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답안 #916167

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
916167 2024-01-25T12:18:24 Z GrindMachine Gap (APIO16_gap) C++17
100 / 100
 42 ms 3628 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

/*

read some solutions a long time ago, slightly remember some ideas
may have still solved it if not for those ideas

T = 1:
can restore the whole array
in 1st op, find a[1] and a[n]
in 2nd op, find a[2] and a[n-1] (set s = a[1]+1, t = a[n]-1)
in 3rd op, find a[3] and a[n-2] (set s = a[2]+1, t = a[n-1]-1)
...

after restoring the whole array, find the max gap

T = 2:
key idea:
ans >= ceil2(mx-mn,n-1) (lower bound on ans)

proof by contradiction
b = ceil2(mx-mn,n-1)
if max gap < b, then mn+(n-1)*b < mx, so max must be lesser than mx, which is a contradiction

how does this help?

split the range [mn,mx] into blocks of size b+1
note that 2 adj guys with gap > b occur in 2 adj blocks (a[i] = last guy of block x, a[i+1] = first guy of block x+1)
ans = max(max_gap_between_the_ends_of_adj_blocks,b)

cost:
n+1 to find (mn,mx)
n in total for all guys (+1 for each guy), because each guy occurs in exactly 1 block (just contribution of each guy, +1 for query not added)
<= n-1 for all queries (<= n-1 queries in total)

in total, cost <= 3n

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

#include "gap.h"

long long findGap(int T, int n)
{
    if(T == 1){
        vector<ll> a(n+5);
        ll l = 0, r = inf2;
        ll mn,mx;

        rep1(i,ceil2(n,2)){
            MinMax(l,r,&mn,&mx);
            a[i] = mn;
            a[n-i+1] = mx;
            l = mn+1, r = mx-1;
        }

        ll ans = 0;
        rep1(i,n-1) amax(ans,a[i+1]-a[i]);

        return ans;
    }

    ll mn,mx;
    MinMax(0,inf2,&mn,&mx);
    ll b = ceil2(mx-mn,n-1);
    ll ptr = mn;
    ll prev_guy = -1;
    ll ans = b;

    while(ptr <= mx){
        ll curr_mn,curr_mx;
        MinMax(ptr,ptr+b,&curr_mn,&curr_mx);
        if(curr_mn != -1){
        	if(prev_guy != -1){
        		amax(ans,curr_mn-prev_guy);
        	}
        	prev_guy = curr_mx;
        }

    	ptr += b+1;
    }

    return ans;
}

Subtask #1
30.0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 2392 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 1 ms 2392 KB Output is correct
5 Correct 1 ms 2392 KB Output is correct
6 Correct 1 ms 2392 KB Output is correct
7 Correct 1 ms 2392 KB Output is correct
8 Correct 1 ms 2392 KB Output is correct
9 Correct 1 ms 2392 KB Output is correct
10 Correct 1 ms 2392 KB Output is correct
11 Correct 1 ms 2392 KB Output is correct
12 Correct 1 ms 2392 KB Output is correct
13 Correct 1 ms 2392 KB Output is correct
14 Correct 1 ms 2392 KB Output is correct
15 Correct 1 ms 2392 KB Output is correct
16 Correct 8 ms 2588 KB Output is correct
17 Correct 8 ms 2592 KB Output is correct
18 Correct 8 ms 2576 KB Output is correct
19 Correct 8 ms 2588 KB Output is correct
20 Correct 7 ms 2568 KB Output is correct
21 Correct 30 ms 3628 KB Output is correct
22 Correct 29 ms 3628 KB Output is correct
23 Correct 30 ms 3624 KB Output is correct
24 Correct 31 ms 3412 KB Output is correct
25 Correct 28 ms 3612 KB Output is correct
26 Correct 31 ms 3616 KB Output is correct
27 Correct 30 ms 3528 KB Output is correct
28 Correct 30 ms 3628 KB Output is correct
29 Correct 35 ms 3628 KB Output is correct
30 Correct 26 ms 3624 KB Output is correct
31 Correct 1 ms 2392 KB Output is correct
32 Correct 1 ms 2392 KB Output is correct

Subtask #2
70.0 / 70.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2392 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 1 ms 2392 KB Output is correct
5 Correct 1 ms 2392 KB Output is correct
6 Correct 1 ms 2392 KB Output is correct
7 Correct 1 ms 2392 KB Output is correct
8 Correct 1 ms 2392 KB Output is correct
9 Correct 1 ms 2488 KB Output is correct
10 Correct 1 ms 2392 KB Output is correct
11 Correct 1 ms 2392 KB Output is correct
12 Correct 1 ms 2392 KB Output is correct
13 Correct 1 ms 2392 KB Output is correct
14 Correct 1 ms 2392 KB Output is correct
15 Correct 1 ms 2392 KB Output is correct
16 Correct 10 ms 2584 KB Output is correct
17 Correct 11 ms 2584 KB Output is correct
18 Correct 11 ms 2800 KB Output is correct
19 Correct 13 ms 2580 KB Output is correct
20 Correct 6 ms 2556 KB Output is correct
21 Correct 42 ms 2860 KB Output is correct
22 Correct 42 ms 2856 KB Output is correct
23 Correct 41 ms 3020 KB Output is correct
24 Correct 42 ms 2864 KB Output is correct
25 Correct 41 ms 2848 KB Output is correct
26 Correct 42 ms 2856 KB Output is correct
27 Correct 41 ms 2856 KB Output is correct
28 Correct 42 ms 2856 KB Output is correct
29 Correct 42 ms 3096 KB Output is correct
30 Correct 24 ms 3064 KB Output is correct
31 Correct 1 ms 2392 KB Output is correct
32 Correct 1 ms 2392 KB Output is correct