47 lines
1.5 KiB
Python
47 lines
1.5 KiB
Python
from __future__ import annotations
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def clamp_manhattan_with_diagonal_priority(dx: int, dy: int, step: int) -> tuple[int, int]:
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"""
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在不超过给定曼哈顿步长 step 的前提下，对 (dx, dy) 进行裁剪，且优先斜向移动。
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规则：
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- 返回的 (mx, my) 满足 |mx| + |my| <= step
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- 每轴不超过原目标量：|mx| <= |dx|, |my| <= |dy|
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- 优先分配斜向步（即同时占用 x 与 y 各 1 步），其后再把剩余步数分配给剩余距离更大的轴
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- 保持原方向（符号）
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"""
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if step <= 0 or (dx == 0 and dy == 0):
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return 0, 0
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abs_dx = abs(dx)
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abs_dy = abs(dy)
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sign_x = 1 if dx > 0 else (-1 if dx < 0 else 0)
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sign_y = 1 if dy > 0 else (-1 if dy < 0 else 0)
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# 实际可用预算不超过所需的曼哈顿距离
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budget = min(step, abs_dx + abs_dy)
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# 先分配尽量多的斜向步：每个斜向步消耗 2 点预算
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diagonal_steps = min(min(abs_dx, abs_dy), budget // 2)
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move_x = diagonal_steps
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move_y = diagonal_steps
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remaining = budget - 2 * diagonal_steps
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# 若还有剩余预算，分配给剩余距离更大的轴
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rem_x = abs_dx - move_x
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rem_y = abs_dy - move_y
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if remaining > 0:
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if rem_x >= rem_y:
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add_x = min(remaining, rem_x)
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move_x += add_x
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remaining -= add_x
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if remaining > 0:
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add_y = min(remaining, rem_y)
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move_y += add_y
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return move_x * sign_x, move_y * sign_y
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