QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#34619 | #4235. Transparency | YaoBIG# | AC ✓ | 30ms | 3848kb | C++ | 5.3kb | 2022-06-11 23:55:21 | 2022-06-11 23:55:22 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
// For every pair of nodes, find shortest path using only small characters, and a distinct shortest path using only small characters
// For every pair of nodes, find shortest path to the goal such that both have the same large letters on the path, and sum of small letter count is minimised.
// Then, do the same, but this time guarantee that the strings produced by the walks are distinct.
// To do this, loop next node for first, loop next node for second, and loop large character they take from there
// -> Complexity O(n^2 * n^2)
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
template<class T>
T rand(T a, T b) {
return uniform_int_distribution<T>(a, b)(rng);
}
template<class T>
T rand() {
return uniform_int_distribution<T>()(rng);
}
// Struct for priority queue operations on index set [0, n-1]
// push(i, v) overwrites value at position i if one already exists
// decKey is faster but requires that the new key is smaller than the old one
struct Prique {
const ll INF = 4 * (ll)1e18;
vector<pair<ll, int>> data;
const int n;
Prique(int siz) : n(siz), data(2*siz, {INF, -1}) { data[0] = {-INF, -1}; }
bool empty() const { return data[1].second >= INF; }
pair<ll, int> top() const { return data[1]; }
void push(int i, ll v) {
data[i+n] = {v, (v >= INF ? -1 : i)};
for (i += n; i > 1; i >>= 1) data[i>>1] = min(data[i], data[i^1]);
}
void decKey(int i, ll v) {
for (int j = i+n; data[j].first > v; j >>= 1) data[j] = {v, i};
}
pair<ll, int> pop() {
auto res = data[1];
push(res.second, INF);
return res;
}
};
const ull MOD = (ull)4e9 + 7;
const ull MULT = rand(2ull, MOD - 2);
const int INF = 1e9 + 7;
const int N = 50;
const int C = 26;
vector<pair<int, int>> big_in[N];
pair<int, ull> opt[N][N][2]; // Two distinct shortest paths using only small characters from a to b
int dp[N][N][4];
int nxt[N][C];
bool goal[N];
pair<int, ull> extend(pair<int, ull> cur, int c) {
return {cur.first + 1, (cur.second * MULT + c) % MOD};
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
// "What is the maximum k, such that exists i < n - k, such that str[i, i + k) = str[n - k, n)
// -> reverse string. Need to find suffix occurring after i, with maximum LCA with i
int n, k, m;
cin >> n >> k >> m;
for (int i = 0; i < k; ++i) {
int t;
cin >> t;
goal[t - 1] = 1;
}
for (int i = 0; i < n; ++i) {
for (int c = 0; c < C; ++c) nxt[i][c] = -1;
}
for (int j = 0; j < m; ++j) {
int a, b;
char c;
cin >> a >> c >> b;
--a; --b;
if ('a' <= c && c <= 'z') {
nxt[a][c - 'a'] = b;
} else {
big_in[b].emplace_back(c - 'A', a);
}
}
for (int s = 0; s < n; ++s) {
for (int t = 0; t < n; ++t) {
opt[s][t][0] = {INF, 0ull};
opt[s][t][1] = {INF, 0ull};
}
opt[s][s][0] = {0, 0ull};
vector<pair<int, int>> que = {{s, 0}};
for (int ind = 0; ind < que.size(); ++ind) {
int i = que[ind].first;
auto cur = opt[s][i][que[ind].second];
for (int c = 0; c < C; ++c) {
int t = nxt[i][c];
if (t == -1) continue;
auto off = extend(cur, c);
if (off.first < opt[s][t][0].first) {
opt[s][t][0] = off;
que.emplace_back(t, 0);
} else if (off != opt[s][t][0] && off.first < opt[s][t][1].first) {
opt[s][t][1] = off;
que.emplace_back(t, 1);
}
}
}
// for (int t = 0; t < n; ++t) cerr << s << ' ' << t << ": " << opt[s][t][0].first << ' ' << opt[s][t][1].first << '\n';
}
Prique pq(4*n*n);
for (int a = 0; a < n; ++a) {
for (int b = a; b < n; ++b) {
for (int j = 0; j < 4; ++j) dp[a][b][j] = INF;
if (goal[a] && goal[b]) {
dp[a][b][0] = 0;
pq.decKey(a + n*b, 0);
}
}
}
while(pq.top().second != -1) {
auto pr = pq.pop();
int ind = pr.second;
int a = ind % n;
int b = (ind / n) % n;
int s = ind / (n * n) % 2;
int r = ind / (2 * n * n);
int base = dp[a][b][s + 2*r];
// cerr << a << ' ' << b << ' ' << s << ' ' << r << ": " << base << '\n';
if (s == 0) {
for (int x = 0; x < n; ++x) {
if (opt[x][a][0].first >= INF) continue;
for (int y = 0; y < n; ++y) {
if (opt[y][b][0].first >= INF) continue;
int off = base + opt[x][a][0].first + opt[y][b][0].first;
int off2 = base + min(opt[x][a][0].first + opt[y][b][1].first, opt[x][a][1].first + opt[y][b][0].first);
if (r == 1 || opt[x][a][0] != opt[y][b][0]) off2 = off;
int pa = min(x, y);
int pb = max(x, y);
if (dp[pa][pb][1] > off) {
dp[pa][pb][1] = off;
pq.decKey(pa + n*pb + n*n, off);
}
if (dp[pa][pb][3] > off2) {
dp[pa][pb][3] = off2;
pq.decKey(pa + n*pb + 3*n*n, off2);
}
}
}
} else {
for (auto pr : big_in[a]) {
for (auto pr2 : big_in[b]) {
if (pr.first != pr2.first) continue;
int x = pr.second;
int y = pr2.second;
int pa = min(x, y);
int pb = max(x, y);
int off = base + 2;
if (dp[pa][pb][2*r] > off) {
dp[pa][pb][2*r] = off;
pq.decKey(pa + n*pb + 2*r * n*n, off);
}
}
}
}
}
int res = min(dp[0][0][2], dp[0][0][3]);
if (res < INF) {
cout << res << '\n';
} else {
cout << -1 << '\n';
}
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 2ms
memory: 3680kb
input:
4 1 8 3 1 F 1 1 A 2 2 b 1 2 F 3 2 d 3 3 B 3 3 y 4 4 d 1
output:
10
result:
ok single line: '10'
Test #2:
score: 0
Accepted
time: 0ms
memory: 3648kb
input:
4 1 8 3 1 F 1 1 A 2 2 b 1 2 F 3 2 d 3 3 B 3 3 y 4 4 d 4
output:
-1
result:
ok single line: '-1'
Test #3:
score: 0
Accepted
time: 2ms
memory: 3660kb
input:
5 2 5 1 5 1 i 2 2 c 3 3 p 4 4 c 1 1 I 5
output:
4
result:
ok single line: '4'
Test #4:
score: 0
Accepted
time: 0ms
memory: 3608kb
input:
8 2 96 4 8 1 x 2 1 y 5 2 A 3 3 A 4 4 A 2 5 A 6 6 A 7 7 A 8 8 A 5 5 B 2 6 B 2 7 B 2 8 B 2 5 C 2 6 C 2 7 C 2 8 C 2 5 D 2 6 D 2 7 D 2 8 D 2 5 E 2 6 E 2 7 E 2 8 E 2 5 F 2 6 F 2 7 F 2 8 F 2 5 G 2 6 G 2 7 G 2 8 G 2 5 H 2 6 H 2 7 H 2 8 H 2 5 I 2 6 I 2 7 I 2 8 I 2 5 J 2 6 J 2 7 J 2 8 J 2 5 K 2 6 K 2 7 K 2 8...
output:
24
result:
ok single line: '24'
Test #5:
score: 0
Accepted
time: 0ms
memory: 3524kb
input:
4 1 4 1 1 d 2 2 A 3 3 A 4 4 d 1
output:
-1
result:
ok single line: '-1'
Test #6:
score: 0
Accepted
time: 2ms
memory: 3596kb
input:
7 1 8 1 1 d 2 2 A 3 3 A 4 4 d 1 1 A 5 5 d 6 6 d 7 7 A 1
output:
8
result:
ok single line: '8'
Test #7:
score: 0
Accepted
time: 2ms
memory: 3616kb
input:
1 1 1 1 1 a 1
output:
1
result:
ok single line: '1'
Test #8:
score: 0
Accepted
time: 2ms
memory: 3712kb
input:
1 1 1 1 1 A 1
output:
-1
result:
ok single line: '-1'
Test #9:
score: 0
Accepted
time: 2ms
memory: 3644kb
input:
2 1 2 2 1 a 2 1 b 2
output:
2
result:
ok single line: '2'
Test #10:
score: 0
Accepted
time: 2ms
memory: 3700kb
input:
2 2 1 1 2 1 a 2
output:
1
result:
ok single line: '1'
Test #11:
score: 0
Accepted
time: 2ms
memory: 3732kb
input:
4 2 3 3 4 1 A 2 2 a 3 2 b 4
output:
4
result:
ok single line: '4'
Test #12:
score: 0
Accepted
time: 3ms
memory: 3740kb
input:
50 1 149 50 1 A 2 2 B 3 3 C 4 4 D 5 5 E 6 6 F 7 7 G 8 8 H 9 9 I 10 10 J 11 11 K 12 12 L 13 13 M 14 14 N 15 15 O 16 16 P 17 17 Q 18 18 R 19 19 S 20 20 T 21 21 U 22 22 V 23 23 W 24 24 X 25 25 Y 26 26 Z 27 27 A 28 28 B 29 29 C 30 30 D 31 31 E 32 32 F 33 33 G 34 34 H 35 35 I 36 36 J 37 37 K 38 38 L 39 3...
output:
288
result:
ok single line: '288'
Test #13:
score: 0
Accepted
time: 1ms
memory: 3632kb
input:
50 1 500 50 1 A 2 1 Z 2 1 Y 2 1 X 2 1 W 2 1 V 2 1 U 2 1 T 2 1 S 2 1 R 2 2 B 3 2 A 3 2 Z 3 2 Y 3 2 X 3 2 W 3 2 V 3 2 U 3 2 T 3 2 S 3 3 C 4 3 B 4 3 A 4 3 Z 4 3 Y 4 3 X 4 3 W 4 3 V 4 3 U 4 3 T 4 4 D 5 4 C 5 4 B 5 4 A 5 4 Z 5 4 Y 5 4 X 5 4 W 5 4 V 5 4 U 5 5 E 6 5 D 6 5 C 6 5 B 6 5 A 6 5 Z 6 5 Y 6 5 X 6 ...
output:
533
result:
ok single line: '533'
Test #14:
score: 0
Accepted
time: 2ms
memory: 3832kb
input:
50 1 500 50 1 A 2 1 Z 2 1 Y 2 1 X 2 1 W 2 1 V 2 1 U 2 1 T 2 1 S 2 1 R 2 2 B 3 2 A 3 2 Z 3 2 Y 3 2 X 3 2 W 3 2 V 3 2 U 3 2 T 3 2 S 3 3 C 4 3 B 4 3 A 4 3 Z 4 3 Y 4 3 X 4 3 W 4 3 V 4 3 U 4 3 T 4 4 D 5 4 C 5 4 B 5 4 A 5 4 Z 5 4 Y 5 4 X 5 4 W 5 4 V 5 4 U 5 5 E 6 5 D 6 5 C 6 5 B 6 5 A 6 5 Z 6 5 Y 6 5 X 6 ...
output:
-1
result:
ok single line: '-1'
Test #15:
score: 0
Accepted
time: 2ms
memory: 3768kb
input:
50 2 67 2 26 1 x 3 1 w 27 2 Z 3 3 Z 4 4 Z 5 5 Z 6 6 Z 7 7 Z 8 8 Z 9 9 Z 10 10 Z 11 11 Z 12 12 Z 13 13 Z 14 14 Z 15 15 Z 16 16 Z 17 17 Z 18 18 Z 19 19 Z 20 20 Z 21 21 Z 22 22 Z 23 23 Z 24 24 Z 25 25 Z 2 26 Z 27 27 Z 28 28 Z 29 29 Z 30 30 Z 31 31 Z 32 32 Z 33 33 Z 34 34 Z 35 35 Z 36 36 Z 37 37 Z 38 38...
output:
1200
result:
ok single line: '1200'
Test #16:
score: 0
Accepted
time: 30ms
memory: 3800kb
input:
50 5 2600 12 10 36 19 9 1 A 6 1 B 12 1 C 2 1 D 35 1 E 12 1 F 50 1 G 46 1 H 13 1 I 30 1 J 24 1 K 39 1 L 21 1 M 23 1 N 46 1 O 41 1 P 5 1 Q 43 1 R 24 1 S 43 1 T 8 1 U 50 1 V 41 1 W 47 1 X 11 1 Y 4 1 Z 26 1 a 33 1 b 34 1 c 30 1 d 37 1 e 4 1 f 42 1 g 22 1 h 14 1 i 44 1 j 18 1 k 50 1 l 16 1 m 24 1 n 41 1 ...
output:
2
result:
ok single line: '2'
Test #17:
score: 0
Accepted
time: 2ms
memory: 3848kb
input:
50 20 2600 8 45 50 40 10 13 27 2 21 34 31 25 36 46 39 15 16 20 35 26 1 A 45 1 B 39 1 C 21 1 D 10 1 E 22 1 F 50 1 G 18 1 H 23 1 I 19 1 J 40 1 K 17 1 L 45 1 M 42 1 N 10 1 O 35 1 P 45 1 Q 7 1 R 6 1 S 19 1 T 40 1 U 21 1 V 39 1 W 17 1 X 30 1 Y 31 1 Z 26 1 a 18 1 b 49 1 c 18 1 d 18 1 e 29 1 f 18 1 g 49 1 ...
output:
-1
result:
ok single line: '-1'
Test #18:
score: 0
Accepted
time: 5ms
memory: 3708kb
input:
50 20 2600 8 45 50 40 10 13 27 2 21 34 31 25 36 46 39 15 16 20 35 26 1 A 45 1 B 39 1 C 21 1 D 10 1 E 22 1 F 50 1 G 18 1 H 23 1 I 19 1 J 40 1 K 17 1 L 45 1 M 42 1 N 10 1 O 35 1 P 45 1 Q 7 1 R 6 1 S 19 1 T 40 1 U 21 1 V 39 1 W 17 1 X 30 1 Y 31 1 Z 26 1 a 18 1 b 49 1 c 18 1 d 38 1 e 29 1 f 18 1 g 49 1 ...
output:
5
result:
ok single line: '5'
Test #19:
score: 0
Accepted
time: 2ms
memory: 3704kb
input:
9 2 15 6 3 1 A 2 1 f 3 2 c 4 2 H 6 2 b 5 3 G 1 4 H 4 4 e 7 4 D 1 5 d 8 5 L 3 7 F 9 8 F 9 9 H 6 9 p 1
output:
10
result:
ok single line: '10'
Test #20:
score: 0
Accepted
time: 3ms
memory: 3644kb
input:
7 3 62 5 6 7 1 A 2 2 a 5 2 b 3 2 c 4 3 a 4 3 b 4 3 c 4 3 d 4 3 e 4 3 f 4 3 g 4 3 h 4 3 i 4 3 j 4 3 k 4 3 l 4 3 m 4 3 n 4 3 o 4 3 p 4 3 q 4 3 r 4 3 s 4 3 t 4 3 u 4 3 v 4 3 w 4 3 x 4 3 y 4 3 z 4 4 a 3 4 b 3 4 c 3 4 d 3 4 e 3 4 f 3 4 g 3 4 h 3 4 i 3 4 j 3 4 k 3 4 l 3 4 m 3 4 n 3 4 o 3 4 p 3 4 q 3 4 r 3...
output:
-1
result:
ok single line: '-1'
Test #21:
score: 0
Accepted
time: 0ms
memory: 3608kb
input:
9 2 15 6 3 1 A 2 1 f 3 2 c 4 2 H 6 2 b 5 3 G 1 4 H 4 4 e 7 4 D 1 5 d 8 5 L 3 7 r 9 8 t 9 9 H 6 9 p 1
output:
7
result:
ok single line: '7'
Test #22:
score: 0
Accepted
time: 2ms
memory: 3828kb
input:
24 4 30 2 3 15 23 1 B 2 2 C 3 3 D 2 3 f 4 3 A 17 4 A 5 5 g 6 5 R 2 6 Z 7 6 N 5 7 b 8 8 g 9 9 r 10 10 h 11 10 S 10 11 T 12 12 r 13 13 K 14 14 m 15 15 L 16 16 G 1 17 x 18 18 f 19 19 Z 20 20 V 2 20 T 21 21 K 22 22 m 23 23 F 24 24 C 1
output:
23
result:
ok single line: '23'
Test #23:
score: 0
Accepted
time: 2ms
memory: 3636kb
input:
7 2 6 4 7 1 f 2 2 A 3 3 b 4 1 g 5 5 A 6 6 c 7
output:
6
result:
ok single line: '6'
Test #24:
score: 0
Accepted
time: 2ms
memory: 3692kb
input:
26 4 32 2 3 15 25 1 B 2 2 C 3 3 D 2 3 f 4 3 A 17 4 A 5 5 g 6 5 R 2 6 Z 7 6 N 5 7 b 8 8 g 9 9 r 10 10 h 11 10 S 10 11 T 12 12 r 13 13 K 14 14 m 15 15 L 16 16 G 1 17 x 18 18 f 19 19 Z 20 20 V 2 20 T 21 21 K 22 22 m 23 23 i 24 24 k 25 25 F 26 26 C 1
output:
25
result:
ok single line: '25'
Test #25:
score: 0
Accepted
time: 0ms
memory: 3584kb
input:
4 1 4 4 1 m 2 2 X 3 3 a 4 3 b 4
output:
6
result:
ok single line: '6'
Test #26:
score: 0
Accepted
time: 3ms
memory: 3748kb
input:
50 1 2600 1 1 A 35 1 B 18 1 C 24 1 D 43 1 E 9 1 F 50 1 G 5 1 H 9 1 I 6 1 J 6 1 K 26 1 L 37 1 M 48 1 N 29 1 O 18 1 P 21 1 Q 50 1 R 33 1 S 47 1 T 27 1 U 31 1 V 39 1 W 27 1 X 24 1 Y 44 1 Z 33 1 a 16 1 b 7 1 c 38 1 d 7 1 e 49 1 f 12 1 g 47 1 h 20 1 i 5 1 j 42 1 k 29 1 l 14 1 m 32 1 n 28 1 o 28 1 p 30 1 ...
output:
-1
result:
ok single line: '-1'