oj.uz

Submission #1073292

# Submission time Handle Problem Language Result Execution time Memory
1073292 2024-08-24T11:55:55 Z GrindMachine Rarest Insects (IOI22_insects) C++17
99.56 / 100
 47 ms 676 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 for full score:
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) {
    int d = 0;

    {
        vector<int> v;
        rep(i,n){
            move_inside(i);
            if(press_button() > 1){
                move_outside(i);
            }       
            else{
                v.pb(i);
                d++;
            }  
        }

        trav(i,v){
            move_outside(i);
        }
    }

    vector<bool> state(n,1); // 0 = ignored, 1 = active
    int lo = 1, hi = n/d;
    int ans = -1;
    int cnt = 0;

    auto ok = [&](int mid){
        vector<int> stay,leave;
        rep(i,n){
            if(!state[i]) conts;
            move_inside(i);
            cnt++; 
            if(press_button() > mid){
                move_outside(i);
                cnt--;
                leave.pb(i);
            }
            else{
                stay.pb(i);
            }
        }

        bool res = (cnt == mid*d);
        
        if(res){
            trav(i,stay){
                state[i] = 0;
            }
        }
        else{
            trav(i,stay){
                move_outside(i);
                cnt--;
            }
            trav(i,leave){
                state[i] = 0;
            }
        }

        return res;
    };

    while(lo <= hi){
        int mid = (lo+hi) >> 1;
        if(ok(mid)){
            ans = mid;
            lo = mid+1;
        }
        else{
            hi = mid-1;
        }
    }

    return ans;
}

Subtask #1
10.0 / 10.0

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

Subtask #2
15.0 / 15.0

# 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 1 ms 344 KB Output is correct
4 Correct 0 ms 344 KB Output is correct
5 Correct 1 ms 344 KB Output is correct
6 Correct 3 ms 436 KB Output is correct
7 Correct 2 ms 344 KB Output is correct
8 Correct 5 ms 344 KB Output is correct
9 Correct 3 ms 344 KB Output is correct
10 Correct 3 ms 600 KB Output is correct
11 Correct 3 ms 344 KB Output is correct
12 Correct 3 ms 344 KB Output is correct
13 Correct 3 ms 344 KB Output is correct
14 Correct 4 ms 344 KB Output is correct
15 Correct 4 ms 344 KB Output is correct
16 Correct 5 ms 344 KB Output is correct
17 Correct 4 ms 344 KB Output is correct
18 Correct 3 ms 600 KB Output is correct
19 Correct 4 ms 436 KB Output is correct
20 Correct 2 ms 344 KB Output is correct
21 Correct 3 ms 344 KB Output is correct
22 Correct 2 ms 344 KB Output is correct
23 Correct 13 ms 344 KB Output is correct
24 Correct 12 ms 344 KB Output is correct
25 Correct 12 ms 444 KB Output is correct
26 Correct 21 ms 432 KB Output is correct
27 Correct 8 ms 344 KB Output is correct
28 Correct 10 ms 436 KB Output is correct
29 Correct 13 ms 600 KB Output is correct
30 Correct 11 ms 344 KB Output is correct
31 Correct 20 ms 600 KB Output is correct
32 Correct 17 ms 344 KB Output is correct
33 Correct 19 ms 600 KB Output is correct
34 Correct 9 ms 344 KB Output is correct
35 Correct 19 ms 668 KB Output is correct
36 Correct 13 ms 440 KB Output is correct
37 Correct 13 ms 344 KB Output is correct
38 Correct 13 ms 344 KB Output is correct
39 Correct 19 ms 592 KB Output is correct
40 Correct 7 ms 592 KB Output is correct
41 Correct 15 ms 344 KB Output is correct

Subtask #3
74.56 / 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 0 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 37 ms 344 KB Output is correct
8 Correct 20 ms 344 KB Output is correct
9 Correct 28 ms 668 KB Output is correct
10 Correct 33 ms 432 KB Output is correct
11 Correct 22 ms 424 KB Output is correct
12 Correct 36 ms 440 KB Output is correct
13 Correct 36 ms 596 KB Output is correct
14 Correct 30 ms 600 KB Output is correct
15 Correct 34 ms 596 KB Output is correct
16 Correct 34 ms 432 KB Output is correct
17 Correct 28 ms 436 KB Output is correct
18 Correct 31 ms 440 KB Output is correct
19 Partially correct 33 ms 340 KB Output is partially correct
20 Correct 41 ms 436 KB Output is correct
21 Correct 36 ms 420 KB Output is correct
22 Correct 42 ms 600 KB Output is correct
23 Correct 32 ms 428 KB Output is correct
24 Correct 23 ms 344 KB Output is correct
25 Correct 24 ms 440 KB Output is correct
26 Correct 18 ms 592 KB Output is correct
27 Partially correct 31 ms 428 KB Output is partially correct
28 Partially correct 37 ms 592 KB Output is partially correct
29 Partially correct 47 ms 424 KB Output is partially correct
30 Partially correct 39 ms 600 KB Output is partially correct
31 Correct 31 ms 676 KB Output is correct
32 Correct 27 ms 344 KB Output is correct
33 Correct 28 ms 344 KB Output is correct
34 Correct 40 ms 432 KB Output is correct
35 Partially correct 33 ms 432 KB Output is partially correct
36 Partially correct 27 ms 416 KB Output is partially correct
37 Correct 27 ms 344 KB Output is correct
38 Correct 37 ms 592 KB Output is correct
39 Partially correct 39 ms 344 KB Output is partially correct
40 Partially correct 45 ms 672 KB Output is partially correct
41 Partially correct 28 ms 592 KB Output is partially correct
42 Partially correct 38 ms 668 KB Output is partially correct
43 Correct 6 ms 344 KB Output is correct
44 Correct 18 ms 344 KB Output is correct
45 Correct 42 ms 592 KB Output is correct
46 Correct 33 ms 600 KB Output is correct
47 Correct 30 ms 420 KB Output is correct
48 Correct 28 ms 344 KB Output is correct