数据结构-线段树（区间树）（Java）

自定义线段树

/**
 * @Author: FangJu
 * @Date: 2019/8/21
 */
public class SegmentTree<E> {
    private E[] tree;
    private E[] data;
    private Merger<E> merger;

    public SegmentTree(E[] arr, Merger<E> merger) {
        if (merger == null) {
            throw new IllegalArgumentException("Require merger is not null.");
        }
        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, arr.length - 1);
    }

    // 在treeIndex的位置创建表示区间[l...r]的线段树
    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]);
    }

    //获取树中元素个数
    public int getSize() {
        return data.length;
    }

    //获取树中某个索引的值
    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孩子节点的索引
    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孩子节点的索引
    private int rightChild(int index) {
        return 2 * index + 2;
    }

    // 返回区间[queryL, queryR]的值
    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);
    }

    private E query(int treeIndex, int l, int r, int queryL, int queryR) {
        if (l == queryL && r == queryR)
            return tree[treeIndex];
        int leftTreeIndex = leftChild(treeIndex);
        int rightTreeIndex = rightChild(treeIndex);
        int mid = l + (r - l) / 2;

        if (queryL > mid) {//在区间右边
            return query(rightTreeIndex, mid + 1, r, queryL, queryR);
        } else if (queryR <= mid) {//在区间左边
            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
    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
    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;
        // 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();
    }

}

扩展
线段树还可以扩展到二维数组或者多维其他结构

相关例题 见 算法-区域和检索
其他数据结构 见 数据结构知识点汇总