#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<double> vd;
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
vi B; // bitvector interpretation of the group a person belongs to
vvi mg; // groupmember
vl dp; // the results are only 1/2 away from integers, so i store 2 * res in the dp
vvvl pre1, pre2; // pre1[g1][g2][p] = count of passes for the first p people of g1 with people of group g2 (coming from the left)
ll calc(ll k1, ll k2)
{
return (k1 * (k1 - 1) + k2 * (k2 - 1)) / 2;
}
ll calc(int group, int others, int posInGroup)
{
ll res = 0;
for (int g = 0; g < sz(pre1); ++g)
{
if (g == group)
{
if (posInGroup >= 0)
res += pre1[group][g][posInGroup];
if (posInGroup + 1 < sz(pre2[group][g]))
res += pre2[group][g][posInGroup + 1];
}
else if ((1 << g) & others)
{
if (posInGroup >= 0)
res += 2 * pre1[group][g][posInGroup];
if (posInGroup + 1 < sz(pre2[group][g]))
res += 2 * pre2[group][g][posInGroup + 1];
}
}
return res;
}
ll compute(int mask, int lg) // lg is the number of the last group
{
int l = -1, r = sz(mg[lg]) - 1; // starting with -1 because it is possible, that noone of that group will come from the left side
int others = mask ^ (1 << lg);
int m1, m2;
ll res = min(calc(lg, others, l), calc(lg, others, r));
while (r - l > 1)
{
m1 = (2 * l + r) / 3;
m2 = (l + 2 * r) / 3;
ll res1 = calc(lg, others, m1);
ll res2 = calc(lg, others, m2);
res = min(res, min(res1, res2));
if (res1 < res2)
r = m2 - 1;
else if (res1 > res2)
l = m1 + 1;
else
l = m1, r = m2;
}
for (int i = l; i <= r; ++i)
res = min(res, calc(lg, others, i));
return res + dp[others];
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(0);
string P;
cin >> P;
ll N = sz(P);
int G = 0;
B.resize(N);
for (int i = 0; i < N; ++i)
{
B[i] = (1 << (P[i] - 'A'));
G = max(G, P[i] - 'A');
}
++G; // to get the size
mg.resize(G);
for (int i = 0; i < N; ++i)
mg[P[i] - 'A'].push_back(i);
// precompute
pre1.assign(G, vvl(G));
for (int g1 = 0; g1 < G; ++g1)
{
if (sz(mg[g1]) == 0)
continue;
for (int g2 = 0; g2 < G; ++g2)
{
pre1[g1][g2].resize(sz(mg[g1]));
int j = 0;
while (j < sz(mg[g2]) && mg[g2][j] < mg[g1][0])
++j;
pre1[g1][g2][0] = j;
for (int i = 1; i < sz(pre1[g1][g2]); ++i)
{
while (j < sz(mg[g2]) && mg[g2][j] < mg[g1][i])
++j;
pre1[g1][g2][i] = pre1[g1][g2][i - 1] + j;
}
}
}
// precompute 2
for (int g = 0; g < G; ++g)
reverse(all(mg[g]));
pre2.assign(G, vvl(G));
for (int g1 = 0; g1 < G; ++g1)
{
if (sz(mg[g1]) == 0)
continue;
for (int g2 = 0; g2 < G; ++g2)
{
pre2[g1][g2].resize(sz(mg[g1]));
int j = 0;
while (j < sz(mg[g2]) && mg[g2][j] > mg[g1][0])
++j;
pre2[g1][g2][0] = j;
for (int i = 1; i < sz(pre2[g1][g2]); ++i)
{
while (j < sz(mg[g2]) && mg[g2][j] > mg[g1][i])
++j;
pre2[g1][g2][i] = pre2[g1][g2][i - 1] + j;
}
reverse(all(pre2[g1][g2]));
}
}
for (int g = 0; g < G; ++g)
reverse(all(mg[g]));
dp.assign(1 << G, calc(100100, 100100));
dp[0] = 0;
for (int i = 1; i < sz(dp); ++i)
{
for (int j = 0; j < G; ++j)
{ // last group to enter
if (((1 << j) & i) == 0)
continue;
dp[i] = min(dp[i], compute(i, j));
}
}
// double res = expectOneGroup(N);
printf("%f\n", dp[(1 << G) - 1] / (double)2);
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 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 |
0 ms |
212 KB |
found '0.0000000000', expected '0.0000000000', error '-0.0000000000' |
| 4 |
Correct |
1 ms |
212 KB |
found '1.0000000000', expected '1.0000000000', error '0.0000000000' |
| 5 |
Correct |
0 ms |
340 KB |
found '124002.0000000000', expected '124002.0000000000', error '0.0000000000' |
| 6 |
Correct |
3 ms |
2448 KB |
found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000' |
| 7 |
Correct |
3 ms |
2832 KB |
found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000' |
| 8 |
Correct |
3 ms |
2960 KB |
found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000' |
| 9 |
Correct |
3 ms |
2960 KB |
found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000' |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
found '1.0000000000', expected '1.0000000000', error '0.0000000000' |
| 2 |
Correct |
1 ms |
212 KB |
found '1225.0000000000', expected '1225.0000000000', error '0.0000000000' |
| 3 |
Correct |
1 ms |
212 KB |
found '1023.0000000000', expected '1023.0000000000', error '0.0000000000' |
| 4 |
Correct |
1 ms |
212 KB |
found '294.0000000000', expected '294.0000000000', error '0.0000000000' |
| 5 |
Correct |
0 ms |
212 KB |
found '1087.0000000000', expected '1087.0000000000', error '0.0000000000' |
| 6 |
Correct |
0 ms |
212 KB |
found '1.5000000000', expected '1.5000000000', error '0.0000000000' |
| 7 |
Correct |
0 ms |
212 KB |
found '703.0000000000', expected '703.0000000000', error '0.0000000000' |
| 8 |
Incorrect |
1 ms |
212 KB |
1st numbers differ - expected: '55.5000000000', found: '63.5000000000', error = '0.1441441441' |
| 9 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
found '1.0000000000', expected '1.0000000000', error '0.0000000000' |
| 2 |
Correct |
1 ms |
212 KB |
found '1225.0000000000', expected '1225.0000000000', error '0.0000000000' |
| 3 |
Correct |
1 ms |
212 KB |
found '1023.0000000000', expected '1023.0000000000', error '0.0000000000' |
| 4 |
Correct |
1 ms |
212 KB |
found '294.0000000000', expected '294.0000000000', error '0.0000000000' |
| 5 |
Correct |
0 ms |
212 KB |
found '1087.0000000000', expected '1087.0000000000', error '0.0000000000' |
| 6 |
Correct |
0 ms |
212 KB |
found '1.5000000000', expected '1.5000000000', error '0.0000000000' |
| 7 |
Correct |
0 ms |
212 KB |
found '703.0000000000', expected '703.0000000000', error '0.0000000000' |
| 8 |
Incorrect |
1 ms |
212 KB |
1st numbers differ - expected: '55.5000000000', found: '63.5000000000', error = '0.1441441441' |
| 9 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 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 |
0 ms |
212 KB |
found '0.0000000000', expected '0.0000000000', error '-0.0000000000' |
| 4 |
Correct |
1 ms |
212 KB |
found '1.0000000000', expected '1.0000000000', error '0.0000000000' |
| 5 |
Correct |
0 ms |
340 KB |
found '124002.0000000000', expected '124002.0000000000', error '0.0000000000' |
| 6 |
Correct |
3 ms |
2448 KB |
found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000' |
| 7 |
Correct |
3 ms |
2832 KB |
found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000' |
| 8 |
Correct |
3 ms |
2960 KB |
found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000' |
| 9 |
Correct |
3 ms |
2960 KB |
found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000' |
| 10 |
Correct |
0 ms |
212 KB |
found '1.0000000000', expected '1.0000000000', error '0.0000000000' |
| 11 |
Correct |
1 ms |
212 KB |
found '1225.0000000000', expected '1225.0000000000', error '0.0000000000' |
| 12 |
Correct |
1 ms |
212 KB |
found '1023.0000000000', expected '1023.0000000000', error '0.0000000000' |
| 13 |
Correct |
1 ms |
212 KB |
found '294.0000000000', expected '294.0000000000', error '0.0000000000' |
| 14 |
Correct |
0 ms |
212 KB |
found '1087.0000000000', expected '1087.0000000000', error '0.0000000000' |
| 15 |
Correct |
0 ms |
212 KB |
found '1.5000000000', expected '1.5000000000', error '0.0000000000' |
| 16 |
Correct |
0 ms |
212 KB |
found '703.0000000000', expected '703.0000000000', error '0.0000000000' |
| 17 |
Incorrect |
1 ms |
212 KB |
1st numbers differ - expected: '55.5000000000', found: '63.5000000000', error = '0.1441441441' |
| 18 |
Halted |
0 ms |
0 KB |
- |
