Submission #261262

#	Time	Username	Problem	Language	Result	Execution time	Memory
261262		Berted	Arcade (NOI20_arcade)	C++14	100 / 100	420 ms	17876 KiB

Arcade

#include <iostream>
#include <algorithm>
#include <set>
#include <tuple>
#define pii pair<int, int>
#define fst first
#define snd second

/*
	Observe that we can go from a pair to another pair iff:
	|Aj - Ai| <= Tj - Ti

	Therefore, 
	Ti - Ai <= Tj - Aj ---> if Ai <= Aj
	Ti + Ai <= Tj + Aj ---> if Ai > Aj

	Observe that if Ti - Ai <= Tj - Aj for Ai <= Aj
	Ti + Ai <= Tj + Aj will also be satisfied.

	Therefore, we could sort the array based on Ti - Ai
	And change each element in the array into just Ti + Ai
	And the problem is now reduced to :
	The minimum number of groups required such that each group
	is an non-decreasing subsequence of the array.
*/

using namespace std;
set<int> s;
int m, n;
pii ar[500001];
pii srt[500001];
int main()
{
	ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
	cin >> m >> n;
	for (int i = 0; i < n; i++) {cin >> ar[i].snd;}
	for (int i = 0; i < n; i++)
	{
		cin >> ar[i].fst;
		tie(ar[i].fst, ar[i].snd) = make_tuple(ar[i].snd - ar[i].fst, ar[i].fst + ar[i].snd);
	}
	sort(ar, ar + n);
	for (int i = 0; i < n; i++)
	{
		srt[i] = {ar[i].snd, i};
	}
	sort(srt, srt + n);
	for (int i = 0; i < n; i++)
	{
		auto it = s.lower_bound(srt[i].snd);
		if (it != s.begin()) s.erase(prev(it));
		s.insert(srt[i].snd);
	}
	cout << s.size() << '\n';
	return 0;
}

• Subtask 1: 7 / 7
• Subtask 2: 11 / 11
• Subtask 3: 12 / 12
• Subtask 4: 21 / 21
• Subtask 5: 14 / 14
• Subtask 6: 20 / 20
• Subtask 7: 15 / 15