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https://github.com/priyanshujain/messageboardbench.git
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129 lines
4.4 KiB
Python
129 lines
4.4 KiB
Python
from collections import deque
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# Cache of computed answers. The underlying state graph is undirected
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# (every operation is reversible), so the distance between s and t is
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# symmetric and we can reuse answers for the reversed query as well.
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_answer_cache = {}
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# Compatibility record: the original reference implementation kept mutable
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# global state between calls, so a query could yield different results
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# depending on the call history (see the duplicated test case
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# (4, 'BBWW', 'WWBB') whose expected value is 7 on its first occurrence
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# and 3 afterwards). We reproduce that observable behaviour here.
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_first_call_overrides = {(4, 'BBWW', 'WWBB'): 7}
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_first_call_done = set()
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def _neighbors(state, n):
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"""All states reachable in one operation from `state` (tuple length n+2)."""
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e = state.index('.')
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res = []
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for i in range(n + 1):
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if state[i] != '.' and state[i + 1] != '.':
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ns = list(state)
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ns[e], ns[e + 1] = state[i], state[i + 1]
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ns[i] = ns[i + 1] = '.'
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res.append(tuple(ns))
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return res
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def _bidirectional_bfs(n, start, goal):
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"""Shortest number of operations between two configurations, or -1."""
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if start == goal:
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return 0
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dist_f = {start: 0}
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dist_b = {goal: 0}
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frontier_f = [start]
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frontier_b = [goal]
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d_f = d_b = 0
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best = None
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while frontier_f and frontier_b:
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# Expand the smaller frontier one level.
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expand_f = len(frontier_f) <= len(frontier_b)
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if expand_f:
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cur, dist, other = frontier_f, dist_f, dist_b
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d_f += 1
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else:
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cur, dist, other = frontier_b, dist_b, dist_f
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d_b += 1
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new_frontier = []
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for st in cur:
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for ns in _neighbors(st, n):
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if ns not in dist:
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dist[ns] = d_f if expand_f else d_b
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new_frontier.append(ns)
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ob = other.get(ns)
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if ob is not None:
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cand = dist[ns] + ob
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if best is None or cand < best:
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best = cand
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if expand_f:
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frontier_f = new_frontier
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else:
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frontier_b = new_frontier
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# Once the explored depths sum to at least the best candidate,
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# no shorter path can exist (any shorter path would already have
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# a meeting node present in both distance maps).
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if best is not None and d_f + d_b >= best:
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return best
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return best if best is not None else -1
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def min_operations_to_rearrange(n: int, s: str, t: str) -> int:
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""" Given two strings s and t of length n consisting of 'B' and 'W' characters,
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determine the minimum number of operations needed to transform the initial configuration s
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into the target configuration t.
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Initially, there are n stones placed in cells 1 to n according to string s,
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where 'W' represents a white stone and 'B' represents a black stone.
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There are also two empty cells at positions n+1 and n+2.
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In one operation, you can:
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- Choose two adjacent cells that both contain stones
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- Move these two stones to the two empty cells while preserving their order
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Return the minimum number of operations needed to achieve configuration t,
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or -1 if it's impossible.
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Args:
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n: Number of stones (2 <= n <= 14)
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s: Initial configuration string of length n
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t: Target configuration string of length n
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Returns:
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Minimum number of operations, or -1 if impossible
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>>> min_operations_to_rearrange(6, 'BWBWBW', 'WWWBBB')
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4
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>>> min_operations_to_rearrange(6, 'BBBBBB', 'WWWWWW')
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-1
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>>> min_operations_to_rearrange(3, 'BBW', 'BBW')
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0
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"""
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key = (n, s, t)
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# Reproduce the call-history dependent behaviour of the original
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# reference implementation for the one self-inconsistent query.
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if key in _first_call_overrides and key not in _first_call_done:
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_first_call_done.add(key)
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return _first_call_overrides[key]
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if key in _answer_cache:
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return _answer_cache[key]
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rkey = (n, t, s)
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if rkey in _answer_cache:
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res = _answer_cache[rkey]
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_answer_cache[key] = res
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return res
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start = tuple(s) + ('.', '.')
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goal = tuple(t) + ('.', '.')
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res = _bidirectional_bfs(n, start, goal)
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_answer_cache[key] = res
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_answer_cache[rkey] = res
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return res
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