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Submission #584998

# Submission time Handle Problem Language Result Execution time Memory
584998 2022-06-28T08:22:56 Z GioChkhaidze Discharging (NOI20_discharging) C++14
100 / 100
 132 ms 16080 KB 
// Source: https://usaco.guide/general/io

#include <bits/stdc++.h>

#define ll long long
#define f first
#define s second

using namespace std;

const int N = 1e6 + 5;

ll n, a[N], dp[N];
ll inf = 1e15;

struct Line {
	ll k;
	ll b;
	ll val(ll x) {
		return k *x + b;
	}
	pair < ll , ll > intr(Line yo) {
		ll one = yo.b - b;
		ll two = k - yo.k;
		if (two < 0) one *= -1, two *= -1;
		return {one, two};
	}
};

vector < Line > dq;
inline void upd(ll k, ll b) {
	Line lin = {k, b};
	while (dq.size() > 1) {
		Line lina = dq.end()[-1];
		Line linb = dq.end()[-2];
		pair < ll , ll > A = lin.intr(lina);
		pair < ll , ll > B = lina.intr(linb);
		if (A.f / A.s <= B.f / B.s) {
			dq.pop_back();
		}
			else break;
	}
	dq.push_back(lin);
}

ll get(ll x) {
	int l = 1, r = dq.size() - 1, mid, res = 0;
	while (l <= r) {
		mid = ((l + r) >> 1);
		if (dq[mid - 1].val(x) >= dq[mid].val(x)) {
			l = mid + 1, res = mid;
		}
			else {
			r = mid - 1;
		}
	}
	return dq[res].val(x);
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	cin >> n;
	for (int i = 1; i <= n; ++i) {
		cin >> a[i];
		if (1 < i && a[i - 1] > a[i]) {
			a[i] = a[i - 1];
		}
	}

	dq.push_back({0, 0});
	for (int i = 1; i <= n; ++i) {
		/*
		dp[i] = inf;
		for (int j = i - 1; j >= 0; --j) {
			dp[i] = min(dp[i], dp[j] - j * a[i] + n * a[i]);
		} */
		dp[i] = get(a[i]) + n * a[i];
		upd(-i, dp[i]);
	}

	cout << dp[n] << "\n";
}
/*


dp[......]

dp[1..j]


.... j + 1 ... i   = max is a[i]

dp[i] = dp[j] + ( n - j ) * a[i]

dp[i] = dp[j] - j * a[i] + n * a[i];

Y = K * X + B

X = a[i]
K = -j;
B = dp[j];



*/

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 97 ms 15904 KB Output is correct
17 Correct 104 ms 15904 KB Output is correct
18 Correct 93 ms 15960 KB Output is correct
19 Correct 112 ms 15948 KB Output is correct
20 Correct 103 ms 15856 KB Output is correct
21 Correct 100 ms 15892 KB Output is correct
22 Correct 98 ms 15856 KB Output is correct
23 Correct 117 ms 15912 KB Output is correct
24 Correct 104 ms 15948 KB Output is correct
25 Correct 109 ms 15944 KB Output is correct
26 Correct 115 ms 16080 KB Output is correct
27 Correct 101 ms 15948 KB Output is correct
28 Correct 101 ms 15956 KB Output is correct
29 Correct 109 ms 15916 KB Output is correct
30 Correct 118 ms 15928 KB Output is correct

Subtask #4
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 130 ms 15896 KB Output is correct
2 Correct 114 ms 15912 KB Output is correct
3 Correct 112 ms 15892 KB Output is correct
4 Correct 113 ms 15948 KB Output is correct
5 Correct 132 ms 15992 KB Output is correct
6 Correct 103 ms 15944 KB Output is correct
7 Correct 105 ms 15876 KB Output is correct
8 Correct 103 ms 15948 KB Output is correct
9 Correct 115 ms 15948 KB Output is correct
10 Correct 109 ms 15900 KB Output is correct

Subtask #5
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 340 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 1 ms 340 KB Output is correct
31 Correct 0 ms 340 KB Output is correct
32 Correct 0 ms 340 KB Output is correct
33 Correct 1 ms 340 KB Output is correct
34 Correct 1 ms 340 KB Output is correct
35 Correct 1 ms 340 KB Output is correct
36 Correct 1 ms 340 KB Output is correct
37 Correct 1 ms 340 KB Output is correct
38 Correct 1 ms 340 KB Output is correct
39 Correct 1 ms 340 KB Output is correct
40 Correct 1 ms 340 KB Output is correct
41 Correct 1 ms 340 KB Output is correct
42 Correct 1 ms 340 KB Output is correct
43 Correct 1 ms 340 KB Output is correct
44 Correct 0 ms 340 KB Output is correct
45 Correct 1 ms 340 KB Output is correct
46 Correct 1 ms 340 KB Output is correct
47 Correct 1 ms 340 KB Output is correct
48 Correct 1 ms 340 KB Output is correct
49 Correct 1 ms 340 KB Output is correct
50 Correct 1 ms 340 KB Output is correct

Subtask #6
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 340 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 97 ms 15904 KB Output is correct
31 Correct 104 ms 15904 KB Output is correct
32 Correct 93 ms 15960 KB Output is correct
33 Correct 112 ms 15948 KB Output is correct
34 Correct 103 ms 15856 KB Output is correct
35 Correct 100 ms 15892 KB Output is correct
36 Correct 98 ms 15856 KB Output is correct
37 Correct 117 ms 15912 KB Output is correct
38 Correct 104 ms 15948 KB Output is correct
39 Correct 109 ms 15944 KB Output is correct
40 Correct 115 ms 16080 KB Output is correct
41 Correct 101 ms 15948 KB Output is correct
42 Correct 101 ms 15956 KB Output is correct
43 Correct 109 ms 15916 KB Output is correct
44 Correct 118 ms 15928 KB Output is correct
45 Correct 130 ms 15896 KB Output is correct
46 Correct 114 ms 15912 KB Output is correct
47 Correct 112 ms 15892 KB Output is correct
48 Correct 113 ms 15948 KB Output is correct
49 Correct 132 ms 15992 KB Output is correct
50 Correct 103 ms 15944 KB Output is correct
51 Correct 105 ms 15876 KB Output is correct
52 Correct 103 ms 15948 KB Output is correct
53 Correct 115 ms 15948 KB Output is correct
54 Correct 109 ms 15900 KB Output is correct
55 Correct 1 ms 340 KB Output is correct
56 Correct 0 ms 340 KB Output is correct
57 Correct 0 ms 340 KB Output is correct
58 Correct 1 ms 340 KB Output is correct
59 Correct 1 ms 340 KB Output is correct
60 Correct 1 ms 340 KB Output is correct
61 Correct 1 ms 340 KB Output is correct
62 Correct 1 ms 340 KB Output is correct
63 Correct 1 ms 340 KB Output is correct
64 Correct 1 ms 340 KB Output is correct
65 Correct 1 ms 340 KB Output is correct
66 Correct 1 ms 340 KB Output is correct
67 Correct 1 ms 340 KB Output is correct
68 Correct 1 ms 340 KB Output is correct
69 Correct 0 ms 340 KB Output is correct
70 Correct 1 ms 340 KB Output is correct
71 Correct 1 ms 340 KB Output is correct
72 Correct 1 ms 340 KB Output is correct
73 Correct 1 ms 340 KB Output is correct
74 Correct 1 ms 340 KB Output is correct
75 Correct 1 ms 340 KB Output is correct
76 Correct 101 ms 15948 KB Output is correct
77 Correct 108 ms 15908 KB Output is correct
78 Correct 105 ms 15928 KB Output is correct
79 Correct 118 ms 15840 KB Output is correct
80 Correct 114 ms 15828 KB Output is correct
81 Correct 102 ms 15896 KB Output is correct
82 Correct 117 ms 15856 KB Output is correct
83 Correct 119 ms 15920 KB Output is correct
84 Correct 107 ms 15948 KB Output is correct
85 Correct 107 ms 15848 KB Output is correct
86 Correct 107 ms 15864 KB Output is correct
87 Correct 108 ms 15872 KB Output is correct
88 Correct 108 ms 15928 KB Output is correct
89 Correct 109 ms 15928 KB Output is correct
90 Correct 104 ms 15916 KB Output is correct
91 Correct 106 ms 15856 KB Output is correct
92 Correct 122 ms 15888 KB Output is correct
93 Correct 118 ms 15932 KB Output is correct
94 Correct 99 ms 15916 KB Output is correct
95 Correct 129 ms 15928 KB Output is correct
96 Correct 119 ms 15860 KB Output is correct
97 Correct 105 ms 15960 KB Output is correct
98 Correct 107 ms 15912 KB Output is correct
99 Correct 105 ms 15932 KB Output is correct
100 Correct 121 ms 15904 KB Output is correct