Java线段树

线段树不是完全二叉树，是平衡二叉树

堆也是平衡二叉树

堆满二叉树：

h层，一共有2^h-1个节点（大约是2^h）

最后一层（h-1层）有2^(h-1)个节点

最后一层的节点数大致等于前面所有层节点之和

如果区间有n个元素，数组表示需要4n的空间

不考虑添加元素，使用4n的静态空间即可

接口：

public interface Merger<E> {
    E merge(E a, E b);
}

　　

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, 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) / 2;
        int mid = l + (r - l) / 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;
    }

    @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();
    }
}

　　测试：

public class Main {

    public static void main(String[] args) {

        Integer[] nums = {-2, 0, 3, -5, 2, -1};
//        SegmentTree<Integer> segTree = new SegmentTree<>(nums,
//                new Merger<Integer>() {
//                    @Override
//                    public Integer merge(Integer a, Integer b) {
//                        return a + b;
//                    }
//                });

        SegmentTree<Integer> segTree = new SegmentTree<>(nums,
                (a, b) -> a + b);
        System.out.println(segTree);
    }
}

　　查找方法：

// 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);
    }

    // 在以treeIndex为根的线段树中[l...r]的范围里，搜索区间[queryL...queryR]的值
    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;
        // treeIndex的节点分为[l...mid]和[mid+1...r]两部分

        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);
    }

　　

public class Main {
    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));
}
}

　　

线段树添加：

public class NumArray {

	private SegmentTree<Integer> segmentTree;
	public NumArray(int[] nums){
		if(nums.length>0){
			Integer[] data=new Integer[nums.length];
			for(int i=0;i<nums.length;i++)
				data[i]=nums[i];
			segmentTree =new SegmentTree<>(data, (a,b)->a+b);
		}
	}
	public int sumRange(int i,int j){
		if(segmentTree==null)
			throw new IllegalArgumentException("Segment Tree is null");
		return segmentTree.query(i, j);
	}
}

　　不用线段树添加：

public class NumArray2 {
	 private int[] sum;//sum[i]存储前i个元素和 sum[0]=0
     public NumArray2(int[] nums){
    	 sum=new int[nums.length+1];
    	 sum[0]=0;
    	 for(int i=01;i<sum.length;i++)
    		 sum[i]=sum[i-1]+nums[i-1];
     }
	 public int sumRange(int i,int j){
		 return sum[j+1]-sum[i];
	 }
}

　　不用线段树修改：(效率很低)

public class NumArray3 {
    private int[] sum;
    private int[] data;
    public NumArray3(int[] nums){
    	data=new int[nums.length];
    	for(int i=0;i<data.length;i++)
    		data[i]=nums[i];
    	sum=new int[nums.length+1];
    	sum[0]=0;
    	for(int i=1;i<sum.length;i++)
    		sum[i]=sum[i-1]+nums[i-1];
    }
    public void update(int index,int val){
    	data[index]=val;
    	for(int i=index+1;i<sum.length;i++)
    		sum[i]=sum[i-1]+data[i-1];
    }
    public int sumRange(int i,int j){
    	return sum[j+1]-sum[i];
    }
}

　　用线段树更新：

//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;
    	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]);
    }

　　

public void update(int index,int val){
		if(segmentTree==null)
			throw new IllegalArgumentException("Segment Tree is null");
		segmentTree.set(index,val);
	}