Submission #283998

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
283998	2020-08-26T11:11:21 Z	Berted	Long Distance Coach (JOI17_coach)	C++14	100 / 100	171 ms	18648 KB

coach

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#define ll long long
#define pii pair<ll, ll>
#define fst first
#define snd second
#define ppi pair<ll, pii>
using namespace std;

/*
	Solution :
	Due to the existence of the driver, therefore we cannot remove cyclically
	i.e. 6, 7, 0, 1, 2
	Therefore, we can only remove "segments" at a time.

	Obs. 2:
	In each removal, it will be optimal to not "jump through" segments
	i.e. removal 1 removes 2, removal 2 removes 1,3 (this is not optimal)
	As if removal 1 is better than removal 2, it is optimal to place 1 in removal 1
	on the other hand, therefore it is optimal to place 2 in removal 2.	

	Therefore, we can solve it with a single state DP with O(N) transition (71 points)
	To get AC, optimize DP with CHT
*/

const ll INF = 5e18;

ll x, w, t, s[200051], pref[200051], v[200051], dp[200051], res;
int n, m;
pii d[200051];

vector<pii> lines;
vector<ll> val;

inline bool check(pii l1, pii l2, pii l3)
{
	return (long double)(l2.snd - l1.snd) / (l1.fst - l2.fst) >= (long double)(l3.snd - l2.snd) / (l2.fst - l3.fst);
}

inline ll getX(pii l1, pii l2)
{
	return ceill((long double)(l2.snd - l1.snd) / (l1.fst - l2.fst));
}

int main()
{
	ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
	cin >> x >> n >> m >> w >> t;
	s[0] = 0;
	for (int i = 1; i <= n; i++) {cin >> s[i];}
	s[n + 1] = x;
	for (int i = 1; i <= m; i++) {cin >> d[i].fst >> d[i].snd; v[i] = INF;}
	sort(s, s + n + 2); sort(d + 1, d + m + 1);
	res += w * (s[n + 1] / t + 1);
	for (int i = 1; i <= m; i++)
	{
		pref[i] = d[i].snd;
		if (s[n + 1] >= d[i].fst) 
		{
			pref[i] -= w * ((s[n + 1] - d[i].fst) / t + 1);
			res += w * ((s[n + 1] - d[i].fst) / t + 1);
		}
		pref[i] += pref[i - 1];
	}
	for (int i = 1; i <= n + 1; i++)
	{
		if (s[i] % t > d[1].fst)
		{
			int idx = upper_bound(d + 1, d + m + 1, make_pair(s[i] % t, -1LL)) - d - 1;
			if (v[idx] == INF && (s[i] - s[i - 1] >= t || s[i - 1] % t > s[i] % t || (s[i - 1] % t < d[idx].fst && d[idx].fst < s[i] % t))) 
			{
				v[idx] = w * (s[i] / t);
			}
		}
	}
	dp[0] = 0; lines.push_back({0, 0}); val.push_back(-INF);
	for (int i = 1; i <= m; i++)
	{
		int idx = prev(upper_bound(val.begin(), val.end(), v[i])) - val.begin();
		if (v[i] < INF)
		{
			dp[i] = min(dp[i - 1], pref[i] + i * v[i] + lines[idx].fst * v[i] + lines[idx].snd);
		}
		else {dp[i] = dp[i - 1];}
		
		pii nl = {-i, dp[i] - pref[i]};
		while (lines.size() > 1 && check(lines[lines.size() - 2], lines.back(), nl)) {lines.pop_back(); val.pop_back();}
		val.push_back(getX(lines.back(), nl));
		lines.push_back(nl);
	}
	cout << res + dp[m] << "\n";
	return 0;
}

Subtask #1
16.0 / 16.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	384 KB	Output is correct
2	Correct	0 ms	384 KB	Output is correct
3	Correct	1 ms	384 KB	Output is correct
4	Correct	0 ms	384 KB	Output is correct
5	Correct	0 ms	384 KB	Output is correct
6	Correct	1 ms	384 KB	Output is correct
7	Correct	1 ms	512 KB	Output is correct
8	Correct	1 ms	384 KB	Output is correct
9	Correct	0 ms	384 KB	Output is correct
10	Correct	0 ms	384 KB	Output is correct
11	Correct	0 ms	384 KB	Output is correct
12	Correct	1 ms	384 KB	Output is correct
13	Correct	0 ms	384 KB	Output is correct
14	Correct	1 ms	384 KB	Output is correct
15	Correct	1 ms	384 KB	Output is correct
16	Correct	1 ms	384 KB	Output is correct
17	Correct	1 ms	384 KB	Output is correct
18	Correct	1 ms	384 KB	Output is correct
19	Correct	1 ms	384 KB	Output is correct
20	Correct	1 ms	384 KB	Output is correct
21	Correct	0 ms	384 KB	Output is correct
22	Correct	0 ms	384 KB	Output is correct

Subtask #2
30.0 / 30.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	384 KB	Output is correct
2	Correct	0 ms	384 KB	Output is correct
3	Correct	1 ms	384 KB	Output is correct
4	Correct	0 ms	384 KB	Output is correct
5	Correct	0 ms	384 KB	Output is correct
6	Correct	1 ms	384 KB	Output is correct
7	Correct	1 ms	512 KB	Output is correct
8	Correct	1 ms	384 KB	Output is correct
9	Correct	0 ms	384 KB	Output is correct
10	Correct	0 ms	384 KB	Output is correct
11	Correct	0 ms	384 KB	Output is correct
12	Correct	1 ms	384 KB	Output is correct
13	Correct	0 ms	384 KB	Output is correct
14	Correct	1 ms	384 KB	Output is correct
15	Correct	1 ms	384 KB	Output is correct
16	Correct	1 ms	384 KB	Output is correct
17	Correct	1 ms	384 KB	Output is correct
18	Correct	1 ms	384 KB	Output is correct
19	Correct	1 ms	384 KB	Output is correct
20	Correct	1 ms	384 KB	Output is correct
21	Correct	0 ms	384 KB	Output is correct
22	Correct	0 ms	384 KB	Output is correct
23	Correct	1 ms	384 KB	Output is correct
24	Correct	1 ms	384 KB	Output is correct
25	Correct	1 ms	384 KB	Output is correct
26	Correct	1 ms	384 KB	Output is correct
27	Correct	1 ms	384 KB	Output is correct
28	Correct	1 ms	384 KB	Output is correct
29	Correct	1 ms	384 KB	Output is correct
30	Correct	1 ms	384 KB	Output is correct
31	Correct	1 ms	384 KB	Output is correct
32	Correct	1 ms	384 KB	Output is correct
33	Correct	1 ms	384 KB	Output is correct
34	Correct	1 ms	384 KB	Output is correct
35	Correct	1 ms	384 KB	Output is correct
36	Correct	1 ms	384 KB	Output is correct
37	Correct	1 ms	384 KB	Output is correct

Subtask #3
25.0 / 25.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	384 KB	Output is correct
2	Correct	0 ms	384 KB	Output is correct
3	Correct	1 ms	384 KB	Output is correct
4	Correct	0 ms	384 KB	Output is correct
5	Correct	0 ms	384 KB	Output is correct
6	Correct	1 ms	384 KB	Output is correct
7	Correct	1 ms	512 KB	Output is correct
8	Correct	1 ms	384 KB	Output is correct
9	Correct	0 ms	384 KB	Output is correct
10	Correct	0 ms	384 KB	Output is correct
11	Correct	0 ms	384 KB	Output is correct
12	Correct	1 ms	384 KB	Output is correct
13	Correct	0 ms	384 KB	Output is correct
14	Correct	1 ms	384 KB	Output is correct
15	Correct	1 ms	384 KB	Output is correct
16	Correct	1 ms	384 KB	Output is correct
17	Correct	1 ms	384 KB	Output is correct
18	Correct	1 ms	384 KB	Output is correct
19	Correct	1 ms	384 KB	Output is correct
20	Correct	1 ms	384 KB	Output is correct
21	Correct	0 ms	384 KB	Output is correct
22	Correct	0 ms	384 KB	Output is correct
23	Correct	1 ms	384 KB	Output is correct
24	Correct	1 ms	384 KB	Output is correct
25	Correct	1 ms	384 KB	Output is correct
26	Correct	1 ms	384 KB	Output is correct
27	Correct	1 ms	384 KB	Output is correct
28	Correct	1 ms	384 KB	Output is correct
29	Correct	1 ms	384 KB	Output is correct
30	Correct	1 ms	384 KB	Output is correct
31	Correct	1 ms	384 KB	Output is correct
32	Correct	1 ms	384 KB	Output is correct
33	Correct	1 ms	384 KB	Output is correct
34	Correct	1 ms	384 KB	Output is correct
35	Correct	1 ms	384 KB	Output is correct
36	Correct	1 ms	384 KB	Output is correct
37	Correct	1 ms	384 KB	Output is correct
38	Correct	2 ms	512 KB	Output is correct
39	Correct	2 ms	512 KB	Output is correct
40	Correct	2 ms	512 KB	Output is correct
41	Correct	2 ms	512 KB	Output is correct
42	Correct	2 ms	512 KB	Output is correct
43	Correct	2 ms	512 KB	Output is correct
44	Correct	2 ms	512 KB	Output is correct
45	Correct	2 ms	512 KB	Output is correct
46	Correct	1 ms	512 KB	Output is correct
47	Correct	2 ms	512 KB	Output is correct
48	Correct	2 ms	512 KB	Output is correct
49	Correct	2 ms	512 KB	Output is correct
50	Correct	2 ms	512 KB	Output is correct
51	Correct	2 ms	512 KB	Output is correct

Subtask #4
29.0 / 29.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	384 KB	Output is correct
2	Correct	0 ms	384 KB	Output is correct
3	Correct	1 ms	384 KB	Output is correct
4	Correct	0 ms	384 KB	Output is correct
5	Correct	0 ms	384 KB	Output is correct
6	Correct	1 ms	384 KB	Output is correct
7	Correct	1 ms	512 KB	Output is correct
8	Correct	1 ms	384 KB	Output is correct
9	Correct	0 ms	384 KB	Output is correct
10	Correct	0 ms	384 KB	Output is correct
11	Correct	0 ms	384 KB	Output is correct
12	Correct	1 ms	384 KB	Output is correct
13	Correct	0 ms	384 KB	Output is correct
14	Correct	1 ms	384 KB	Output is correct
15	Correct	1 ms	384 KB	Output is correct
16	Correct	1 ms	384 KB	Output is correct
17	Correct	1 ms	384 KB	Output is correct
18	Correct	1 ms	384 KB	Output is correct
19	Correct	1 ms	384 KB	Output is correct
20	Correct	1 ms	384 KB	Output is correct
21	Correct	0 ms	384 KB	Output is correct
22	Correct	0 ms	384 KB	Output is correct
23	Correct	1 ms	384 KB	Output is correct
24	Correct	1 ms	384 KB	Output is correct
25	Correct	1 ms	384 KB	Output is correct
26	Correct	1 ms	384 KB	Output is correct
27	Correct	1 ms	384 KB	Output is correct
28	Correct	1 ms	384 KB	Output is correct
29	Correct	1 ms	384 KB	Output is correct
30	Correct	1 ms	384 KB	Output is correct
31	Correct	1 ms	384 KB	Output is correct
32	Correct	1 ms	384 KB	Output is correct
33	Correct	1 ms	384 KB	Output is correct
34	Correct	1 ms	384 KB	Output is correct
35	Correct	1 ms	384 KB	Output is correct
36	Correct	1 ms	384 KB	Output is correct
37	Correct	1 ms	384 KB	Output is correct
38	Correct	2 ms	512 KB	Output is correct
39	Correct	2 ms	512 KB	Output is correct
40	Correct	2 ms	512 KB	Output is correct
41	Correct	2 ms	512 KB	Output is correct
42	Correct	2 ms	512 KB	Output is correct
43	Correct	2 ms	512 KB	Output is correct
44	Correct	2 ms	512 KB	Output is correct
45	Correct	2 ms	512 KB	Output is correct
46	Correct	1 ms	512 KB	Output is correct
47	Correct	2 ms	512 KB	Output is correct
48	Correct	2 ms	512 KB	Output is correct
49	Correct	2 ms	512 KB	Output is correct
50	Correct	2 ms	512 KB	Output is correct
51	Correct	2 ms	512 KB	Output is correct
52	Correct	164 ms	15352 KB	Output is correct
53	Correct	152 ms	15532 KB	Output is correct
54	Correct	128 ms	14584 KB	Output is correct
55	Correct	131 ms	14840 KB	Output is correct
56	Correct	131 ms	15224 KB	Output is correct
57	Correct	138 ms	14916 KB	Output is correct
58	Correct	131 ms	15352 KB	Output is correct
59	Correct	130 ms	14840 KB	Output is correct
60	Correct	131 ms	14584 KB	Output is correct
61	Correct	134 ms	14968 KB	Output is correct
62	Correct	132 ms	14840 KB	Output is correct
63	Correct	99 ms	18648 KB	Output is correct
64	Correct	112 ms	15608 KB	Output is correct
65	Correct	157 ms	15608 KB	Output is correct
66	Correct	149 ms	15480 KB	Output is correct
67	Correct	153 ms	15608 KB	Output is correct
68	Correct	148 ms	15480 KB	Output is correct
69	Correct	162 ms	15224 KB	Output is correct
70	Correct	165 ms	15224 KB	Output is correct
71	Correct	162 ms	15224 KB	Output is correct
72	Correct	162 ms	15224 KB	Output is correct
73	Correct	166 ms	15376 KB	Output is correct
74	Correct	169 ms	15352 KB	Output is correct
75	Correct	166 ms	15352 KB	Output is correct
76	Correct	171 ms	15512 KB	Output is correct
77	Correct	132 ms	15096 KB	Output is correct
78	Correct	137 ms	15480 KB	Output is correct
79	Correct	158 ms	14828 KB	Output is correct
80	Correct	155 ms	14836 KB	Output is correct

Submission #283998

Compilation message

Subtask #1 16.0 / 16.0

Subtask #2 30.0 / 30.0

Subtask #3 25.0 / 25.0

Subtask #4 29.0 / 29.0

Subtask #1
16.0 / 16.0

Subtask #2
30.0 / 30.0

Subtask #3
25.0 / 25.0

Subtask #4
29.0 / 29.0