168 lines
6.6 KiB
Python
168 lines
6.6 KiB
Python
# -*- coding: utf-8 -*-
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import math
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import heapq
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def boss_fight(B, PlayerSkills):
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"""
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使用分支限界法求解Boss战斗的最优策略
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参数:
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B: Boss血量序列 [boss1_hp, boss2_hp, ...]
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PlayerSkills: 玩家技能列表 [(damage1, cooldown1), (damage2, cooldown2), ...]
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返回:
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每个Boss对应的攻击序列列表，例如：[[0, 1, 0], [2, -1, 1], ...]
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其中数字表示技能索引，-1表示等待
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如果无解则返回None
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"""
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n = len(B) # Boss数量
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m = len(PlayerSkills) # 技能数量
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if n == 0:
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return []
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# 计算最大平均伤害（用于启发式估计）
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max_avg = 0.0
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for damage, cooldown in PlayerSkills:
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if cooldown + 1 > 0:
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avg_damage = damage / (cooldown + 1)
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if avg_damage > max_avg:
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max_avg = avg_damage
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# 如果所有技能伤害为0，则无法击败Boss
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if max_avg == 0:
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return None
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# 初始状态：Boss索引0，血量B[0]，所有技能冷却为0，回合数0
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start_cooldown = tuple([0] * m)
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total_remaining = sum(B)
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# 启发式函数：当前回合数 + 估计剩余回合数
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f_value = math.ceil(total_remaining / max_avg) if max_avg > 0 else total_remaining
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# 初始化优先队列 (f_value, round_count, boss_idx, boss_remaining_hp, cooldown_tuple, boss_paths)
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# boss_paths是一个列表，每个元素是对应Boss的攻击序列
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initial_boss_paths = [[] for _ in range(n)]
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queue = [(f_value, 0, 0, B[0], start_cooldown, initial_boss_paths)]
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# 记录访问过的状态 (boss_idx, boss_remaining_hp, cooldown_tuple) -> 最小回合数
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visited = {}
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visited[(0, B[0], start_cooldown)] = 0
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# A*搜索主循环
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while queue:
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# 弹出f_value最小的状态进行扩展
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f_value, round_count, boss_idx, boss_rem, cooldown, boss_paths = heapq.heappop(queue)
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state_key = (boss_idx, boss_rem, cooldown)
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# 状态剪枝：如果已有更好的状态到达当前状态，跳过
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if visited.get(state_key, float('inf')) < round_count:
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continue
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# 目标状态：所有Boss都被击败
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if boss_idx >= n:
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return boss_paths
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# 动作1：等待（所有技能冷却时间-1，回合数+1）
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new_cooldown_list = [max(0, c - 1) for c in cooldown]
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new_cooldown = tuple(new_cooldown_list)
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new_round = round_count + 1
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new_state_key = (boss_idx, boss_rem, new_cooldown)
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# 如果这个等待状态更优，则加入队列
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if new_state_key not in visited or visited[new_state_key] > new_round:
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visited[new_state_key] = new_round
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# 重新计算启发式值
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total_remaining = boss_rem + sum(B[boss_idx+1:])
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estimate_rounds = math.ceil(total_remaining / max_avg) if max_avg > 0 else 0
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new_f = new_round + estimate_rounds
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# 复制boss_paths并给当前Boss添加等待动作
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new_boss_paths = [path[:] for path in boss_paths]
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new_boss_paths[boss_idx].append(-1) # -1表示等待
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heapq.heappush(queue, (new_f, new_round, boss_idx, boss_rem, new_cooldown, new_boss_paths))
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# 动作2：使用技能
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for skill_idx, (damage, skill_cooldown) in enumerate(PlayerSkills):
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# 检查技能是否可用（冷却时间为0）
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if cooldown[skill_idx] != 0:
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continue
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new_boss_idx = boss_idx
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new_boss_rem = boss_rem - damage
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# 复制boss_paths并给当前Boss添加技能使用
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new_boss_paths = [path[:] for path in boss_paths]
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new_boss_paths[boss_idx].append(skill_idx)
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# 检查是否击败了当前Boss
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if new_boss_rem <= 0:
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new_boss_idx += 1
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if new_boss_idx < n:
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new_boss_rem = B[new_boss_idx] # 切换到下一个Boss
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else:
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new_boss_rem = 0 # 所有Boss都被击败
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# 更新技能冷却时间
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new_cooldown_list = [max(0, c - 1) for c in cooldown]
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new_cooldown_list[skill_idx] = skill_cooldown # 设置使用技能的冷却时间
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new_cooldown = tuple(new_cooldown_list)
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new_round = round_count + 1
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# 如果所有Boss都被击败，直接返回结果
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if new_boss_idx >= n:
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return new_boss_paths
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new_state_key = (new_boss_idx, new_boss_rem, new_cooldown)
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# 如果这个技能使用状态更优，则加入队列
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if new_state_key not in visited or visited[new_state_key] > new_round:
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visited[new_state_key] = new_round
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# 重新计算启发式值
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total_remaining = new_boss_rem + sum(B[new_boss_idx+1:])
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estimate_rounds = math.ceil(total_remaining / max_avg) if max_avg > 0 else 0
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new_f = new_round + estimate_rounds
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heapq.heappush(queue, (new_f, new_round, new_boss_idx, new_boss_rem, new_cooldown, new_boss_paths))
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return None # 无解
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if __name__ == '__main__':
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# 测试用例
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B = [10, 20, 30, 40, 50]
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PlayerSkills = [(5, 2), (8, 3), (3, 1)]
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print("Boss血量序列:", B)
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print("玩家技能 (伤害, 冷却):", PlayerSkills)
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print()
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result = boss_fight(B, PlayerSkills)
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for i in result:
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print(i)
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# if result:
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# print("每个Boss的最优攻击序列:")
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# for i, boss_sequence in enumerate(result):
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# print(f"Boss {i+1} (血量{B[i]}): {boss_sequence}")
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# # 显示详细的技能使用说明
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# skill_details = []
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# total_damage = 0
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# for action in boss_sequence:
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# if action == -1:
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# skill_details.append("等待")
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# else:
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# damage, cooldown = PlayerSkills[action]
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# total_damage += damage
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# skill_details.append(f"技能{action}(伤害{damage},冷却{cooldown})")
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# print(f" 详细: {' -> '.join(skill_details)}")
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# print(f" 总伤害: {total_damage}, Boss血量: {B[i]}")
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# print()
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# else:
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# print("无解 - 无法击败所有Boss") |