【数据结构】SegmentTree 线段树
作者:互联网
数据结构源码
接口
public interface Merger<E> {
E merge(E a, E b);
}
实现类
public class SegmentTree<E> {
private E[] tree;
private E[] data;
private Merger<E> merger;
public SegmentTree(E[] arr, Merger<E> merger) {
this.merger = merger;
data = (E[]) new Object[arr.length];
for (int i = 0; i < arr.length; i++) {
data[i] = arr[i];
}
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
* @param l
* @param r
*/
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) / 2;
buildSegmentTree(leftTreeIndex, l, mid);
buildSegmentTree(rightTreeIndex, mid + 1, r);
tree[treeIndex] = merger.merge(tree[leftTreeIndex], tree[rightTreeIndex]);
}
public int getSize() {
return data.length;
}
public E get(int index) {
if (index < 0 || index >= data.length)
throw new IllegalArgumentException("Index is illegal!");
return data[index];
}
/**
* 返回完全二叉树的数组表示中,一个索引所表示的元素的左子节点的索引
* @param index
* @return
*/
private int leftChild(int index) {
return 2 * index + 1;
}
/**
* 返回完全二叉树的数组表示中,一个索引所表示的元素的右子节点的索引
* @param index
* @return
*/
private int rightChild(int index) {
return 2 * index + 2;
}
/**
* 返回区间[queryL, queryR]的值
* @param queryL
* @param queryR
* @return
*/
public E query(int queryL, int queryR) {
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treeID为根的线段树中[l..r]的范围里,搜索区间[queryL..queryR]的值
* @param treeIndex
* @param l
* @param r
* @return
*/
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) / 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);
}
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
* @param e
*/
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
* @param l
* @param r
* @param index
* @param e
*/
private void set(int treeIndex, int l, int r, int index, E e) {
if (l == r) {
tree[treeIndex] = e;
return;
}
int mid = (l + r) / 2;
// treeIndex的节点分为[l...mid]和[mid+1...r]两部分
int leftTreeIndex = leftChild(treeIndex);
int rightTreeIndex = rightChild(treeIndex);
if (index >= mid + 1)
set(rightTreeIndex, mid + 1, r, index, e);
else // index <= mid
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 - 1) {
res.append(", ");
}
}
res.append(']');
return res.toString();
}
public static void main(String[] args) {
Integer[] nums = {-2, 0, 3, -5, 2, -1};
SegmentTree<Integer> segTree = new SegmentTree<>(nums, (a, b) -> a + b);
System.out.println(segTree.query(0, 2));
System.out.println(segTree.query(2, 5));
System.out.println(segTree.query(0, 5));
}
}
数据结构拆解
维护字段和内部类
private E[] tree;
private E[] data;
private Merger<E> merger;
构造函数
public SegmentTree(E[] arr, Merger<E> merger) {
this.merger = merger;
data = (E[]) new Object[arr.length];
for (int i = 0; i < arr.length; i++) {
data[i] = arr[i];
}
tree = (E[]) new Object[4 * arr.length];
buildSegmentTree(0, 0, data.length - 1);
}
增
/**
* 在treeIndex的位置创建表示区间[l .. r]的线段树
* @param treeIndex
* @param l
* @param r
*/
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) / 2;
buildSegmentTree(leftTreeIndex, l, mid);
buildSegmentTree(rightTreeIndex, mid + 1, r);
tree[treeIndex] = merger.merge(tree[leftTreeIndex], tree[rightTreeIndex]);
}
删
改
/**
* 将index位置的值,更新为e
* @param index
* @param e
*/
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
* @param l
* @param r
* @param index
* @param e
*/
private void set(int treeIndex, int l, int r, int index, E e) {
if (l == r) {
tree[treeIndex] = e;
return;
}
int mid = (l + r) / 2;
// treeIndex的节点分为[l...mid]和[mid+1...r]两部分
int leftTreeIndex = leftChild(treeIndex);
int rightTreeIndex = rightChild(treeIndex);
if (index >= mid + 1)
set(rightTreeIndex, mid + 1, r, index, e);
else // index <= mid
set(leftTreeIndex, l, mid, index, e);
tree[treeIndex] = merger.merge(tree[leftTreeIndex], tree[rightTreeIndex]);
}
查
public int getSize() {
return data.length;
}
public E get(int index) {
if (index < 0 || index >= data.length)
throw new IllegalArgumentException("Index is illegal!");
return data[index];
}
/**
* 返回完全二叉树的数组表示中,一个索引所表示的元素的左子节点的索引
* @param index
* @return
*/
private int leftChild(int index) {
return 2 * index + 1;
}
/**
* 返回完全二叉树的数组表示中,一个索引所表示的元素的右子节点的索引
* @param index
* @return
*/
private int rightChild(int index) {
return 2 * index + 2;
}
/**
* 返回区间[queryL, queryR]的值
* @param queryL
* @param queryR
* @return
*/
public E query(int queryL, int queryR) {
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treeID为根的线段树中[l..r]的范围里,搜索区间[queryL..queryR]的值
* @param treeIndex
* @param l
* @param r
* @return
*/
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) / 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);
}
E leftResult = query(leftTreeIndex, l, mid, queryL, mid);
E rightResult = query(rightTreeIndex, mid + 1, r, mid + 1, queryR);
return merger.merge(leftResult, rightResult);
}
标签:index,return,treeIndex,int,线段,param,SegmentTree,数据结构,data 来源: https://blog.csdn.net/fisherish/article/details/121742116