写在前面
本系列代码Gitee地址为点击这里
实现的方法
/**
* 返回区间内的元素个数
*
* @return 区间内的元素个数
*/
public int getSize();
/**
* 获取index索引位置的元素
*
* @param index 索引
* @return 该索引位置的元素
*/
public E get(int index);
/**
* 返回区间[queryL, queryR]的值
*
* @param queryL 左边界
* @param queryR 右边界
* @return 合并值
*/
public E query(int queryL, int queryR);
/**
* 将index位置的值，更新为e
*
* @param index 索引
* @param e 更新值
*/
public void set(int index, E e)
@Override
public String toString();
实现
Merger.java
public interface Merger {
/**
* 合并规则
*
* @param a 参数a
* @param b 参数b
* @return 按照合并规则合并a和b之后的值
*/
E merge(E a, E b);
}
SegmentTree.java
@SuppressWarnings("unchecked")
public class SegmentTree {
/**
* 原数组
*/
private E[] data;
/**
* 线段树
*/
private E[] tree;
private Merger merger;
/**
* 构造函数
*
* @param arr 数组
* @param merger 合并规则
*/
public SegmentTree(E[] arr, Merger merger) {
this.merger = merger;
data = (E[]) new Object[arr.length];
System.arraycopy(arr, 0, data, 0, arr.length);
tree = (E[]) new Object[4 * arr.length];
buildSegmentTree(0, 0, data.length - 1);
}
/**
* 在treeIndex的位置创建表示区间[l...r]的线段树
*
* @param treeIndex 当前要创建的线段树的对应的根节点的索引
* @param l 线段对应的左端点
* @param r 线段对应的右端点
*/
private void buildSegmentTree(int treeIndex, int l, int r) {
if (l == r) {
tree[treeIndex] = data[l];
return;
}
int leftTreeIndex = leftChild(treeIndex);
int rightTreeIndex = rightChild(treeIndex);
int mid = l + (r - l) / 2;
buildSegmentTree(leftTreeIndex, l, mid);
buildSegmentTree(rightTreeIndex, mid + 1, r);
tree[treeIndex] = merger.merge(tree[leftTreeIndex], tree[rightTreeIndex]);
}
/**
* 返回区间内的元素个数
*
* @return 区间内的元素个数
*/
public int getSize() {
return data.length;
}
/**
* 获取index索引位置的元素
*
* @param index 索引
* @return 该索引位置的元素
*/
public E get(int index) {
if (index < 0 || index >= data.length) {
throw new IllegalArgumentException("Index is illegal.");
}
return data[index];
}
/**
* 返回左孩子节点的索引
*
* @param index 索引
* @return 该索引左孩子的索引
*/
private int leftChild(int index) {
return index * 2 + 1;
}
/**
* 返回右孩子节点的索引
*
* @param index 索引
* @return 该索引右孩子的索引
*/
private int rightChild(int index) {
return index * 2 + 2;
}
/**
* 返回区间[queryL, queryR]的值
*
* @param queryL 左边界
* @param queryR 右边界
* @return 合并值
*/
public E query(int queryL, int queryR) {
// 参数不合法
if (queryL < 0 || queryL >= data.length ||
queryR < 0 || queryR >= data.length ||
queryL > queryR) {
throw new IllegalArgumentException("Index is illegal.");
}
return query(0, 0, data.length - 1, queryL, queryR);
}
/**
* 在以treeIndex为根的线段树中[l...r]的范围里，搜索区间[queryL, queryR]的值
*
* @param treeIndex 根节点索引
* @param l 线段树左边界
* @param r 线段树右边界
* @param queryL 搜索区间左边界
* @param queryR 搜索区间右边界
* @return 搜索值
*/
private E query(int treeIndex, int l, int r, int queryL, int queryR) {
if (l == queryL && r == queryR) {
return tree[treeIndex];
}
int mid = l + (r - l) / 2;
int leftTreeIndex = leftChild(treeIndex);
int rightTreeIndex = rightChild(treeIndex);
if (queryL >= mid + 1) {
return query(rightTreeIndex, mid + 1, r, queryL, queryR);
} else if (queryR <= mid) {
return query(leftTreeIndex, l, mid, queryL, queryR);
} else {
E leftResult = query(leftTreeIndex, l, mid, queryL, mid);
E rightResult = query(rightTreeIndex, mid + 1, r, mid + 1, queryR);
return merger.merge(leftResult, rightResult);
}
}
/**
* 将index位置的值，更新为e
*
* @param index 索引
* @param e 更新值
*/
public void set(int index, E e) {
if (index < 0 || index >= data.length) {
throw new IllegalArgumentException("Index is illegal");
}
data[index] = e;
set(0, 0, data.length - 1, index, e);
}
/**
* 在以treeIndex为根的线段树中更新index的值为e
*
* @param treeIndex 根节点索引
* @param l 左边界
* @param r 右边界
* @param index 更新索引值
* @param e 更新值
*/
private void set(int treeIndex, int l, int r, int index, E e) {
if (l == r) {
tree[treeIndex] = e;
return;
}
int mid = l + (r - l) / 2;
int leftTreeIndex = leftChild(treeIndex);
int rightTreeIndex = rightChild(treeIndex);
if (index >= mid + 1) {
set(rightTreeIndex, mid + 1, r, index, e);
} else {
set(leftTreeIndex, l, mid, index, e);
}
tree[treeIndex] = merger.merge(tree[leftTreeIndex], tree[rightTreeIndex]);
}
@Override
public String toString() {
StringBuilder res = new StringBuilder();
res.append('[');
for (int i = 0; i < tree.length; i++) {
if (tree[i] != null) {
res.append(tree[i]);
} else {
res.append("null");
}
if (i != tree.length) {
res.append(',');
} else {
res.append(']');
}
}
return res.toString();
}
}
LinkedListSegmentTree.java
public class LinkedListSegmentTree {
/**
* 节点内部类
*/
private class Node {
E e;
int l;
int r;
Node left;
Node right;
Node(E e, int l, int r) {
this.e = e;
this.l = l;
this.r = r;
this.left = null;
this.right = null;
}
Node(int l, int r) {
this(null, l, r);
}
@Override
public String toString() {
return "Node{" +
"e=" + e +
", l=" + l +
", r=" + r +
'}';
}
}
/**
* 原数组
*/
private E[] data;
/**
* 线段树
*/
private Node root;
/**
* 合并规则
*/
private Merger merger;
/**
* 利用一个数组个合并规则创建一棵线段树
*
* @param arr 原始数组
* @param merger 合并规则
*/
public LinkedListSegmentTree(E[] arr, Merger merger) {
this.merger = merger;
data = (E[]) new Object[arr.length];
System.arraycopy(arr, 0, data, 0, arr.length);
root = buildSegmentTree(0, data.length - 1);
}
/**
* 构建l到r之间的线段树，并返回线段树的根节点
*
* @param l 左边界
* @param r 右边界
* @return 线段树根节点
*/
private Node buildSegmentTree(int l, int r) {
if (l == r) {
return new Node(data[l], l, r);
}
int mid = l + (r - l) / 2;
Node node = new Node(l, r);
node.left = buildSegmentTree(l, mid);
node.right = buildSegmentTree(mid + 1, r);
node.e = merger.merge(node.left.e, node.right.e);
return node;
}
/**
* 返回区间内的元素个数
*
* @return 区间内的元素个数
*/
public int getSize() {
return data.length;
}
/**
* 获取index索引位置的元素
*
* @param index 索引
* @return 该索引位置的元素
*/
public E get(int index) {
if (index < 0 || index >= data.length) {
throw new IllegalArgumentException("Index is illegal.");
}
return data[index];
}
/**
* 返回区间[queryL, queryR]的值
*
* @param queryL 左边界
* @param queryR 右边界
* @return 合并值
*/
public E query(int queryL, int queryR) {
// 参数不合法
if (queryL < 0 || queryL >= data.length ||
queryR < 0 || queryR >= data.length ||
queryL > queryR) {
throw new IllegalArgumentException("Index is illegal.");
}
return query(root, 0, data.length - 1, queryL, queryR);
}
/**
* 在以node为根的线段树中[l...r]的范围里，搜索区间[queryL, queryR]的值
*
* @param node 根节点索引
* @param l 线段树左边界
* @param r 线段树右边界
* @param queryL 搜索区间左边界
* @param queryR 搜索区间右边界
* @return 搜索值
*/
private E query(Node node, int l, int r, int queryL, int queryR) {
if (l == queryL && r == queryR) {
return node.e;
}
int mid = l + (r - l) / 2;
Node leftNode = node.left;
Node rightNode = node.right;
if (queryL >= mid + 1) {
return query(rightNode, mid + 1, r, queryL, queryR);
} else if (queryR <= mid) {
return query(leftNode, l, mid, queryL, queryR);
} else {
E leftResult = query(leftNode, l, mid, queryL, mid);
E rightResult = query(rightNode, mid + 1, r, mid + 1, queryR);
return merger.merge(leftResult, rightResult);
}
}
/**
* 将index位置的值，更新为e
*
* @param index 索引
* @param e 更新值
*/
public void set(int index, E e) {
if (index < 0 || index >= data.length) {
throw new IllegalArgumentException("Index is illegal");
}
data[index] = e;
set(root, 0, data.length - 1, index, e);
}
/**
* 在以node为根的线段树中更新index的值为e
*
* @param node 根节点索引
* @param l 左边界
* @param r 右边界
* @param index 更新索引值
* @param e 更新值
*/
private void set(Node node, int l, int r, int index, E e) {
if (l == r) {
node.e = e;
return;
}
int mid = l + (r - l) / 2;
Node leftNode = node.left;
Node rightNode = node.right;
if (index >= mid + 1) {
set(rightNode, mid + 1, r, index, e);
} else {
set(leftNode, l, mid, index, e);
}
node.e = merger.merge(leftNode.e, rightNode.e);
}
private String toString(Node node) {
if (node == null) {
return "null ";
}
return node + " " + toString(node.left) + toString(node.right);
}
@Override
public String toString() {
return toString(root);
}
}