swadhinbiswas update on git · 11/9/2024
4beca37
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from typing import List, Tuple
class RookMover:
def __init__(self, n: int, perm: List[int]):
self.n = n
self.target = [p-1 for p in perm] # Convert to 0-based indexing
self.moves = []
self.board = [[False] * 8 for _ in range(n)]
# Place initial rooks on bottom row
for i in range(n):
self.board[i][0] = True
def is_path_clear(self, start_col: int, start_row: int, end_col: int, end_row: int) -> bool:
"""Check if path is clear for horizontal then vertical movement"""
# Check horizontal path
if start_row == end_row:
min_col = min(start_col, end_col)
max_col = max(start_col, end_col)
return not any(self.board[col][start_row] for col in range(min_col+1, max_col))
# Check vertical path
min_row = min(start_row, end_row)
max_row = max(start_row, end_row)
return not any(self.board[start_col][row] for row in range(min_row+1, max_row))
def move_rook(self, start_col: int, start_row: int, end_col: int, end_row: int):
"""Move rook and record the move"""
# Update board
self.board[start_col][start_row] = False
self.board[end_col][end_row] = True
# Record move (convert to 1-based indexing for output)
self.moves.append((start_col+1, start_row+1, end_col+1, end_row+1))
def solve(self) -> List[Tuple[int, int, int, int]]:
"""Find optimal sequence of moves to arrange rooks according to permutation"""
rook_positions = list(range(self.n)) # Current column positions of rooks
def move_to_target(rook_idx: int, intermediate_row: int = 7):
"""Move rook to its target position using an intermediate row if needed"""
curr_col = rook_positions[rook_idx]
target_col = self.target[rook_idx]
if curr_col == target_col:
return
# If direct path is clear, move directly
if self.is_path_clear(curr_col, 0, target_col, 0):
self.move_rook(curr_col, 0, target_col, 0)
rook_positions[rook_idx] = target_col
return
# Move up to intermediate row if path is clear
if self.is_path_clear(curr_col, 0, curr_col, intermediate_row):
self.move_rook(curr_col, 0, curr_col, intermediate_row)
# Move horizontally
self.move_rook(curr_col, intermediate_row, target_col, intermediate_row)
# Move down
self.move_rook(target_col, intermediate_row, target_col, 0)
rook_positions[rook_idx] = target_col
return
# Try different intermediate rows if needed
for row in range(6, 0, -1):
if (self.is_path_clear(curr_col, 0, curr_col, row) and
self.is_path_clear(curr_col, row, target_col, row) and
self.is_path_clear(target_col, row, target_col, 0)):
self.move_rook(curr_col, 0, curr_col, row)
self.move_rook(curr_col, row, target_col, row)
self.move_rook(target_col, row, target_col, 0)
rook_positions[rook_idx] = target_col
return
# Try to move each rook to its target position
for i in range(self.n):
move_to_target(i)
return self.moves
def solve_test_case():
n = int(input())
perm = list(map(int, input().split()))
solver = RookMover(n, perm)
moves = solver.solve()
print(len(moves))
for move in moves:
print(*move)
def main():
T = int(input())
for _ in range(T):
solve_test_case()
if __name__ == "__main__":
main()