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Submission #1092169

# Submission time Handle Problem Language Result Execution time Memory
1092169 2024-09-23T12:26:50 Z ByeWorld Discharging (NOI20_discharging) C++14
100 / 100
 272 ms 45324 KB 
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#define int long long
#define ll long long
#define pb push_back
#define fi first
#define se second
#define lf (id<<1)
#define rg ((id<<1)|1)
#define md ((l+r)>>1)
#define ld long double
using namespace std;
typedef pair<ll,ll> pii;
typedef pair<ll,pii> ipii;
const int MAXN = 1e6+10;
const ll INF = 1e18+10;
const int MOD = 998244353;
const int LOG = 20;
const int ADD = 1e10;

int n, x;
int a[MAXN];
vector <pii> vec;
int dp[MAXN], cnt[MAXN], val[MAXN];
int pr[MAXN];

struct Line {
	int m, c;
	int getY(int x){
		return m*x+c;
	}
	pii cut(Line oth){
		return pii(oth.c-c, m-oth.m);
	}
};
vector <Line> ch;

bool cek(Line a, Line b, Line c){
	int A = b.cut(a).fi, B = b.cut(a).se;
	int C = c.cut(b).fi, D = c.cut(b).se;
	// A/B < C/D
	if(A/B == C/D){
		return (A%B)*D > (C%D)*B;
	}
	return A/B > C/D;
}
void add(Line nw){
	while(ch.size()>=2 && 
		!cek(ch[ch.size()-2], ch.back(), nw) ) ch.pop_back();
	ch.pb(nw);
	// for(auto in : ch) cout << in.m << ' ' << in.c << " mc\n";
	// 	cout << "done\n";
}
int que(int x){
	if(ch.size() == 1) return ch[0].getY(x);

	int l=1, r=ch.size()-1, mid=0, cnt=INF;
	while(r-l>=5){
		mid = md;
		int le = ch[mid-1].getY(x), ri = ch[mid].getY(x);
		cnt = min(cnt, min(le, ri));
		if(le > ri) l = mid+2;
		else r = mid-2;
	}
	for(int i=max(0ll,l-1); i<=min(r+1,(int)ch.size()-1); i++) 
		cnt = min(cnt, ch[i].getY(x));
	return cnt;
}
signed main(){
	cin >> n;
	for(int i=1; i<=n; i++) cin >> a[i];
	vec.pb({-1,-1});
	for(int i=1; i<=n; i++){
		int te = a[i], id = i;
		while(i+1<=n && te>=a[i+1]) i++;
		vec.pb({te, i-id+1});
	}
	n = vec.size()-1;
	for(int i=1; i<=n; i++){
		val[i] = vec[i].fi, cnt[i] = vec[i].se;
		pr[i] = pr[i-1] + cnt[i];
	}
	
	for(int i=1; i<=n; i++) dp[i] = INF;
	Line nw; nw.m = -val[n]; nw.c = val[n]*pr[n];
	add(nw);

	for(int i=n; i>=1; i--){
		dp[i] = que(pr[i-1]);

		Line nw; nw.m = -val[i-1]; nw.c = dp[i] + val[i-1]*pr[n];
		add(nw);
	}
	// for(int i=n; i>=1; i--){
	// 	for(int j=i; j<=n; j++){
	// 		dp[i] = min(dp[i], dp[j+1] + val[j]*pr[n] - val[j]*pr[i-1]);
	// 	}
	// }
	cout << dp[1] << '\n';
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 344 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 604 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 344 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 604 KB Output is correct
10 Correct 1 ms 856 KB Output is correct
11 Correct 1 ms 600 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 392 KB Output is correct
14 Correct 1 ms 604 KB Output is correct
15 Correct 1 ms 348 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 604 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 344 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 604 KB Output is correct
10 Correct 1 ms 856 KB Output is correct
11 Correct 1 ms 600 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 1 ms 392 KB Output is correct
14 Correct 1 ms 604 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 179 ms 31932 KB Output is correct
17 Correct 199 ms 35260 KB Output is correct
18 Correct 155 ms 26036 KB Output is correct
19 Correct 197 ms 34868 KB Output is correct
20 Correct 192 ms 37048 KB Output is correct
21 Correct 195 ms 35260 KB Output is correct
22 Correct 181 ms 32736 KB Output is correct
23 Correct 220 ms 42936 KB Output is correct
24 Correct 200 ms 39196 KB Output is correct
25 Correct 211 ms 39596 KB Output is correct
26 Correct 226 ms 45324 KB Output is correct
27 Correct 185 ms 29876 KB Output is correct
28 Correct 198 ms 36024 KB Output is correct
29 Correct 209 ms 40088 KB Output is correct
30 Correct 243 ms 43952 KB Output is correct

Subtask #4
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 256 ms 17748 KB Output is correct
2 Correct 254 ms 17768 KB Output is correct
3 Correct 272 ms 17936 KB Output is correct
4 Correct 245 ms 17748 KB Output is correct
5 Correct 242 ms 17748 KB Output is correct
6 Correct 254 ms 17908 KB Output is correct
7 Correct 267 ms 17952 KB Output is correct
8 Correct 269 ms 17840 KB Output is correct
9 Correct 260 ms 17712 KB Output is correct
10 Correct 259 ms 17744 KB Output is correct

Subtask #5
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 344 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 344 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 604 KB Output is correct
23 Correct 1 ms 604 KB Output is correct
24 Correct 1 ms 856 KB Output is correct
25 Correct 1 ms 600 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 1 ms 392 KB Output is correct
28 Correct 1 ms 604 KB Output is correct
29 Correct 1 ms 348 KB Output is correct
30 Correct 1 ms 348 KB Output is correct
31 Correct 1 ms 452 KB Output is correct
32 Correct 1 ms 348 KB Output is correct
33 Correct 1 ms 348 KB Output is correct
34 Correct 0 ms 348 KB Output is correct
35 Correct 1 ms 348 KB Output is correct
36 Correct 1 ms 348 KB Output is correct
37 Correct 1 ms 348 KB Output is correct
38 Correct 1 ms 348 KB Output is correct
39 Correct 1 ms 348 KB Output is correct
40 Correct 1 ms 348 KB Output is correct
41 Correct 1 ms 344 KB Output is correct
42 Correct 1 ms 348 KB Output is correct
43 Correct 1 ms 348 KB Output is correct
44 Correct 1 ms 348 KB Output is correct
45 Correct 0 ms 348 KB Output is correct
46 Correct 1 ms 348 KB Output is correct
47 Correct 0 ms 348 KB Output is correct
48 Correct 1 ms 348 KB Output is correct
49 Correct 1 ms 348 KB Output is correct
50 Correct 1 ms 348 KB Output is correct

Subtask #6
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 344 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 344 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 604 KB Output is correct
23 Correct 1 ms 604 KB Output is correct
24 Correct 1 ms 856 KB Output is correct
25 Correct 1 ms 600 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 1 ms 392 KB Output is correct
28 Correct 1 ms 604 KB Output is correct
29 Correct 1 ms 348 KB Output is correct
30 Correct 179 ms 31932 KB Output is correct
31 Correct 199 ms 35260 KB Output is correct
32 Correct 155 ms 26036 KB Output is correct
33 Correct 197 ms 34868 KB Output is correct
34 Correct 192 ms 37048 KB Output is correct
35 Correct 195 ms 35260 KB Output is correct
36 Correct 181 ms 32736 KB Output is correct
37 Correct 220 ms 42936 KB Output is correct
38 Correct 200 ms 39196 KB Output is correct
39 Correct 211 ms 39596 KB Output is correct
40 Correct 226 ms 45324 KB Output is correct
41 Correct 185 ms 29876 KB Output is correct
42 Correct 198 ms 36024 KB Output is correct
43 Correct 209 ms 40088 KB Output is correct
44 Correct 243 ms 43952 KB Output is correct
45 Correct 256 ms 17748 KB Output is correct
46 Correct 254 ms 17768 KB Output is correct
47 Correct 272 ms 17936 KB Output is correct
48 Correct 245 ms 17748 KB Output is correct
49 Correct 242 ms 17748 KB Output is correct
50 Correct 254 ms 17908 KB Output is correct
51 Correct 267 ms 17952 KB Output is correct
52 Correct 269 ms 17840 KB Output is correct
53 Correct 260 ms 17712 KB Output is correct
54 Correct 259 ms 17744 KB Output is correct
55 Correct 1 ms 348 KB Output is correct
56 Correct 1 ms 452 KB Output is correct
57 Correct 1 ms 348 KB Output is correct
58 Correct 1 ms 348 KB Output is correct
59 Correct 0 ms 348 KB Output is correct
60 Correct 1 ms 348 KB Output is correct
61 Correct 1 ms 348 KB Output is correct
62 Correct 1 ms 348 KB Output is correct
63 Correct 1 ms 348 KB Output is correct
64 Correct 1 ms 348 KB Output is correct
65 Correct 1 ms 348 KB Output is correct
66 Correct 1 ms 344 KB Output is correct
67 Correct 1 ms 348 KB Output is correct
68 Correct 1 ms 348 KB Output is correct
69 Correct 1 ms 348 KB Output is correct
70 Correct 0 ms 348 KB Output is correct
71 Correct 1 ms 348 KB Output is correct
72 Correct 0 ms 348 KB Output is correct
73 Correct 1 ms 348 KB Output is correct
74 Correct 1 ms 348 KB Output is correct
75 Correct 1 ms 348 KB Output is correct
76 Correct 170 ms 14164 KB Output is correct
77 Correct 177 ms 14312 KB Output is correct
78 Correct 154 ms 13612 KB Output is correct
79 Correct 163 ms 13772 KB Output is correct
80 Correct 177 ms 14384 KB Output is correct
81 Correct 179 ms 13604 KB Output is correct
82 Correct 182 ms 13648 KB Output is correct
83 Correct 167 ms 14160 KB Output is correct
84 Correct 175 ms 13956 KB Output is correct
85 Correct 167 ms 14200 KB Output is correct
86 Correct 158 ms 13544 KB Output is correct
87 Correct 175 ms 13396 KB Output is correct
88 Correct 162 ms 13908 KB Output is correct
89 Correct 176 ms 13764 KB Output is correct
90 Correct 167 ms 13648 KB Output is correct
91 Correct 159 ms 13500 KB Output is correct
92 Correct 209 ms 39356 KB Output is correct
93 Correct 191 ms 35652 KB Output is correct
94 Correct 171 ms 13064 KB Output is correct
95 Correct 178 ms 14508 KB Output is correct
96 Correct 155 ms 13392 KB Output is correct
97 Correct 167 ms 13652 KB Output is correct
98 Correct 167 ms 14016 KB Output is correct
99 Correct 178 ms 13648 KB Output is correct
100 Correct 160 ms 13652 KB Output is correct