Expert · Graphs · 228 of 264
Knight's journey
On an n by n chessboard, what is the smallest number of knight moves from one square to another? Squares are given as row and column from 1.
Input: n, then the start "r c", then the target "r c". Output: the number of moves, or -1.
Examples
Input
8 1 1 8 8
Output
6
Input
8 4 4 4 4
Output
0
Input
3 1 1 2 2
Output
-1
One more test checks other inputs when you press Check.
Stuck? The idea behind graphs
A graph is places (nodes) joined by edges. Keep it as a dictionary of neighbours: graph[a] is the list of nodes next to a.
Breadth-first search, with a queue, finds the shortest path when every step costs the same; Dijkstra's algorithm, with a heap, when steps cost different amounts.
from collections import deque
graph = {1: [2, 3], 2: [4], 3: [4], 4: []}
dist = {1: 0}
queue = deque([1])
while queue:
node = queue.popleft()
for nxt in graph[node]:
if nxt not in dist:
dist[nxt] = dist[node] + 1
queue.append(nxt)
print(dist[4])Watch for: Mark a node as seen when you add it to the queue, not when you take it out, or it is added many times.