct 1 ms 1112 KB Output is correct
6 Correct 1 ms 1108 KB Output is correct
7 Correct 1 ms 1108 KB Output is correct
8 Correct 1 ms 1108 KB Output is correct
9 Correct 1 ms 1108 KB Output is correct
10 Correct 1 ms 1108 KB Output is correct
11 Correct 1 ms 1108 KB Output is correct
12 Correct 2 ms 1620 KB Output is correct
13 Correct 2 ms 1620 KB Output is correct
14 Correct 2 ms 1620 KB Output is correct
15 Correct 2 ms 1620 KB Output is correct
16 Correct 3 ms 1620 KB Output is correct
17 Correct 2 ms 1620 KB Output is correct
18 Correct 2 ms 1620 KB Output is correct
19 Correct 4 ms 2184 KB Output is correct
20 Correct 6 ms 2388 KB Output is correct
21 Correct 5 ms 2260 KB Output is correct
22 Correct 6 ms 2592 KB Output is correct
23 Correct 33 ms 18788 KB Output is correct
24 Correct 31 ms 18796 KB Output is correct
25 Correct 30 ms 18888 KB Output is correct
26 Correct 31 ms 18816 KB Output is correct
27 Correct 32 ms 18892 KB Output is correct
28 Correct 76 ms 30636 KB Output is correct
29 Correct 40 ms 20480 KB Output is correct
30 Correct 143 ms 35520 KB Output is correct
31 Correct 161 ms 40220 KB Output is correct
32 Correct 38 ms 19524 KB Output is correct
33 Correct 60 ms 23052 KB Output is correct
34 Correct 5 ms 2132 KB Output is correct
35 Correct 6 ms 2132 KB Output is correct
36 Correct 5 ms 2132 KB Output is correct
37 Correct 5 ms 2132 KB Output is correct
38 Correct 6 ms 2148 KB Output is correct
39 Correct 4 ms 2260 KB Output is correct
40 Correct 3 ms 2132 KB Output is correct
41 Correct 9 ms 2824 KB Output is correct
42 Correct 8 ms 2924 KB Output is correct
43 Correct 10 ms 2716 KB Output is correct
44 Correct 8 ms 2900 KB Output is correct
45 Correct 39 ms 19808 KB Output is correct
46 Correct 38 ms 19836 KB Output is correct
47 Correct 41 ms 19908 KB Output is correct
48 Correct 38 ms 19876 KB Output is correct
49 Correct 42 ms 19868 KB Output is correct
50 Correct 75 ms 30660 KB Output is correct
51 Correct 78 ms 31952 KB Output is correct
52 Correct 227 ms 47888 KB Output is correct
53 Correct 221 ms 46640 KB Output is correct
54 Correct 208 ms 45036 KB Output is correct
55 Correct 266 ms 52400 KB Output is correct
56 Correct 2439 ms 331592 KB Output is correct
57 Correct 581 ms 99672 KB Output is correct
58 Correct 552 ms 95648 KB Output is correct
59 Correct 563 ms 95024 KB Output is correct