BZOJ3156 防御准备

 1 /**************************************************************
 2     Problem: 3156
 3     User: rausen
 4     Language: C++
 5     Result: Accepted
 6     Time:1532 ms
 7     Memory:28152 kb
 8 ****************************************************************/
 9  
10 #include <cstdio>
11 #include <algorithm>
12  
13 using namespace std;
14 typedef long long ll;
15 const int N = 1000005;
16 ll a[N], f[N], g[N], ans;
17 int n, l, r, q[N];
18  
19 inline int read(){
20     int x = 0;
21     char ch = getchar();
22     while (ch < ‘0‘ || ch > ‘9‘)
23         ch = getchar();
24     while (ch >= ‘0‘ && ch <= ‘9‘){
25         x = x * 10 + ch - ‘0‘;
26         ch = getchar();
27     }
28     return x;
29 }
30  
31 inline ll calc_f(ll i, ll x){
32     return (ll) g[x] + a[i] - i * x * 2 + (i - 1) * i;
33 }
34  
35 inline ll calc_g(ll x){
36     return (ll) f[x] + x * (x + 1);
37 }
38  
39 inline ll calc_ans(ll x){
40     return (ll) f[x] + (n - x) * (n - x + 1);
41 }
42  
43 bool pop_head(ll i){
44     ll x = q[l], y = q[l + 1];
45     return ((ll) i * (y - x) * 2 >= (ll) g[y] - g[x]);
46 }
47  
48 bool pop_tail(ll i){
49     ll x = q[r - 1], y = q[r];
50     return ((ll) (g[i] - g[y]) * (y - x) < (ll) (g[y] - g[x]) * (i - y));
51 }
52  
53 int main(){
54     n = read();
55     for (int i = n; i; --i)
56         a[i] = read() << 1;
57     f[1] = a[1], g[1] = calc_g(1), ans = calc_ans(1);
58     q[1] = l = r = 1;
59     for (int i = 2; i <= n; ++i){
60         while (l < r && pop_head(i)) ++l;
61         f[i] = calc_f(i, q[l]);
62         g[i] = calc_g(i);
63         ans = min(ans, calc_ans(i));
64         while (l < r && pop_tail(i)) --r;
65         q[++r] = i;
66     }
67     printf("%lld\n", ans >> 1);
68     return 0;
69 }