[模板]线段树的建树、查询、单点更新、区间更新

最新推荐文章于 2024-12-01 18:07:32 发布

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最新推荐文章于 2024-12-01 18:07:32 发布

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分类专栏：树

本文链接：https://blog.youkuaiyun.com/soundwave_/article/details/52214685

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本文详细介绍线段树的基本构造方法，包括建树、查询、单点更新及区间更新等操作，并提供具体的实现代码。

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此线段树以求区间最小值为例，求区间和只需适当更改pushup()函数即可

建树

int arr[N];
int SetTree[N*4];
int pushup(int root)
{
    return min(SetTree[root<<1], SetTree[root<<1|1]);
}
void build(int root, int left, int right)
{
    if(left == right)
    {
        SetTree[root] = arr[left];
        return;
    }
    int mid = (left + right) >> 1;
    build(root<<1, left, mid);
    build(root<<1|1, mid+1, right);
    SetTree[root] = pushup(root);
}

查询

int query(int root, int left, int right, int L, int R)
{
    if(L > right || R < left)
        return 1<<29;
    if(L <= left && R >= right)
        return SetTree[root];
    int mid = (left + right) >> 1;
    int l = query(root<<1, left, mid, L, R);
    int r = query(root<<1|1, mid+1, right, L, R);
    return min(l, r);
}

单点更新

int pushup(int root)
{
    return min(SetTree[root<<1], SetTree[root<<1|1]);
}
void update(int root, int left, int right, int index, int value)
{
    if(left == right)
    {
        if(index == left)
            SetTree[root] = value;
        return;
    }
    int mid = (left + right) >> 1;
    if(index <= mid)
        update(root<<1, left, mid, index, value);
    else
        update(root<<1|1, mid+1, right, index, value);
    SetTree[root] = pushup(root);
}

区间更新（注意延迟标记这个概念）

struct{
    int val;
    int mark;
}SetTree[N*4];
int pushup(int root)
{
    return SetTree[root<<1].val + SetTree[root<<1|1].val;
}
//传递延迟标记给子节点
void pushdown(int root, int left, int mid, int right)
{
    if(SetTree[root].mark != 0)
    {
        //延迟标记传递
        SetTree[root<<1].mark = SetTree[root].mark;
        SetTree[root<<1|1].mark = SetTree[root].mark;
        //区间和也要变化
        SetTree[root<<1].val = SetTree[root].mark * (mid-left+1);
        SetTree[root<<1|1].val = SetTree[root].mark * (right-mid);
        //向下传递后，root的mark清空
        SetTree[root].mark = 0;
    }
}
//区间更新
void update(int root, int left, int right, int l, int r, int mark)
{
    if(l > right || r < left)
        return;
    if(l <= left && r >= right)
    {
        SetTree[root].mark = mark;
        SetTree[root].val = mark * (right-left+1);
        return;
    }
    int mid = (left + right) >> 1;
    pushdown(root, left, mid, right);
    update(root<<1, left, mid, l, r, mark);
    update(root<<1|1, mid+1, right, l, r, mark);
    SetTree[root].val = pushup(root);
}

或者

struct{
    int val;
    int mark;
    int l;//区间下界
    int r;//区间上界
}Tree[N*4];
int pushup(int root)
{
    return Tree[root<<1].val + Tree[root<<1|1].val;
}
//传递延迟标记给子节点
void pushdown(int root)
{
    if(Tree[root].mark != 0)
    {
        int mid = (Tree[root].l + Tree[root].r) >> 1;
        Tree[root<<1].mark = Tree[root].mark;
        Tree[root<<1|1].mark = Tree[root].mark;
        Tree[root<<1].val = Tree[root].mark * (mid-Tree[root].l+1);
        Tree[root<<1|1].val = Tree[root].mark * (Tree[root].r-mid);
        Tree[root].mark = 0;
    }
}
//区间更新
void update(int root, int l, int r, int value)
{
    if(l > Tree[root].r || r < Tree[root].l)
        return;
    if(l <= Tree[root].l && r >= Tree[root].r)
    {
        Tree[root].mark = value;
        Tree[root].val = value * (Tree[root].r-Tree[root].l+1);
        return;
    }
    pushdown(root);
    update(root<<1, l, r, value);
    update(root<<1|1, l , r, value);
    Tree[root].val = pushup(root);
}