dfs+dp (java)
Intuition\n Describe your first thoughts on how to solve this problem. \n\n# Approach\n Describe your approach to solving the problem. \n\n# Complexity\n- Time 
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\n\n# Code\n```java []\nclass Solution {\n    public int maxx =0;\n    public int maxMoves(int[][] grid) {\n        int[][]dp = new int[grid.length][grid[0].length];\n        HashMap<Integer,Integer>s2= new HashMap<>();\n        for(int w=0;w<dp.length;w++){\n            for(int a=0;a<dp[w].length;a++){\n                dp[w][a]=-1;\n            }\n        }\n        for(int i=0;i<grid.length;i++){\n        int cur = grid[i][0];\n        preorder(grid,i,0,cur,0,dp,i,s2);\n        }\n        return maxx;\n    }\n    public void preorder(int[][]grid,int in, int jn, int cur, int em, int[][]dp, int de, HashMap<Integer,Integer>s2){\n        maxx = Math.max(maxx,em);\n        if(s2.containsKey(de)){\n            s2.put(de,Math.max(s2.get(de),maxx));\n        }\n        else{\n            s2.put(de,maxx);\n        }\n\n        dp[in][jn]=de;\n\n        if(jn+1<grid[in].length){\n        if(in-1>=0){\n            if(grid[in-1][jn+1]>cur){\n                if(dp[in-1][jn+1]!=-1){\n                    int elf = s2.get(de);\n                    int jk = elf-em; \n                    maxx = Math.max(maxx,em+jk);\n                }\n                else{\n                preorder(grid,in-1,jn+1,grid[in-1][jn+1],em+1,dp,de,s2);\n                }\n            }    \n        }\n        if(in>=0 && in<grid.length){\n             if(grid[in][jn+1]>cur){\n                if(dp[in][jn+1]!=-1){\n                    int el = s2.get(de);\n                    int js = el-em; \n                    maxx = Math.max(maxx,em+js);\n                }\n                else{\n                preorder(grid,in,jn+1,grid[in][jn+1],em+1,dp,de,s2);\n            }} \n        }\n\n         if(in+1<grid.length){\n             if(grid[in+1][jn+1]>cur){\n                if(dp[in+1][jn+1]!=-1){\n                    int elx = s2.get(de);\n                    int ja = elx-em; \n                    maxx = Math.max(maxx,em+ja);\n                }\n                else{\n                preorder(grid,in+1,jn+1,grid[in+1][jn+1],em+1,dp,de,s2);\n            }}\n        }      \n        }\n    }\n}\n```
['Dynamic Programming', 'Depth-First Search', 'Java']