oj.uz

Submission #937052

# Submission time Handle Problem Language Result Execution time Memory
937052 2024-03-03T10:09:57 Z GrindMachine Rarest Insects (IOI22_insects) C++17
100 / 100
 36 ms 1368 KB 
#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:
https://youtu.be/mm5Nv81P5u8?t=19948
edi

first, figure out the #of distinct guys in the array

b.s on answer
let's say we want to check if ans < mid
go over all indices and put each value into the machine
if val > mid, then pop the recently added value from the machine
at the end, count the #of guys that were added to the machine
if cnt == mid*unique, then each guy appears at least mid #of times, so return false
otherwise, cnt < mid*unique, so there is at least 1 guy that appears < mid #of times, so return true
gets around 50 points

key idea for 100 points:
try to save operations between successive calls of b.s

cnt == mid*unique:
we increase the left bound of the b.s
there are only good guys in the machine
because we increase the left bound, these good guys will remain forever
no need to remove them and add them again (put them forever in the machine)

cnt < mid*unique:
we decrease the right bound of the b.s
if a guy is bad in this iteration, he would be bad in the successive iteration too
so ignore the bad guys
also, remember to remove the good guys in this iteration from the machine

if case 1 is true, mid*unique guys removed from consideration
if case 2 is true, at least active-mid*unique guys removed from consideration
mid*unique splits the active set into almost 2 equal halves
so at each stage, around n/2 guys are removed from consideration

so we get n+n/2+n/4+... = 2n queries
n queries for finding the #of unique guys
so around 3n queries in total
refer https://codeforces.com/blog/entry/105835?#comment-942719 for more details

further optimizations:
set l and r bounds of the b.s optimally (l = 1, r = (n/unique)-1, ans = n/unique) (ans is at most n/unique)
stop adding guys to the machine once the limit (cnt == mid*unique) is reached
randomize the order in which the guys are added to the machine

*/
 
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
 
#include "insects.h"

int min_cardinality(int n) {
    mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
    vector<int> order(n);
    rep(i,n) order[i] = i;

    vector<int> uniq_guys;

    rep(i,n){
        move_inside(i);
        int res = press_button();
        if(res >= 2){
            move_outside(i);
        }
        else{
            uniq_guys.pb(i);
        }
    }

    trav(i,uniq_guys){
        move_outside(i);
    }
    
    if(sz(uniq_guys) == 1){
        return n;
    }

    if(sz(uniq_guys) == n){
        return 1;
    }

    vector<bool> ignore(n);
    vector<int> in_machine;

    auto ok = [&](int mid){
        // check if ans <= mid
        // check if ans < mid+1

        vector<int> good, bad;
        shuffle(all(order),rng);

        rep(ind,n){
            int i = order[ind];
            if(ignore[i]) conts;
            if(sz(in_machine)+sz(good) == sz(uniq_guys)*(mid+1)){
                break;
            }
            move_inside(i);
            int res = press_button();
            if(res > mid+1){
                bad.pb(i);
                move_outside(i);
            }
            else{
                good.pb(i);
            }
        }

        if(sz(in_machine)+sz(good) == sz(uniq_guys)*(mid+1)){
            // everybody occurs at least mid+1 times
            // anybody in the machine would stay in the machine forever
            trav(i,good){
                in_machine.pb(i);
                ignore[i] = 1;
            }

            return false;
        }
        else{
            // at least one guy occurs < (mid+1) #of times
            // i.e at least one guys occurs <= mid #of times
            // right endpoint of range decreases
            // so ignore all bad guys in future iterations
            // remove all good guys in this iteration from the machine
            trav(i,bad){
                ignore[i] = 1;
            }
            trav(i,good){
                move_outside(i);
            }

            return true;
        }
    };

    int l = 1, r = n/sz(uniq_guys)-1;
    int ans = n/sz(uniq_guys);
 
    while(l <= r){
        int mid = (l+r) >> 1;
        // is min <= mid?
        if(ok(mid)){
            ans = mid;
            r = mid-1;
        }
        else{
            l = mid+1;
        }
    }
 
    return ans;
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 0 ms 344 KB Output is correct
5 Correct 0 ms 344 KB Output is correct
6 Correct 1 ms 344 KB Output is correct
7 Correct 2 ms 344 KB Output is correct
8 Correct 2 ms 600 KB Output is correct
9 Correct 2 ms 440 KB Output is correct
10 Correct 2 ms 600 KB Output is correct
11 Correct 1 ms 344 KB Output is correct
12 Correct 2 ms 600 KB Output is correct
13 Correct 2 ms 600 KB Output is correct
14 Correct 2 ms 600 KB Output is correct
15 Correct 2 ms 600 KB Output is correct
16 Correct 2 ms 440 KB Output is correct
17 Correct 2 ms 600 KB Output is correct
18 Correct 3 ms 344 KB Output is correct
19 Correct 2 ms 436 KB Output is correct
20 Correct 2 ms 600 KB Output is correct
21 Correct 3 ms 600 KB Output is correct
22 Correct 1 ms 344 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 0 ms 344 KB Output is correct
5 Correct 0 ms 344 KB Output is correct
6 Correct 1 ms 344 KB Output is correct
7 Correct 2 ms 344 KB Output is correct
8 Correct 2 ms 600 KB Output is correct
9 Correct 2 ms 440 KB Output is correct
10 Correct 2 ms 600 KB Output is correct
11 Correct 1 ms 344 KB Output is correct
12 Correct 2 ms 600 KB Output is correct
13 Correct 2 ms 600 KB Output is correct
14 Correct 2 ms 600 KB Output is correct
15 Correct 2 ms 600 KB Output is correct
16 Correct 2 ms 440 KB Output is correct
17 Correct 2 ms 600 KB Output is correct
18 Correct 3 ms 344 KB Output is correct
19 Correct 2 ms 436 KB Output is correct
20 Correct 2 ms 600 KB Output is correct
21 Correct 3 ms 600 KB Output is correct
22 Correct 1 ms 344 KB Output is correct
23 Correct 4 ms 344 KB Output is correct
24 Correct 5 ms 600 KB Output is correct
25 Correct 10 ms 440 KB Output is correct
26 Correct 13 ms 852 KB Output is correct
27 Correct 11 ms 600 KB Output is correct
28 Correct 4 ms 600 KB Output is correct
29 Correct 12 ms 952 KB Output is correct
30 Correct 13 ms 856 KB Output is correct
31 Correct 10 ms 956 KB Output is correct
32 Correct 11 ms 600 KB Output is correct
33 Correct 21 ms 444 KB Output is correct
34 Correct 10 ms 856 KB Output is correct
35 Correct 10 ms 600 KB Output is correct
36 Correct 13 ms 1104 KB Output is correct
37 Correct 11 ms 688 KB Output is correct
38 Correct 13 ms 696 KB Output is correct
39 Correct 12 ms 592 KB Output is correct
40 Correct 8 ms 860 KB Output is correct
41 Correct 5 ms 600 KB Output is correct

Subtask #3
75.0 / 75.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 1 ms 344 KB Output is correct
5 Correct 0 ms 344 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 10 ms 344 KB Output is correct
8 Correct 10 ms 856 KB Output is correct
9 Correct 21 ms 704 KB Output is correct
10 Correct 32 ms 704 KB Output is correct
11 Correct 35 ms 600 KB Output is correct
12 Correct 17 ms 1112 KB Output is correct
13 Correct 24 ms 944 KB Output is correct
14 Correct 26 ms 688 KB Output is correct
15 Correct 17 ms 848 KB Output is correct
16 Correct 20 ms 692 KB Output is correct
17 Correct 24 ms 696 KB Output is correct
18 Correct 22 ms 936 KB Output is correct
19 Correct 18 ms 676 KB Output is correct
20 Correct 23 ms 932 KB Output is correct
21 Correct 33 ms 592 KB Output is correct
22 Correct 36 ms 592 KB Output is correct
23 Correct 27 ms 856 KB Output is correct
24 Correct 24 ms 1368 KB Output is correct
25 Correct 20 ms 700 KB Output is correct
26 Correct 9 ms 712 KB Output is correct
27 Correct 28 ms 704 KB Output is correct
28 Correct 23 ms 592 KB Output is correct
29 Correct 22 ms 452 KB Output is correct
30 Correct 22 ms 444 KB Output is correct
31 Correct 31 ms 592 KB Output is correct
32 Correct 24 ms 1188 KB Output is correct
33 Correct 28 ms 936 KB Output is correct
34 Correct 26 ms 676 KB Output is correct
35 Correct 22 ms 1104 KB Output is correct
36 Correct 21 ms 692 KB Output is correct
37 Correct 23 ms 684 KB Output is correct
38 Correct 21 ms 1104 KB Output is correct
39 Correct 21 ms 692 KB Output is correct
40 Correct 22 ms 440 KB Output is correct
41 Correct 20 ms 696 KB Output is correct
42 Correct 22 ms 696 KB Output is correct
43 Correct 6 ms 344 KB Output is correct
44 Correct 20 ms 676 KB Output is correct
45 Correct 20 ms 424 KB Output is correct
46 Correct 16 ms 860 KB Output is correct
47 Correct 15 ms 1108 KB Output is correct
48 Correct 17 ms 1100 KB Output is correct