#include <bits/stdc++.h>
#define int long long
#define lgd long double
using namespace std;
lgd dp[(int)(1 << 15) + 42];
vector<int> vals[16];
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
string s;
cin >> s;
int n = (int)s.size();
/*for (int i = 0; i < n; i++)
s += 'A';*/
int g = 0;
vector<char> comp {};
for (int i = 0; i < n; i++)
comp.push_back(s[i]);
sort(comp.begin(), comp.end());
comp.resize(unique(comp.begin(), comp.end()) - comp.begin());
for (int i = 0; i < n; i++)
vals[lower_bound(comp.begin(), comp.end(), s[i]) - comp.begin()].push_back(i);
g = (int)comp.size();
//cout << g << '\n';
dp[0] = 0;
for (int mask = 1; mask < (1 << g); mask++) {
dp[mask] = 1e18;
vector<int> pref (n, 0);
for (int group = 0; group < g; group++)
if (mask & (1 << group))
for (auto& x: vals[group])
pref[x]++;
for (int pos = 1; pos < n; pos++)
pref[pos] += pref[pos - 1];
for (int lst = 0; lst < g; lst++) {
if (mask & (1 << lst)) {
// put everyone to the left
lgd esp = 0;
for (int id = 0; id < (int)vals[lst].size(); id++) {
// inversions bcs of other groups, remove the ones from lst
esp += pref[vals[lst][id]] - (id + 1);
}
// add expected inversions from lst permutations
lgd transi = esp + ((int)vals[lst].size() * ((int)vals[lst].size() - 1)) / 4.;
// fix right limit
for (int id = (int)vals[lst].size() - 1; id >= 0; id--) {
// remove from the left side
esp -= pref[vals[lst][id]];
esp += (id + 1);
// inversions bcs of other groups
esp += pref.back() - pref[vals[lst][id]];
// remove from lst
esp -= (int)vals[lst].size() - (id + 1);
transi = min(transi, esp + (((id) * (id - 1)) + ((int)vals[lst].size() - id) * ((int)vals[lst].size() - (id + 1))) / 4.);
}
dp[mask] = min(dp[mask], dp[mask ^ (1 << lst)] + transi);
}
}
}
cout << setprecision(42) << dp[(1 << g) - 1] << '\n';
}
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
340 KB |
Output is correct |
2 |
Correct |
0 ms |
212 KB |
Output is correct |
3 |
Correct |
1 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 |
4 ms |
1864 KB |
Output is correct |
7 |
Correct |
4 ms |
2120 KB |
Output is correct |
8 |
Correct |
4 ms |
2248 KB |
Output is correct |
9 |
Correct |
4 ms |
2248 KB |
Output is correct |
# |
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 |
1 ms |
212 KB |
Output is correct |
4 |
Correct |
1 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 |
1 ms |
212 KB |
Output is correct |
8 |
Correct |
0 ms |
212 KB |
Output is correct |
9 |
Correct |
1 ms |
212 KB |
Output is correct |
10 |
Correct |
0 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 |
1 ms |
212 KB |
Output is correct |
14 |
Correct |
0 ms |
212 KB |
Output is correct |
15 |
Correct |
0 ms |
212 KB |
Output is correct |
16 |
Correct |
0 ms |
212 KB |
Output is correct |
17 |
Correct |
0 ms |
212 KB |
Output is correct |
# |
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 |
1 ms |
212 KB |
Output is correct |
4 |
Correct |
1 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 |
1 ms |
212 KB |
Output is correct |
8 |
Correct |
0 ms |
212 KB |
Output is correct |
9 |
Correct |
1 ms |
212 KB |
Output is correct |
10 |
Correct |
0 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 |
1 ms |
212 KB |
Output is correct |
14 |
Correct |
0 ms |
212 KB |
Output is correct |
15 |
Correct |
0 ms |
212 KB |
Output is correct |
16 |
Correct |
0 ms |
212 KB |
Output is correct |
17 |
Correct |
0 ms |
212 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 |
212 KB |
Output is correct |
21 |
Correct |
1 ms |
212 KB |
Output is correct |
22 |
Correct |
0 ms |
212 KB |
Output is correct |
23 |
Correct |
0 ms |
212 KB |
Output is correct |
24 |
Correct |
1 ms |
212 KB |
Output is correct |
25 |
Correct |
0 ms |
212 KB |
Output is correct |
26 |
Correct |
1 ms |
212 KB |
Output is correct |
27 |
Correct |
0 ms |
212 KB |
Output is correct |
28 |
Correct |
1 ms |
212 KB |
Output is correct |
29 |
Correct |
0 ms |
212 KB |
Output is correct |
30 |
Correct |
0 ms |
212 KB |
Output is correct |
31 |
Correct |
0 ms |
212 KB |
Output is correct |
32 |
Correct |
0 ms |
212 KB |
Output is correct |
33 |
Correct |
0 ms |
212 KB |
Output is correct |
34 |
Correct |
0 ms |
212 KB |
Output is correct |
35 |
Correct |
1 ms |
468 KB |
Output is correct |
36 |
Correct |
1 ms |
468 KB |
Output is correct |
37 |
Correct |
86 ms |
468 KB |
Output is correct |
38 |
Correct |
85 ms |
468 KB |
Output is correct |
39 |
Correct |
92 ms |
580 KB |
Output is correct |
40 |
Correct |
85 ms |
532 KB |
Output is correct |
41 |
Correct |
81 ms |
472 KB |
Output is correct |
42 |
Correct |
82 ms |
572 KB |
Output is correct |
43 |
Correct |
82 ms |
576 KB |
Output is correct |
44 |
Correct |
87 ms |
476 KB |
Output is correct |
45 |
Correct |
84 ms |
556 KB |
Output is correct |
46 |
Correct |
83 ms |
572 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
340 KB |
Output is correct |
2 |
Correct |
0 ms |
212 KB |
Output is correct |
3 |
Correct |
1 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 |
4 ms |
1864 KB |
Output is correct |
7 |
Correct |
4 ms |
2120 KB |
Output is correct |
8 |
Correct |
4 ms |
2248 KB |
Output is correct |
9 |
Correct |
4 ms |
2248 KB |
Output is correct |
10 |
Correct |
0 ms |
212 KB |
Output is correct |
11 |
Correct |
0 ms |
212 KB |
Output is correct |
12 |
Correct |
1 ms |
212 KB |
Output is correct |
13 |
Correct |
1 ms |
212 KB |
Output is correct |
14 |
Correct |
1 ms |
212 KB |
Output is correct |
15 |
Correct |
1 ms |
212 KB |
Output is correct |
16 |
Correct |
1 ms |
212 KB |
Output is correct |
17 |
Correct |
0 ms |
212 KB |
Output is correct |
18 |
Correct |
1 ms |
212 KB |
Output is correct |
19 |
Correct |
0 ms |
212 KB |
Output is correct |
20 |
Correct |
1 ms |
212 KB |
Output is correct |
21 |
Correct |
0 ms |
212 KB |
Output is correct |
22 |
Correct |
1 ms |
212 KB |
Output is correct |
23 |
Correct |
0 ms |
212 KB |
Output is correct |
24 |
Correct |
0 ms |
212 KB |
Output is correct |
25 |
Correct |
0 ms |
212 KB |
Output is correct |
26 |
Correct |
0 ms |
212 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 |
212 KB |
Output is correct |
30 |
Correct |
1 ms |
212 KB |
Output is correct |
31 |
Correct |
0 ms |
212 KB |
Output is correct |
32 |
Correct |
0 ms |
212 KB |
Output is correct |
33 |
Correct |
1 ms |
212 KB |
Output is correct |
34 |
Correct |
0 ms |
212 KB |
Output is correct |
35 |
Correct |
1 ms |
212 KB |
Output is correct |
36 |
Correct |
0 ms |
212 KB |
Output is correct |
37 |
Correct |
1 ms |
212 KB |
Output is correct |
38 |
Correct |
0 ms |
212 KB |
Output is correct |
39 |
Correct |
0 ms |
212 KB |
Output is correct |
40 |
Correct |
0 ms |
212 KB |
Output is correct |
41 |
Correct |
0 ms |
212 KB |
Output is correct |
42 |
Correct |
0 ms |
212 KB |
Output is correct |
43 |
Correct |
0 ms |
212 KB |
Output is correct |
44 |
Correct |
1 ms |
468 KB |
Output is correct |
45 |
Correct |
1 ms |
468 KB |
Output is correct |
46 |
Correct |
86 ms |
468 KB |
Output is correct |
47 |
Correct |
85 ms |
468 KB |
Output is correct |
48 |
Correct |
92 ms |
580 KB |
Output is correct |
49 |
Correct |
85 ms |
532 KB |
Output is correct |
50 |
Correct |
81 ms |
472 KB |
Output is correct |
51 |
Correct |
82 ms |
572 KB |
Output is correct |
52 |
Correct |
82 ms |
576 KB |
Output is correct |
53 |
Correct |
87 ms |
476 KB |
Output is correct |
54 |
Correct |
84 ms |
556 KB |
Output is correct |
55 |
Correct |
83 ms |
572 KB |
Output is correct |
56 |
Correct |
1 ms |
212 KB |
Output is correct |
57 |
Correct |
12 ms |
724 KB |
Output is correct |
58 |
Correct |
0 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 |
212 KB |
Output is correct |
62 |
Correct |
1 ms |
340 KB |
Output is correct |
63 |
Correct |
5 ms |
1864 KB |
Output is correct |
64 |
Correct |
5 ms |
2120 KB |
Output is correct |
65 |
Correct |
5 ms |
2244 KB |
Output is correct |
66 |
Correct |
5 ms |
2248 KB |
Output is correct |
67 |
Correct |
0 ms |
212 KB |
Output is correct |
68 |
Correct |
1 ms |
212 KB |
Output is correct |
69 |
Correct |
1 ms |
212 KB |
Output is correct |
70 |
Correct |
1 ms |
212 KB |
Output is correct |
71 |
Correct |
1 ms |
212 KB |
Output is correct |
72 |
Correct |
1 ms |
212 KB |
Output is correct |
73 |
Correct |
0 ms |
212 KB |
Output is correct |
74 |
Correct |
1 ms |
212 KB |
Output is correct |
75 |
Correct |
0 ms |
212 KB |
Output is correct |
76 |
Correct |
1 ms |
212 KB |
Output is correct |
77 |
Correct |
0 ms |
212 KB |
Output is correct |
78 |
Correct |
1 ms |
212 KB |
Output is correct |
79 |
Correct |
1 ms |
212 KB |
Output is correct |
80 |
Correct |
1 ms |
212 KB |
Output is correct |
81 |
Correct |
0 ms |
212 KB |
Output is correct |
82 |
Correct |
0 ms |
212 KB |
Output is correct |
83 |
Correct |
1 ms |
212 KB |
Output is correct |
84 |
Correct |
1 ms |
468 KB |
Output is correct |
85 |
Correct |
1 ms |
468 KB |
Output is correct |
86 |
Correct |
87 ms |
572 KB |
Output is correct |
87 |
Correct |
93 ms |
524 KB |
Output is correct |
88 |
Correct |
86 ms |
572 KB |
Output is correct |
89 |
Correct |
84 ms |
648 KB |
Output is correct |
90 |
Correct |
83 ms |
580 KB |
Output is correct |
91 |
Correct |
85 ms |
468 KB |
Output is correct |
92 |
Correct |
89 ms |
576 KB |
Output is correct |
93 |
Correct |
88 ms |
548 KB |
Output is correct |
94 |
Correct |
81 ms |
572 KB |
Output is correct |
95 |
Correct |
82 ms |
468 KB |
Output is correct |
96 |
Execution timed out |
2057 ms |
2400 KB |
Time limit exceeded |
97 |
Halted |
0 ms |
0 KB |
- |