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);
    }