Bottom-up 解法

遇到一些题目, 用递归加 bottom-up 解法能得到更优的时间复杂度, 对这些题目做一个汇总

1. google code jam Rational Number Tree

2. 二叉树的公共祖先节点

3. leetcode convert sorted list to balanced search tree

1. Rational Number Tree

void getPQ(int n, int &p, int &q) {

    if(n == 1) {

        p = q = 1;

        return ;

    }

   

    getPQ(n/2, p, q);

      

    int newp, newq;

    if(n & 1) { /* 右孩子 */

        newp = p + q;

        newq = q;

   

    }else {

        newp = p;

        newq = p + q;

    }

    p = newp;

    q = newq;

}

   

void getN(int &n, int p, int q) {

    if(p == 1 && q == 1) {

        n = 1;

        return;

    }

   

    int newp, newq;

    if(p > q) { /* 右孩子 */

        newp = p - q;

        newq = q;

        getN(n, newp, newq);

        n = n*2 + 1;

    }else {

        newp = p;

        newq = q-p;

        getN(n, newp, newq);

        n = n*2;

    }

}

2. 二叉树的公共节点

Node* LCA(Node *root, Node *p, Node *q) {

    if(root == NULL) return NULL;

    if(p == root || q == root) return root;

    Node* lchild = LCA(root->left, p, q);

    Node* rchild = LCA(root->right, p, q);

    if(lchild && rchild) return root;

    if(lchild) return lchild;

    return rchild;

}

3. Convert Sorted List to Balanced Search Tree

TreeNode* buildTree(ListNode* &head, int st, int ed)  {
	if(st > ed) return NULL;

	int mid = (st+ed)>>1;

	TreeNode* lchild = buildTree(head, st, mid-1);
	TreeNode* parent = new TreeNode(head->val);
	head = head->next;
	TreeNode* rchild = buildTree(head, mid+1, ed);

	parent->left = lchild;
	parent->right = rchild;

	return parent;
}