/*
CEOI 2020 Chessrush
- Pawns
- There's only either 0 or 1 possible fixed-length paths
- O(1)
- Rooks
- If the start and end columns are equal, there's 1 path of length 1
- Otherwise, there are 2 paths of length 2
- O(1)
- Queens
- If the start and end columns or diagonals are equal, there's
1 path of length 1
- Otherwise, there are at least 4 paths of length 2
- If the start or end column is at an extremity and the board is
square, add a path
- If the start and end squares are the same colour and the queen
can travel on two diagonals to reach the end, add a path
- O(1)
- Bishops
- If the start and end squares are the same colour, then there's at
least 1 path
- Consider what happens if we just wildly bounce around between sides
- We might miss the end block, but this is at most 1 move less than
the optimal path
- If we cut the last bounce early, we'll hit the desired square
- Let's say we cut it F blocks early, and it took N moves
- We can distribute these F blocks amongst the first N - 1 moves
- Not the Nth move because that can't be cut short
- The number of ways to do this is (F + N - 2 choose F)
- We can compute this values naively because F is small
- O(QC)
- Kings
- There's always at least 1 fixed-length path
- dp[i][j][m - 1] = Ways to go from cell (1, i) to cell (m - 1, j)
= dp[i][j - 1][m - 2] + dp[i][j][m - 2] + dp[i][j + 1][m - 2]
= sum(dp[i][k][m / 2] * dp[k][j][m / 2])
- TOOD: Optimize (O(C^3 log R) right now)
*/
#include <bits/stdc++.h>
#include "arithmetics.h"
typedef long long ll;
using namespace std;
const int MOD = 1e9 + 7;
int pow(int base, int exp) {
base %= MOD;
int result = 1;
while (exp > 0) {
if (exp & 1) result = (1ll * result * base) % MOD;
base = (1ll * base * base) % MOD;
exp >>= 1;
}
return result;
}
pair<int, int> solve_bishop(int x, int y, int r, int c) {
int moves = 1 + (r - x + c - 2) / (c - 1);
x--, y--;
int end_col = 1 + (r - x + c - 3) % (c - 1);
if (moves & 1) y = c - y - 1;
int rem;
if (end_col <= y)
rem = (y - end_col) / 2;
else {
moves++;
rem = c - 1 - (end_col + y) / 2;
}
int ways = 1;
for (int i = 1; i <= rem; i++)
ways = Div(Mul(ways, moves + rem - 1 - i), i);
return {moves, ways};
}
vector<vector<int>> precompute_king(int r, int c) {
vector<vector<int>> nxt(c + 2, vector<int>(c + 2, 0));
if (r == 2) {
for (int i = 1; i <= c; i++)
nxt[i][i - 1] = nxt[i][i] = nxt[i][i + 1] = 1;
for (int i = 1; i <= c; i++)
nxt[i][0] = nxt[i][c + 1] = nxt[0][i] = nxt[c + 1][i] = 0;
} else if (r & 1) {
vector<vector<int>> dp = precompute_king(r / 2 + 1, c);
for (int j = 1; j <= c; j++) {
for (int k = 1; k <= c; k++) {
nxt[1][j] = Add(nxt[1][j], dp[1][k] * dp[k][j]);
}
nxt[j][1] = nxt[c + 1 - j][c] = nxt[c][c + 1 - j] = nxt[1][j];
}
for (int j = 2; j <= (c + 1) / 2; j++)
for (int i = 2; i < j; i++) {
nxt[i][j] = Add(nxt[i - 1][j - 1], nxt[1][1 + i + j]);
nxt[j][i] = nxt[c + 1 - j][c + 1 - i] = nxt[c + 1 - i][c + 1 - j] = nxt[i][j];
}
} else {
vector<vector<int>> dp = precompute_king(r - 1, c);
for (int i = 1; i <= c; i++)
for (int j = 1; j <= c; j++)
nxt[i][j] = Add(dp[i][j - 1], Add(dp[i][j], dp[i][j + 1]));
}
return nxt;
}
int dp[1002][1002][2];
int main() {
cin.tie(0)->sync_with_stdio(0);
int r, c, q;
cin >> r >> c >> q;
vector<vector<int>> dp = precompute_king(r, c);
while (q--) {
char p;
int x, y;
cin >> p >> x >> y;
switch (p) {
case 'P':
if (x == y)
cout << r - 1 << " 1\n";
else
cout << "0 0\n";
break;
case 'R':
if (x == y)
cout << "1 1\n";
else
cout << "2 2\n";
break;
case 'Q':
if (x == y || x + r - 1 == y || x - r + 1 == y)
cout << "1 1\n";
else {
int ways = 4;
// Extremities
if (r == c && (y == 1 || y == r || x == 1 || x == r))
ways++;
if (x + y + r & 1) {
// Double diagonal
if (r - x < y) ways++;
if (r - c + x - 1 < c - y + 1) ways++;
}
cout << "2 " << ways << '\n';
}
break;
case 'B':
if (x + y + r & 1) {
if (r == c && ((x == 1 && y == c) || (x == c && y == 1)))
cout << "1 1\n";
else {
pair<int, int> move_left = solve_bishop(x, y, r, c);
pair<int, int> move_right =
solve_bishop(c - x + 1, c - y + 1, r, c);
if (move_left.first > move_right.first)
move_left = move_right;
else if (move_left.first == move_right.first) {
move_left.second = Add(move_left.second, move_right.second);
}
cout << move_left.first << ' ' << move_left.second
<< '\n';
}
} else
cout << "0 0\n";
break;
case 'K':
cout << r - 1 << ' ' << dp[x][y] << '\n';
break;
}
}
return 0;
}
Compilation message
chessrush.cpp: In function 'int main()':
chessrush.cpp:138:31: warning: suggest parentheses around '+' in operand of '&' [-Wparentheses]
138 | if (x + y + r & 1) {
| ~~~~~~^~~
chessrush.cpp:147:27: warning: suggest parentheses around '+' in operand of '&' [-Wparentheses]
147 | if (x + y + r & 1) {
| ~~~~~~^~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
204 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
2 ms |
332 KB |
Output is correct |
| 3 |
Correct |
1 ms |
204 KB |
Output is correct |
| 4 |
Correct |
31 ms |
7512 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
2 ms |
332 KB |
Output is correct |
| 3 |
Correct |
1 ms |
204 KB |
Output is correct |
| 4 |
Correct |
2 ms |
328 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
2 ms |
332 KB |
Output is correct |
| 3 |
Correct |
1 ms |
204 KB |
Output is correct |
| 4 |
Correct |
2 ms |
328 KB |
Output is correct |
| 5 |
Correct |
348 ms |
67604 KB |
Output is correct |
| 6 |
Correct |
167 ms |
31352 KB |
Output is correct |
| 7 |
Correct |
3 ms |
460 KB |
Output is correct |
| 8 |
Correct |
965 ms |
194404 KB |
Output is correct |
| 9 |
Correct |
1 ms |
332 KB |
Output is correct |
| 10 |
Correct |
13 ms |
1868 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
324 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
324 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
324 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
324 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
204 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
