Submission #748486

#	Time	Username	Problem	Language	Result	Execution time	Memory
748486		GrindMachine	Abduction 2 (JOI17_abduction2)	C++17	100 / 100	2439 ms	331592 KiB

abduction2

// 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 / 13
• Subtask 2: 10 / 10
• Subtask 3: 17 / 17
• Subtask 4: 4 / 4
• Subtask 5: 56 / 56