friend of you is doing research on the Traveling Knight Problem (TKP) where you are to find the shortest closed tour of knight moves that visits each square of a given set of n squares on a chessboard exactly once. He thinks that the most difficult part of the problem is determining the smallest number of knight moves between two given squares and that, once you have accomplished this, finding the tour would be easy. Of course you know that it is vice versa. So you offer him to write a program that solves the "difficult" part. Your job is to write a program that takes two squares a and b as input and then determines the number of knight moves on a shortest route from a to b. Input Specification The input file will contain one or more test cases. Each test case consists of one line containing two squares separated by one space. A square is a string consisting of a letter (a-h) representing the column and a digit (1-8) representing the row on the chessboard. Output Specification For each test case, print one line saying "To get from xx to yy takes n knight moves.".
时间: 2024-02-14 08:06:24 浏览: 35
Sure, I can write a program that solves the "difficult" part of the TKP. Here's an implementation in Python:
```python
# Define a function to convert a square string to a tuple of coordinates
def square_to_coords(square):
col = ord(square[0]) - ord('a')
row = int(square[1]) - 1
return (col, row)
# Define a function to convert a tuple of coordinates to a square string
def coords_to_square(coords):
col = chr(coords[0] + ord('a'))
row = str(coords[1] + 1)
return col + row
# Define a function to find the shortest path between two squares using BFS
def shortest_path(start, end):
# Convert start and end squares to coordinates
start_coords = square_to_coords(start)
end_coords = square_to_coords(end)
# Define the possible knight moves
moves = [(-2,-1), (-1,-2), (1,-2), (2,-1), (2,1), (1,2), (-1,2), (-2,1)]
# Initialize the queue with the starting position and a distance of 0
queue = [(start_coords, 0)]
# Initialize a set to keep track of visited positions
visited = set([start_coords])
# Loop until the queue is empty
while queue:
# Dequeue the next position and distance
position, distance = queue.pop(0)
# Check if we have reached the end position
if position == end_coords:
return distance
# Generate all possible moves from the current position
for move in moves:
new_pos = (position[0] + move[0], position[1] + move[1])
# Check if the new position is within the bounds of the chessboard
if new_pos[0] < 0 or new_pos[0] > 7 or new_pos[1] < 0 or new_pos[1] > 7:
continue
# Check if the new position has already been visited
if new_pos in visited:
continue
# Add the new position to the queue and mark it as visited
queue.append((new_pos, distance + 1))
visited.add(new_pos)
# If we reach this point, there is no path from start to end
return -1
# Read input from file
with open('input.txt', 'r') as f:
for line in f:
# Parse the input
start, end = line.strip().split()
# Find the shortest path and print the result
distance = shortest_path(start, end)
print("To get from {} to {} takes {} knight moves.".format(start, end, distance))
```
This program reads input from a file called 'input.txt' and prints the shortest path between each pair of squares using the BFS algorithm. Each line of the input file should contain two squares separated by a space. The output is in the format "To get from xx to yy takes n knight moves.".