Java与算法（9）

Java与算法（9）

1.给定二叉树头节点，每个节点的值都不同，找到含有节点最多的搜索二叉子树。

public class FindBST {public static class Node {int data;Node left;Node right;public Node(int data) {// TODO Auto-generated constructor stubthis.data = data;left = null;right = null;}}public static ArrayList<Node> trees = new ArrayList<>();public void buildTree(int[] array) {for(int i=0;i<array.length;i++) {trees.add(new Node(array[i]));}for(int index = 0;index<array.length/2-1;index++) {trees.get(index).left =  trees.get(index*2+1);trees.get(index).right = trees.get(index*2+2);}int lastindex = array.length/2-1;trees.get(lastindex).left = trees.get(lastindex*2+1);if (array.length%2==1) {trees.get(lastindex).right = trees.get(lastindex*2+2);}}public Node bigBST(Node root) {int[] record =  new int[3];return find(root, record);}public Node find(Node root,int[] r) {if (root==null) {r[0] = 0;r[1] = Integer.MAX_VALUE;r[2] = Integer.MAX_VALUE;return null;}int data = root.data;Node right = root.right;Node left = root.left;Node lBST = find(left,r);int lSIZE = r[0];int lMIN = r[1];int lMAX = r[2];Node rBST = find(right, r);int rSIZE = r[0];int rMIN = r[1];int rMAX = r[2];r[1] = Math.min(lMIN, data);r[2] = Math.max(rMAX, data);if (left==lBST && right==rBST && lMAX<data && data<rMIN) {r[0] = rSIZE+lSIZE +1;return root;}r[0] = Math.max(rSIZE, lSIZE);return lSIZE>rSIZE?lBST:rBST;}}

2.实现二叉树三种遍历，要求：

时间复杂度O(N)，空间复杂度O(1)

public class MorrisTree {public static class Node {int data;Node left;Node right;public Node(int data) {// TODO Auto-generated constructor stubthis.data = data;left = null;right = null;}}public static ArrayList<Node> trees = new ArrayList<>();public void buildTree(int[] array) {for(int i=0;i<array.length;i++) {trees.add(new Node(array[i]));}for(int index = 0;index<array.length/2-1;index++) {trees.get(index).left =  trees.get(index*2+1);trees.get(index).right = trees.get(index*2+2);}int lastindex = array.length/2-1;trees.get(lastindex).left = trees.get(lastindex*2+1);if (array.length%2==1) {trees.get(lastindex).right = trees.get(lastindex*2+2);}}/** * 先序遍历 * @param head */public static void morrisIn(Node head) {if (head == null) {return;}Node cur1 = head;Node cur2 = null;while (cur1 != null) {cur2 = cur1.left;if (cur2 != null) {while (cur2.right != null && cur2.right != cur1) {cur2 = cur2.right;}if (cur2.right == null) {cur2.right = cur1;cur1 = cur1.left;continue;} else {cur2.right = null;}}System.out.print(cur1.data + " ");cur1 = cur1.right;}System.out.println();}/** * 中序遍历 * @param head */public static void morrisPre(Node head) {if (head == null) {return;}Node cur1 = head;Node cur2 = null;while (cur1 != null) {cur2 = cur1.left;if (cur2 != null) {while (cur2.right != null && cur2.right != cur1) {cur2 = cur2.right;}if (cur2.right == null) {cur2.right = cur1;System.out.print(cur1.data + " ");cur1 = cur1.left;continue;} else {cur2.right = null;}} else {System.out.print(cur1.data + " ");}cur1 = cur1.right;}System.out.println();}/** * 后序遍历 * @param head */public static void morrisPos(Node head) {if (head == null) {return;}Node cur1 = head;Node cur2 = null;while (cur1 != null) {cur2 = cur1.left;if (cur2 != null) {while (cur2.right != null && cur2.right != cur1) {cur2 = cur2.right;}if (cur2.right == null) {cur2.right = cur1;cur1 = cur1.left;continue;} else {cur2.right = null;printEdge(cur1.left);}}cur1 = cur1.right;}printEdge(head);System.out.println();}public static void printEdge(Node head) {Node tail = reverseEdge(head);Node cur = tail;while (cur != null) {System.out.print(cur.data + " ");cur = cur.right;}reverseEdge(tail);}public static Node reverseEdge(Node from) {Node pre = null;Node next = null;while (from != null) {next = from.right;from.right = pre;pre = from;from = next;}return pre;}public static void main(String[] args) {int[] array = {3,6,5,9,10,7,29};MorrisTree tree = new MorrisTree();tree.buildTree(array);tree.morrisIn(trees.get(0));System.out.println();tree.morrisPre(trees.get(0));System.out.println();tree.morrisPos(trees.get(0));}}

3.实现二叉树三种遍历（递归和非递归）

public class BinartTree {public static class Node {int data;Node left;Node right;public Node(int data) {// TODO Auto-generated constructor stubthis.data = data;left = null;right = null;}}public static ArrayList<Node> trees = new ArrayList<>();public void buildTree(int[] array) {for(int i=0;i<array.length;i++) {trees.add(new Node(array[i]));}for(int index = 0;index<array.length/2-1;index++) {trees.get(index).left =  trees.get(index*2+1);trees.get(index).right = trees.get(index*2+2);}int lastindex = array.length/2-1;trees.get(lastindex).left = trees.get(lastindex*2+1);if (array.length%2==1) {trees.get(lastindex).right = trees.get(lastindex*2+2);}}/** * 先序遍历,递归实现 * @param root */public void preOrder(Node root) {if (root==null) {return;}System.out.print(root.data+" ");preOrder(root.left);preOrder(root.right);}/** * 先序遍历，非递归实现 * @param root */public void preOrderNotrecur(Node root) {Stack<Node> stack = new Stack<>();if (root!=null) {stack.push(root);while (!stack.isEmpty()) {root = stack.pop();System.out.print(root.data+" ");if (root.right!=null) {stack.push(root.right);}if (root.left!=null) {stack.push(root.left);}}}System.out.println("");}/** * 中序遍历，递归实现 * @param root */public void inOrder(Node root) {if (root == null) {return;}inOrder(root.left);System.out.print(root.data+" ");inOrder(root.right);}/** * 中序遍历，非递归实现 * @param root */public void inOrderNotrecur(Node root) {Stack<Node> stack = new Stack<>();if (root!=null) {while (!stack.isEmpty() || root!=null) {if (root!=null) {stack.push(root);root=root.left;} else {root = stack.pop();System.out.print(root.data+" ");root = root.right;}}}System.out.println();}/** * 后序遍历，递归实现 * @param root */public void posOrder(Node root) {if (root == null) {return ;}posOrder(root.left);posOrder(root.right);System.out.print(root.data+" ");}public void posOrderNotrecur(Node root) {Stack<Node> stack = new Stack<>();if (root!=null) {stack.push(root);Node node = null;while (!stack.isEmpty()) {node=stack.peek();if (node.left!=null && root!=node.left && root!=node.right) {stack.push(node.left);} else if (node.right!=null && root!=node.right) {stack.push(node.right);} else {System.out.print(stack.pop().data+" ");root = node;}}}System.out.println();}public static void main(String[] args) {int[] array = {3,6,5,9,10,7,29};BinartTree tree = new BinartTree();tree.buildTree(array);System.out.println("先序遍历递归实现");tree.preOrder(trees.get(0));System.out.println("");System.out.println("先序遍历非递归实现");tree.preOrderNotrecur(trees.get(0));System.out.println();System.out.println("中序遍历递归实现");tree.inOrder(trees.get(0));System.out.println();System.out.println("中序遍历递归实现");tree.inOrderNotrecur(trees.get(0));System.out.println();System.out.println("后序遍历递归实现");tree.posOrder(trees.get(0));System.out.println("");System.out.println("后序遍历递归实现");tree.posOrderNotrecur(trees.get(0));}}