Java与算法（13）

 Java与算法（13）

1.高效求解完全二叉树的节点个数

public class GetTreeNodeNumber {
public static class Node {
public int value;
public Node left;
public Node right;

public Node(int data) {
this.value = data;
}
}

public static int nodeNum(Node head) {
if (head == null) {
return 0;
}
return bs(head, 1, mostLeftLevel(head, 1));
}

public static int bs(Node node, int l, int h) {
if (l == h) {
return 1;
}
if (mostLeftLevel(node.right, l + 1) == h) {
return (1 << (h - l)) + bs(node.right, l + 1, h);
} else {
return (1 << (h - l - 1)) + bs(node.left, l + 1, h);
}
}

public static int mostLeftLevel(Node node, int level) {
while (node != null) {
level++;
node = node.left;
}
return level - 1;
}
public static void main(String[] args) {
Node head = new Node(1);
head.left = new Node(2);
head.right = new Node(3);
head.left.left = new Node(4);
head.left.right = new Node(5);
head.right.left = new Node(6);
System.out.println(nodeNum(head));

}

}

2.通过先序和中序数组直接生成后序数组

public class PreAndInArrayToPosArray {
public static int[] getPosArray(int[] pre, int[] in) {
if (pre == null || in == null) {
return null;
}
int len = pre.length;
int[] pos = new int[len];
HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
for (int i = 0; i < len; i++) {
map.put(in[i], i);
}
setPos(pre, 0, len - 1, in, 0, len - 1, pos, len - 1, map);
return pos;
}

public static int setPos(int[] p, int pi, int pj, int[] n, int ni, int nj,
int[] s, int si, HashMap<Integer, Integer> map) {
if (pi > pj) {
return si;
}
s[si--] = p[pi];
int i = map.get(p[pi]);
si = setPos(p, pj - nj + i + 1, pj, n, i + 1, nj, s, si, map);
return setPos(p, pi + 1, pi + i - ni, n, ni, i - 1, s, si, map);
}

public static void main(String[] args) {
int[] pre = { 1, 2, 4, 5, 3, 6, 7 };
int[] in = { 4, 2, 5, 1, 6, 3, 7 };
int[] pos = getPosArray(pre, in);
for(int i=0;i<pos.length;i++) {
System.out.println(pos[i]);
}

}

}

3.先序，后序，中序两两结合重构二叉树

public class ErgtoTree {
public static class Node {
public int value;
public Node left;
public Node right;

public Node(int data) {
this.value = data;
}
}

public static Node preintoTree(int[] pre,int[] in) {
if (pre==null || in==null) {
return null;
}
HashMap<Integer, Integer> hashMap = new HashMap<>();
for(int i=0;i<in.length;i++) {
hashMap.put(in[i], i);
}

return prein(pre, 0, pre.length-1, in, 0, in.length-1, hashMap);

}

public static Node prein(int[] p,int pi,int pj,int[] n,int ni,int nj,HashMap<Integer, Integer> hashMap) {
if (pi>pj) {
return null;
}
Node root = new Node(p[pi]);
int index = hashMap.get(p[pi]);
root.left = prein(p, pi+1,pi+index-ni, n, ni,index-1, hashMap);
root.right = prein(p, pi+index-ni+1, pj, n, index+1, nj, hashMap);
return root;
}

public static void prePrint(Node root) {
if (root==null) {
return;
}
System.out.print(root.value+" ");
prePrint(root.left);
prePrint(root.right);
}

public static Node inPosToTree(int[] in, int[] pos) {
if (in == null || pos == null) {
return null;
}
HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
for (int i = 0; i < in.length; i++) {
map.put(in[i], i);
}
return inPos(in, 0, in.length - 1, pos, 0, pos.length - 1, map);
}

public static Node inPos(int[] n, int ni, int nj, int[] s, int si, int sj,
HashMap<Integer, Integer> map) {
if (si > sj) {
return null;
}
Node head = new Node(s[sj]);
int index = map.get(s[sj]);
head.left = inPos(n, ni, index - 1, s, si, si + index - ni - 1, map);
head.right = inPos(n, index + 1, nj, s, si + index - ni, sj - 1, map);
return head;
}

public static Node prePosToTree(int[] pre, int[] pos) {
if (pre == null || pos == null) {
return null;
}
HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
for (int i = 0; i < pos.length; i++) {
map.put(pos[i], i);
}
return prePos(pre, 0, pre.length - 1, pos, 0, pos.length - 1, map);
}

public static Node prePos(int[] p, int pi, int pj, int[] s, int si, int sj,
HashMap<Integer, Integer> map) {
Node head = new Node(s[sj--]);
if (pi == pj) {
return head;
}
int index = map.get(p[++pi]);
head.left = prePos(p, pi, pi + index - si, s, si, index, map);
head.right = prePos(p, pi + index - si + 1, pj, s, index + 1, sj, map);
return head;
}
public static void main(String[] args) {
int[] pre = { 1, 2, 4, 5, 8, 9, 3, 6, 7 };
int[] in = { 4, 2, 8, 5, 9, 1, 6, 3, 7 };
int[] pos = { 4, 8, 9, 5, 2, 6, 7, 3, 1 };
Node root1 = preintoTree(pre, in);
prePrint(root1);
System.out.println();
Node root2 = inPosToTree(in, pos);
prePrint(root2);
System.out.println();
Node root3 = prePosToTree(pre, pos);
prePrint(root3);
}

}