#include<bits/stdc++.h>
using namespace std;
using ll = long long;
ll exp_inv(ll x) {
return x * (x-1);
}
int main() {
char a = 'A';
string s; cin >> s;
const int G = 15;
int n = s.size();
if (n == 1) {
cout << "0\n";
return 0;
}
vector suml(G, vector(G, vector(n, 0ll)));
vector sumr(G, vector(G, vector(n, 0ll)));
vector cl(G, vector(n, 0ll));
vector cr(G, vector(n, 0ll));
vector ix(G, vector<int>());
for (int c1 = 0; c1 < G; c1++) {
for (int c2 = 0; c2 < G; c2++) {
ll res = 0, cur = 0;
for (int i = 0; i < n; i++) {
if (s[i] == c1+a)
res += cur;
else if (s[i] == c2+a)
cur++;
suml[c1][c2][i] = res;
}
}
}
for (int c1 = 0; c1 < G; c1++) {
for (int c2 = 0; c2 < G; c2++) {
ll res = 0, cur = 0;
for (int i = n-1; i >= 0; i --) {
if (s[i] == c1+a)
res += cur;
else if (s[i] == c2+a)
cur++;
sumr[c1][c2][i] = res;
}
}
}
for (int j = 0; j < G; j++) {
int c = 0;
for (int i = 0; i < n;i ++) {
if (s[i] == j+a)
c++;
cl[j][i] = c;
}
}
for (int j = 0; j < G; j++) {
int c = 0;
for (int i = n-1; i >= 0; i--) {
if (s[i] == j+a)
c++;
cr[j][i] = c;
}
}
for (int i = 0; i < n ;i++)
ix[s[i] - a].push_back(i);
vector memo(1<<G, (ll)1e18);
memo[(1<<G)-1] = 0;
for (int used = (1<<G)-1-1; used >= 0; used--) {
ll& res = memo[used];
for (int i = 0 ;i < G; i++) {
if (used&1<<i) continue;
auto f = [&](int j) {
ll sum = 0;
for (int c2 = 0; c2 < G; c2++) {
if (used&1<<c2) {
if (j) sum += suml[i][c2][j-1];
sum += sumr[i][c2][j];
}
}
return sum * 4 + exp_inv(cr[i][j]) + (j ? exp_inv(cl[i][j-1]) : 0);
};
int l = -1, r = (int)ix[i].size()-2;
while (l < r-1) {
int m = (l+r) / 2;
ll a = f(ix[i][m]), b = f(ix[i][m+1]);
if (a == b) break;
else if (a < b) r = m;
else l = m;
}
for (int j = (l == -1 || l >= (int)ix[i].size()) ? 0 : ix[i][l];
j <= (r >= 0 ? ix[i][r]+1 : 0) && j < n; j++) {
res = min(res, f(j) + memo[used |1<<i]);
}
}
};
ll ans;
if (n > 10000) ans = exp_inv(n / 2) + exp_inv(n - n / 2);
else ans = memo[0];
cout << ans / 4;
if (ans%4 == 1) cout << ".25";
if (ans%4 == 2) cout << ".5";
if (ans%4== 3) cout << ".75";
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
39 ms |
3924 KB |
found '100800.5000000000', expected '100800.5000000000', error '0.0000000000' |
| 2 |
Correct |
0 ms |
212 KB |
found '0.0000000000', expected '0.0000000000', error '-0.0000000000' |
| 3 |
Correct |
14 ms |
596 KB |
found '0.0000000000', expected '0.0000000000', error '-0.0000000000' |
| 4 |
Correct |
19 ms |
604 KB |
found '1.0000000000', expected '1.0000000000', error '0.0000000000' |
| 5 |
Correct |
34 ms |
4308 KB |
found '124002.0000000000', expected '124002.0000000000', error '0.0000000000' |
| 6 |
Correct |
209 ms |
297140 KB |
found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000' |
| 7 |
Correct |
232 ms |
354768 KB |
found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000' |
| 8 |
Correct |
281 ms |
377924 KB |
found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000' |
| 9 |
Correct |
259 ms |
377936 KB |
found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000' |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
22 ms |
596 KB |
found '1.0000000000', expected '1.0000000000', error '0.0000000000' |
| 2 |
Correct |
25 ms |
844 KB |
found '1225.0000000000', expected '1225.0000000000', error '0.0000000000' |
| 3 |
Correct |
91 ms |
944 KB |
found '1023.0000000000', expected '1023.0000000000', error '0.0000000000' |
| 4 |
Correct |
142 ms |
932 KB |
found '294.0000000000', expected '294.0000000000', error '0.0000000000' |
| 5 |
Incorrect |
24 ms |
852 KB |
1st numbers differ - expected: '1087.0000000000', found: '1339.0000000000', error = '0.2318307268' |
| 6 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
22 ms |
596 KB |
found '1.0000000000', expected '1.0000000000', error '0.0000000000' |
| 2 |
Correct |
25 ms |
844 KB |
found '1225.0000000000', expected '1225.0000000000', error '0.0000000000' |
| 3 |
Correct |
91 ms |
944 KB |
found '1023.0000000000', expected '1023.0000000000', error '0.0000000000' |
| 4 |
Correct |
142 ms |
932 KB |
found '294.0000000000', expected '294.0000000000', error '0.0000000000' |
| 5 |
Incorrect |
24 ms |
852 KB |
1st numbers differ - expected: '1087.0000000000', found: '1339.0000000000', error = '0.2318307268' |
| 6 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
39 ms |
3924 KB |
found '100800.5000000000', expected '100800.5000000000', error '0.0000000000' |
| 2 |
Correct |
0 ms |
212 KB |
found '0.0000000000', expected '0.0000000000', error '-0.0000000000' |
| 3 |
Correct |
14 ms |
596 KB |
found '0.0000000000', expected '0.0000000000', error '-0.0000000000' |
| 4 |
Correct |
19 ms |
604 KB |
found '1.0000000000', expected '1.0000000000', error '0.0000000000' |
| 5 |
Correct |
34 ms |
4308 KB |
found '124002.0000000000', expected '124002.0000000000', error '0.0000000000' |
| 6 |
Correct |
209 ms |
297140 KB |
found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000' |
| 7 |
Correct |
232 ms |
354768 KB |
found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000' |
| 8 |
Correct |
281 ms |
377924 KB |
found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000' |
| 9 |
Correct |
259 ms |
377936 KB |
found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000' |
| 10 |
Correct |
22 ms |
596 KB |
found '1.0000000000', expected '1.0000000000', error '0.0000000000' |
| 11 |
Correct |
25 ms |
844 KB |
found '1225.0000000000', expected '1225.0000000000', error '0.0000000000' |
| 12 |
Correct |
91 ms |
944 KB |
found '1023.0000000000', expected '1023.0000000000', error '0.0000000000' |
| 13 |
Correct |
142 ms |
932 KB |
found '294.0000000000', expected '294.0000000000', error '0.0000000000' |
| 14 |
Incorrect |
24 ms |
852 KB |
1st numbers differ - expected: '1087.0000000000', found: '1339.0000000000', error = '0.2318307268' |
| 15 |
Halted |
0 ms |
0 KB |
- |
