The classic recursive algorithm problem

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1. Fibonacci cut (stairs)

class Solution {
    HashMap<Integer,Integer> cache = new HashMap<>();
    
    public int fib(int N) {
        if (cache.containsKey(N)) {
            return cache.get(N);
        }
        
        int result;
        
        if (N < 2) {
            result = N;
        }else {
            result = fib(N-1) + fib(N-2);
        }
        
        cache.put(N,result);
        return result;
    }
}

2. merge two sorted linked list

/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) { val = x; }
 * }
 */
class Solution {
    public ListNode mergeTwoLists(ListNode l1, ListNode l2) {
        if (l1 == null) return l2;
        if (l2 == null) return l1;
        
        ListNode pre = new ListNode(Integer.MIN_VALUE);
        if (l1.val < l2.val) {
            pre.next = l1;
            l1.next = mergeTwoLists(l1.next,l2);
        }else {
            pre.next = l2;
            l2.next = mergeTwoLists(l1,l2.next);
        }
        
        return pre.next;
        
    }
}

3. Reverse list

/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) { val = x; }
 * }
 */
class Solution {
    public ListNode reverseList(ListNode head) {
        ListNode prev = null;
        ListNode cur = head;
        
        return helper(cur,prev);
    }
    
    public ListNode helper(ListNode cur, ListNode prev) {
        if (cur == null) return prev;
        ListNode next = cur.next;
        cur.next = prev;
        
        return helper(next,cur);
    }
}

4. The maximum depth of the binary tree

class Solution {
  public int maxDepth(TreeNode root) {
      if (root == null) return 0;
      
      return Math.max(maxDepth(root.left),maxDepth(root.right)) + 1;
  }
};