leetcode-174. Dungeon Game

本文介绍了一个利用动态规划算法解决的游戏问题——骑士以最少初始血量成功救出公主。通过从终点反向推导至起点的方式,确保了每一步都是向着最优解迈进。
class Solution {
public:
    int calculateMinimumHP(vector<vector<int>>& dungeon){
        //正着看的话,只有局部最优,没有全局最优,类似于贪心
        //应该倒着动态规划
        int m = dungeon.size();
        int n = dungeon[0].size();
        vector<vector<int>> dp(m+1, vector<int>(n+1, INT_MAX));//初始化要为最大值!!!
        //dp中存储在此位置所需要的最小的体力值
        dp[m][n-1] = 1;
        dp[m-1][n] = 1;
        for(int i=m-1;i>=0;i--) //i往上走
            for(int j=n-1;j>=0;j--){ //j往左走
                int need = min(dp[i+1][j], dp[i][j+1]) - dungeon[i][j];
                dp[i][j] = need <= 0 ? 1 : need;
            }
        //体力不能等于0,至少要为1,所以need最小是1
        return dp[0][0];
    }
};

The demons had captured the princess (P) and imprisoned her in the bottom-right corner of a dungeon. The dungeon consists of M x N rooms laid out in a 2D grid. Our valiant knight (K) was initially positioned in the top-left room and must fight his way through the dungeon to rescue the princess.

The knight has an initial health point represented by a positive integer. If at any point his health point drops to 0 or below, he dies immediately.

Some of the rooms are guarded by demons, so the knight loses health (negative integers) upon entering these rooms; other rooms are either empty (0's) or contain magic orbs that increase the knight's health (positiveintegers).

In order to reach the princess as quickly as possible, the knight decides to move only rightward or downward in each step.

 

Write a function to determine the knight's minimum initial health so that he is able to rescue the princess.

For example, given the dungeon below, the initial health of the knight must be at least 7 if he follows the optimal path RIGHT-> RIGHT -> DOWN -> DOWN.

-2 (K)-33
-5-101
1030-5 (P)

 

Note:

  • The knight's health has no upper bound.
  • Any room can contain threats or power-ups, even the first room the knight enters and the bottom-right room where the princess is imprisoned.

内容概要:本文系统介绍了算术优化算法(AOA)的基本原理、核心思想及Python实现方法,并通过图像分割的实际案例展示了其应用价值。AOA是一种基于种群的元启发式算法,其核心思想来源于四则运算,利用乘除运算进行全局勘探,加减运算进行局部开发,通过数学优化器加速函数(MOA)和数学优化概率(MOP)动态控制搜索过程,在全局探索与局部开发之间实现平衡。文章详细解析了算法的初始化、勘探与开发阶段的更新策略,并提供了完整的Python代码实现,结合Rastrigin函数进行测试验证。进一步地,以Flask框架搭建前后端分离系统,将AOA应用于图像分割任务,展示了其在实际工程中的可行性与高效性。最后,通过收敛速度、寻优精度等指标评估算法性能,并提出自适应参数调整、模型优化和并行计算等改进策略。; 适合人群:具备一定Python编程基础和优化算法基础知识的高校学生、科研人员及工程技术人员,尤其适合从事人工智能、图像处理、智能优化等领域的从业者;; 使用场景及目标:①理解元启发式算法的设计思想与实现机制;②掌握AOA在函数优化、图像分割等实际问题中的建模与求解方法;③学习如何将优化算法集成到Web系统中实现工程化应用;④为算法性能评估与改进提供实践参考; 阅读建议:建议读者结合代码逐行调试,深入理解算法流程中MOA与MOP的作用机制,尝试在不同测试函数上运行算法以观察性能差异,并可进一步扩展图像分割模块,引入更复杂的预处理或后处理技术以提升分割效果。
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