#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
typedef tree<int,null_type,less<int>,rb_tree_tag,
tree_order_statistics_node_update> indexed_set;
typedef long long ll;
typedef double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<ld,ld> pld;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
#define pb push_back
#define popb pop_back
#define pp pop_back
#define pf push_front
#define popf pop_front
#define all(x) (x).begin(),(x).end()
#define ff first
#define ss second
#define int ll
int nx[4] = {0,0,1,-1}, ny[4] = {1,-1,0,0};
ll gcd(ll a , ll b) {return b ? gcd(b , a % b) : a ;}
ll lcm(ll a , ll b) {return (a * b) / gcd(a , b);}
const ld MOD = 1e20;
const int nax = 1e5 + 4;
int n, g, sz = 1;
ld dp[(1 << 15)][15];
string s;
vi A[15];
vector<ld> st;
ld exp_front[nax], exp_back[nax];
void update(int i, ld val)
{
i += sz;
st[i] = val;
i /= 2;
while(i)
{
st[i] = st[2 * i] + st[2 * i + 1];
i /= 2;
}
}
ld query(int p, int l, int r, int i, int j)
{
if( i> j)
return 0;
if(l >= i && r <= j)
return st[p];
int m = (l+r)/2;
return query(2 * p,l,m,i,min(j,m))
+ query(2 * p + 1,m+1,r,max(i,m+1),j);
}
ld f(int mask, int b)
{
if(fabs(dp[mask][b] + 1) > 1e-9)
return dp[mask][b];
ld rep = 0, ans = 1e20;
for(auto e: A[b])
{
ld addfront = (ld)(query(1,0,sz-1,0,e));
ld addback = (ld)(query(1,0,sz - 1,e,n-1));
rep += min(exp_front[e] + addfront,exp_back[e] + addback);
}
for(auto e: A[b])
update(e,1);
if(mask == (1 << g)-1)
ans = 0;
for(int j = 0; j < g; j++)
{
if((1 << j) & mask)
continue;
ans = min(ans,f(mask + (1 << j),j));
}
for(auto e: A[b])
update(e,0);
//cout << mask << ' ' << b << ' ' << ans << ' ' << rep << '\n';
return dp[mask][b] = ans + rep;
}
void solve()
{
cin >> s;
n = s.length();
while(sz < n)
sz = (sz << 1);
st.assign(2 * sz + 1,0);
for(int i = 0; i < n ;i ++)
{
int c =s[i] - 'A';
A[c].pb(i);
g= max(g,c + 1);
}
for(int i = 0; i < (1 << g); i++)
{
for(int j = 0; j < g; j++)
dp[i][j] =-1;
}
for(int group = 0; group < g; group ++)
{
int szi = A[group].size();
for(int i =0; i < szi; i++)
{
exp_front[A[group][i]] = (ld)(((ld)(i) * (ld)((i + 1.0)))/2.0);
exp_front[A[group][i]] /= (ld)(i+1.0);
exp_back[A[group][i]] = (ld)(((ld)((szi -i - 1.0))*(ld)((szi - i)))/2.0);
exp_back[A[group][i]] /= (ld)(szi - i);
//cout << A[group][i] << ' ' << exp_front[A[group][i]] << ' ' << exp_back[A[group][i]] << '\n';
}
}
ld ans = 1e20;
for(int i = 0; i < g; i++)
ans = min(ans,f((1 << i),i));
cout << setprecision(100) << ans;
}
int32_t main()
{
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
int tt = 1;
while(tt --)
solve();
}
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
340 KB |
Output is correct |
2 |
Correct |
0 ms |
340 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 |
340 KB |
Output is correct |
6 |
Correct |
34 ms |
4240 KB |
Output is correct |
7 |
Correct |
39 ms |
4496 KB |
Output is correct |
8 |
Correct |
43 ms |
4624 KB |
Output is correct |
9 |
Correct |
39 ms |
4624 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
0 ms |
212 KB |
Output is correct |
2 |
Correct |
0 ms |
340 KB |
Output is correct |
3 |
Correct |
2 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 |
0 ms |
340 KB |
Output is correct |
7 |
Correct |
1 ms |
340 KB |
Output is correct |
8 |
Correct |
0 ms |
340 KB |
Output is correct |
9 |
Correct |
1 ms |
340 KB |
Output is correct |
10 |
Correct |
0 ms |
340 KB |
Output is correct |
11 |
Correct |
0 ms |
340 KB |
Output is correct |
12 |
Correct |
0 ms |
340 KB |
Output is correct |
13 |
Correct |
0 ms |
340 KB |
Output is correct |
14 |
Correct |
0 ms |
340 KB |
Output is correct |
15 |
Correct |
1 ms |
340 KB |
Output is correct |
16 |
Correct |
1 ms |
340 KB |
Output is correct |
17 |
Correct |
0 ms |
340 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
0 ms |
212 KB |
Output is correct |
2 |
Correct |
0 ms |
340 KB |
Output is correct |
3 |
Correct |
2 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 |
0 ms |
340 KB |
Output is correct |
7 |
Correct |
1 ms |
340 KB |
Output is correct |
8 |
Correct |
0 ms |
340 KB |
Output is correct |
9 |
Correct |
1 ms |
340 KB |
Output is correct |
10 |
Correct |
0 ms |
340 KB |
Output is correct |
11 |
Correct |
0 ms |
340 KB |
Output is correct |
12 |
Correct |
0 ms |
340 KB |
Output is correct |
13 |
Correct |
0 ms |
340 KB |
Output is correct |
14 |
Correct |
0 ms |
340 KB |
Output is correct |
15 |
Correct |
1 ms |
340 KB |
Output is correct |
16 |
Correct |
1 ms |
340 KB |
Output is correct |
17 |
Correct |
0 ms |
340 KB |
Output is correct |
18 |
Correct |
0 ms |
212 KB |
Output is correct |
19 |
Correct |
0 ms |
212 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 |
0 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 |
0 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 |
1 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 |
390 ms |
852 KB |
Output is correct |
36 |
Correct |
411 ms |
852 KB |
Output is correct |
37 |
Correct |
1652 ms |
980 KB |
Output is correct |
38 |
Correct |
1522 ms |
852 KB |
Output is correct |
39 |
Correct |
1511 ms |
980 KB |
Output is correct |
40 |
Correct |
1616 ms |
852 KB |
Output is correct |
41 |
Correct |
1708 ms |
980 KB |
Output is correct |
42 |
Correct |
1692 ms |
852 KB |
Output is correct |
43 |
Correct |
1697 ms |
980 KB |
Output is correct |
44 |
Correct |
1686 ms |
852 KB |
Output is correct |
45 |
Correct |
1720 ms |
980 KB |
Output is correct |
46 |
Correct |
1706 ms |
852 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
340 KB |
Output is correct |
2 |
Correct |
0 ms |
340 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 |
340 KB |
Output is correct |
6 |
Correct |
34 ms |
4240 KB |
Output is correct |
7 |
Correct |
39 ms |
4496 KB |
Output is correct |
8 |
Correct |
43 ms |
4624 KB |
Output is correct |
9 |
Correct |
39 ms |
4624 KB |
Output is correct |
10 |
Correct |
0 ms |
212 KB |
Output is correct |
11 |
Correct |
0 ms |
340 KB |
Output is correct |
12 |
Correct |
2 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 |
0 ms |
340 KB |
Output is correct |
16 |
Correct |
1 ms |
340 KB |
Output is correct |
17 |
Correct |
0 ms |
340 KB |
Output is correct |
18 |
Correct |
1 ms |
340 KB |
Output is correct |
19 |
Correct |
0 ms |
340 KB |
Output is correct |
20 |
Correct |
0 ms |
340 KB |
Output is correct |
21 |
Correct |
0 ms |
340 KB |
Output is correct |
22 |
Correct |
0 ms |
340 KB |
Output is correct |
23 |
Correct |
0 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 |
0 ms |
340 KB |
Output is correct |
27 |
Correct |
0 ms |
212 KB |
Output is correct |
28 |
Correct |
0 ms |
212 KB |
Output is correct |
29 |
Correct |
1 ms |
340 KB |
Output is correct |
30 |
Correct |
1 ms |
340 KB |
Output is correct |
31 |
Correct |
1 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 |
0 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 |
0 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 |
390 ms |
852 KB |
Output is correct |
45 |
Correct |
411 ms |
852 KB |
Output is correct |
46 |
Correct |
1652 ms |
980 KB |
Output is correct |
47 |
Correct |
1522 ms |
852 KB |
Output is correct |
48 |
Correct |
1511 ms |
980 KB |
Output is correct |
49 |
Correct |
1616 ms |
852 KB |
Output is correct |
50 |
Correct |
1708 ms |
980 KB |
Output is correct |
51 |
Correct |
1692 ms |
852 KB |
Output is correct |
52 |
Correct |
1697 ms |
980 KB |
Output is correct |
53 |
Correct |
1686 ms |
852 KB |
Output is correct |
54 |
Correct |
1720 ms |
980 KB |
Output is correct |
55 |
Correct |
1706 ms |
852 KB |
Output is correct |
56 |
Correct |
31 ms |
4052 KB |
Output is correct |
57 |
Correct |
62 ms |
4156 KB |
Output is correct |
58 |
Correct |
1 ms |
340 KB |
Output is correct |
59 |
Correct |
0 ms |
212 KB |
Output is correct |
60 |
Correct |
0 ms |
212 KB |
Output is correct |
61 |
Correct |
0 ms |
340 KB |
Output is correct |
62 |
Correct |
1 ms |
340 KB |
Output is correct |
63 |
Correct |
34 ms |
4240 KB |
Output is correct |
64 |
Correct |
42 ms |
4496 KB |
Output is correct |
65 |
Correct |
41 ms |
4624 KB |
Output is correct |
66 |
Correct |
40 ms |
4624 KB |
Output is correct |
67 |
Correct |
0 ms |
212 KB |
Output is correct |
68 |
Correct |
0 ms |
340 KB |
Output is correct |
69 |
Correct |
1 ms |
340 KB |
Output is correct |
70 |
Correct |
1 ms |
340 KB |
Output is correct |
71 |
Correct |
2 ms |
340 KB |
Output is correct |
72 |
Correct |
0 ms |
340 KB |
Output is correct |
73 |
Correct |
1 ms |
340 KB |
Output is correct |
74 |
Correct |
0 ms |
340 KB |
Output is correct |
75 |
Correct |
1 ms |
340 KB |
Output is correct |
76 |
Correct |
1 ms |
340 KB |
Output is correct |
77 |
Correct |
1 ms |
340 KB |
Output is correct |
78 |
Correct |
0 ms |
340 KB |
Output is correct |
79 |
Correct |
1 ms |
340 KB |
Output is correct |
80 |
Correct |
1 ms |
340 KB |
Output is correct |
81 |
Correct |
1 ms |
340 KB |
Output is correct |
82 |
Correct |
1 ms |
340 KB |
Output is correct |
83 |
Correct |
0 ms |
340 KB |
Output is correct |
84 |
Correct |
383 ms |
852 KB |
Output is correct |
85 |
Correct |
403 ms |
852 KB |
Output is correct |
86 |
Correct |
1648 ms |
980 KB |
Output is correct |
87 |
Correct |
1523 ms |
852 KB |
Output is correct |
88 |
Correct |
1514 ms |
980 KB |
Output is correct |
89 |
Correct |
1616 ms |
852 KB |
Output is correct |
90 |
Correct |
1734 ms |
980 KB |
Output is correct |
91 |
Correct |
1752 ms |
852 KB |
Output is correct |
92 |
Correct |
1708 ms |
852 KB |
Output is correct |
93 |
Correct |
1695 ms |
852 KB |
Output is correct |
94 |
Correct |
1716 ms |
852 KB |
Output is correct |
95 |
Correct |
1688 ms |
852 KB |
Output is correct |
96 |
Execution timed out |
2075 ms |
8404 KB |
Time limit exceeded |
97 |
Halted |
0 ms |
0 KB |
- |