菜单
For static relationships: graph structure, grid neighbors, constraint peers. Calculate once at module load, reference throughout program.
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基于 SOC 职业分类
Conducts iterative deep research on any topic using web search, progressive exploration, and structured synthesis. Use when asked for comprehensive research, deep investigation, thorough analysis, or multi-source exploration of any topic. Triggers: research, investigate, deep dive, comprehensive analysis, explore thoroughly, find everything about.
For cross-cutting concerns: add behavior without modifying functions, caching, timing, logging, validation wrappers.
For performance work: measure before changing, profile to find bottlenecks, compare before and after.
For symbolic computation: ASTs, mathematical expressions, code that manipulates code structure, expression transformations.
For ordered processing: A* search, Dijkstra, event simulation, task scheduling. Efficient min/max extraction with heap-based queue.
For dynamic programming: overlapping subproblems, recursive solutions with repeated computations, memoization to avoid redundant work.
| name | precompute-relationships |
| description | For static relationships: graph structure, grid neighbors, constraint peers. Calculate once at module load, reference throughout program. |
Compute all static relationships at module load time. Store in dicts for O(1) lookup.
# Define structure
rows = 'ABCDEFGHI'
cols = '123456789'
# Precompute all squares
squares = [r + c for r in rows for c in cols]
# Precompute all units (rows, cols, boxes)
unit_list = (
[[r + c for c in cols] for r in rows] + # Rows
[[r + c for r in rows] for c in cols] + # Columns
[[r + c for r in rs for c in cs] # Boxes
for rs in ['ABC', 'DEF', 'GHI']
for cs in ['123', '456', '789']]
)
# Precompute which units each square belongs to
units = {s: [u for u in unit_list if s in u] for s in squares}
# Precompute peers (squares that constrain this one)
peers = {s: set(sum(units[s], [])) - {s} for s in squares}
def cross(A, B):
"""Cross product of elements in A and B."""
return [a + b for a in A for b in B]
digits = '123456789'
rows = 'ABCDEFGHI'
cols = digits
# All 81 squares
squares = cross(rows, cols)
# All 27 units
unitlist = ([cross(rows, c) for c in cols] +
[cross(r, cols) for r in rows] +
[cross(rs, cs)
for rs in ('ABC', 'DEF', 'GHI')
for cs in ('123', '456', '789')])
# units[s] = list of 3 units containing square s
units = {s: [u for u in unitlist if s in u]
for s in squares}
# peers[s] = set of 20 squares that see square s
peers = {s: set(sum(units[s], [])) - {s}
for s in squares}
# Now constraint propagation is fast:
def eliminate(values, s, d):
for peer in peers[s]: # O(1) lookup!
eliminate(values, peer, d)
units[square] not find_units(square)