2021-07-31：给定数组father，大小为N，表示一共有N个节点，father[i] = j 表示点i的

2021-07-31：给定数组father，大小为N，表示一共有N个节点，father[i] = j 表示点i的父亲是点j， father表示的树一定是一棵树而不是森林，给定数组values，大小为N，values[i]=v表示节点i的权值是v。实现如下4个方法，保证4个方法都很快！1)让某个子树所有节点值加上v，入参：int head, int v；2)查询某个子树所有节点值的累加和，入参：int head；3)在树上从a到b的整条链上所有加上v，入参：int a, int b, int v；4)查询在树上从a到b的整条链上所有节点值的累加和，入参：int a, int b。

福大大 答案2021-07-31：

时间紧。见代码。

代码用golang编写。代码如下：

package main

import (
    "fmt"
    "math"
)

func main() {
    father := []int{1, 2, 3, 4, 5}
    values := []int{6, 7, 8, 9, 10}
    tc := NewTreeChain(father, values)
    right := NewRight(father, values)
    tc.addSubtree(11, 22)
    right.addSubtree(11, 22)
    tc.addSubtree(33, 44)
    right.addSubtree(33, 44)
    if tc.queryChain(33, 44) != right.queryChain(33, 44) {
        fmt.Println("错误")
    } else {
        fmt.Println("正确")
    }
}

type TreeChain struct {
    // 时间戳 0 1 2 3 4
    tim int
    // 节点个数是n，节点编号是1~n
    n int
    // 谁是头
    h int
    // 朴素树结构
    tree [][]int
    // 权重数组 原始的0节点权重是6 -> val[1] = 6
    val []int
    // father数组一个平移，因为标号要+1
    fa []int
    // 深度数组！
    dep []int
    // son[i] = 0 i这个节点，没有儿子
    // son[i] != 0 j i这个节点，重儿子是j
    son []int
    // siz[i] i这个节点为头的子树，有多少个节点
    siz []int
    // top[i] = j i这个节点，所在的重链，头是j
    top []int
    // dfn[i] = j i这个节点，在dfs序中是第j个
    dfn []int
    // 如果原来的节点a，权重是10
    // 如果a节点在dfs序中是第5个节点, tnw[5] = 10
    tnw []int
    // 线段树，在tnw上，玩连续的区间查询或者更新
    seg *SegmentTree
}

func NewTreeChain(father []int, values []int) *TreeChain {
    ret := &TreeChain{}
    // 原始的树 tree，弄好了，可以从i这个点，找到下级的直接孩子
    // 上面的一大堆结构，准备好了空间，values -> val
    // 找到头部点
    ret.initTree(father, values)
    // fa;
    // dep;
    // son;
    // siz;
    ret.dfs1(ret.h, 0)
    // top;
    // dfn;
    // tnw;
    ret.dfs2(ret.h, ret.h)
    ret.seg = NewSegmentTree(ret.tnw)
    ret.seg.build(1, ret.n, 1)
    return ret
}

func (this *TreeChain) initTree(father []int, values []int) {
    this.tim = 0
    this.n = len(father) + 1
    this.tree = make([][]int, this.n)
    this.val = make([]int, this.n)
    this.fa = make([]int, this.n)
    this.dep = make([]int, this.n)
    this.son = make([]int, this.n)
    this.siz = make([]int, this.n)
    this.top = make([]int, this.n)
    this.dfn = make([]int, this.n)
    this.tnw = make([]int, this.n)
    this.n--
    cnum := make([]int, this.n)
    for i := 0; i < this.n; i++ {
        this.val[i+1] = values[i]
    }
    for i := 0; i < this.n; i++ {
        if father[i] == i {
            this.h = i + 1
        } else {
            cnum[father[i]]++
        }
    }
    this.tree[0] = make([]int, 0)
    for i := 0; i < this.n; i++ {
        this.tree[i+1] = make([]int, cnum[i])
    }
    for i := 0; i < this.n; i++ {
        if i+1 != this.h {
            cnum[father[i]]--
            this.tree[father[i]+1][cnum[father[i]]] = i + 1
        }
    }
}

// u 当前节点
// f u的父节点
func (this *TreeChain) dfs1(u int, f int) {
    this.fa[u] = f
    this.dep[u] = this.dep[f] + 1
    this.siz[u] = 1
    maxSize := -1
    for _, v := range this.tree[u] { // 遍历u节点，所有的直接孩子
        this.dfs1(v, u)
        this.siz[u] += this.siz[v]
        if this.siz[v] > maxSize {
            maxSize = this.siz[v]
            this.son[u] = v
        }
    }
}

// u当前节点
// t是u所在重链的头部
func (this *TreeChain) dfs2(u int, t int) {
    this.tim++
    this.dfn[u] = this.tim
    this.top[u] = t
    this.tnw[this.tim] = this.val[u]
    if this.son[u] != 0 { // 如果u有儿子 siz[u] > 1
        this.dfs2(this.son[u], t)
        for _, v := range this.tree[u] {
            if v != this.son[u] {
                this.dfs2(v, v)
            }
        }
    }
}

// head为头的子树上，所有节点值+value
// 因为节点经过平移，所以head(原始节点) -> head(平移节点)
func (this *TreeChain) addSubtree(head int, value int) {
    // 原始点编号 -> 平移编号
    head++
    // 平移编号 -> dfs编号 dfn[head]
    this.seg.add(this.dfn[head], this.dfn[head]+this.siz[head]-1, value, 1, this.n, 1)
}

func (this *TreeChain) querySubtree(head int) int {
    head++
    return this.seg.query(this.dfn[head], this.dfn[head]+this.siz[head]-1, 1, this.n, 1)
}

func (this *TreeChain) addChain(a int, b int, v int) {
    a++
    b++
    for this.top[a] != this.top[b] {
        if this.dep[this.top[a]] > this.dep[this.top[b]] {
            this.seg.add(this.dfn[this.top[a]], this.dfn[a], v, 1, this.n, 1)
            a = this.fa[this.top[a]]
        } else {
            this.seg.add(this.dfn[this.top[b]], this.dfn[b], v, 1, this.n, 1)
            b = this.fa[this.top[b]]
        }
    }
    if this.dep[a] > this.dep[b] {
        this.seg.add(this.dfn[b], this.dfn[a], v, 1, this.n, 1)
    } else {
        this.seg.add(this.dfn[a], this.dfn[b], v, 1, this.n, 1)
    }
}

func (this *TreeChain) queryChain(a int, b int) int {
    a++
    b++
    ans := 0
    for this.top[a] != this.top[b] {
        if this.dep[this.top[a]] > this.dep[this.top[b]] {
            ans += this.seg.query(this.dfn[this.top[a]], this.dfn[a], 1, this.n, 1)
            a = this.fa[this.top[a]]
        } else {
            ans += this.seg.query(this.dfn[this.top[b]], this.dfn[b], 1, this.n, 1)
            b = this.fa[this.top[b]]
        }
    }
    if this.dep[a] > this.dep[b] {
        ans += this.seg.query(this.dfn[b], this.dfn[a], 1, this.n, 1)
    } else {
        ans += this.seg.query(this.dfn[a], this.dfn[b], 1, this.n, 1)
    }
    return ans
}

type SegmentTree struct {
    MAXN int
    arr  []int
    sum  []int
    lazy []int
}

func NewSegmentTree(origin []int) *SegmentTree {
    ret := &SegmentTree{}
    ret.MAXN = len(origin)
    ret.arr = origin
    ret.sum = make([]int, ret.MAXN<<2)
    ret.lazy = make([]int, ret.MAXN<<2)
    return ret
}

func (this *SegmentTree) pushUp(rt int) {
    this.sum[rt] = this.sum[rt<<1] + this.sum[rt<<1|1]
}

func (this *SegmentTree) pushDown(rt int, ln int, rn int) {
    if this.lazy[rt] != 0 {
        this.lazy[rt<<1] += this.lazy[rt]
        this.sum[rt<<1] += this.lazy[rt] * ln
        this.lazy[rt<<1|1] += this.lazy[rt]
        this.sum[rt<<1|1] += this.lazy[rt] * rn
        this.lazy[rt] = 0
    }
}

func (this *SegmentTree) build(l int, r int, rt int) {
    if l == r {
        this.sum[rt] = this.arr[l]
        return
    }
    mid := (l + r) >> 1
    this.build(l, mid, rt<<1)
    this.build(mid+1, r, rt<<1|1)
    this.pushUp(rt)
}

func (this *SegmentTree) add(L int, R int, C int, l int, r int, rt int) {
    if L <= l && r <= R {
        this.sum[rt] += C * (r - l + 1)
        this.lazy[rt] += C
        return
    }
    mid := (l + r) >> 1
    this.pushDown(rt, mid-l+1, r-mid)
    if L <= mid {
        this.add(L, R, C, l, mid, rt<<1)
    }
    if R > mid {
        this.add(L, R, C, mid+1, r, rt<<1|1)
    }
    this.pushUp(rt)
}

func (this *SegmentTree) query(L int, R int, l int, r int, rt int) int {
    if L <= l && r <= R {
        return this.sum[rt]
    }
    mid := (l + r) >> 1
    this.pushDown(rt, mid-l+1, r-mid)
    ans := 0
    if L <= mid {
        ans += this.query(L, R, l, mid, rt<<1)
    }
    if R > mid {
        ans += this.query(L, R, mid+1, r, rt<<1|1)
    }
    return ans
}

// 为了测试，这个结构是暴力但正确的方法
type Right struct {
    n    int
    tree [][]int
    fa   []int
    val  []int
    path map[int]int
}

func NewRight(father []int, value []int) *Right {
    ret := &Right{}
    ret.n = len(father)
    ret.tree = make([][]int, ret.n)
    ret.fa = make([]int, ret.n)
    ret.val = make([]int, ret.n)
    for i := 0; i < ret.n; i++ {
        ret.fa[i] = father[i]
        ret.val[i] = value[i]
    }
    help := make([]int, ret.n)
    h := 0
    for i := 0; i < ret.n; i++ {
        if father[i] == i {
            h = i
        } else {
            help[father[i]]++
        }
    }
    for i := 0; i < ret.n; i++ {
        ret.tree[i] = make([]int, help[i])
    }
    for i := 0; i < ret.n; i++ {
        if i != h {
            help[father[i]]--
            ret.tree[father[i]][help[father[i]]] = i
        }
    }
    ret.path = make(map[int]int)
    return ret
}

func (this *Right) addSubtree(head int, value int) {
    this.val[head] += value
    for _, next := range this.tree[head] {
        this.addSubtree(next, value)
    }
}

func (this *Right) querySubtree(head int) int {
    ans := this.val[head]
    for _, next := range this.tree[head] {
        ans += this.querySubtree(next)
    }
    return ans
}

func (this *Right) addChain(a int, b int, v int) {
    this.path = make(map[int]int)
    this.path[a] = math.MinInt64
    for a != this.fa[a] {
        this.path[this.fa[a]] = a
        a = this.fa[a]
    }
    _, ok := this.path[b]
    for !ok {
        this.val[b] += v
        b = this.fa[b]
    }
    this.val[b] += v
    for this.path[b] != math.MaxInt64 {
        b = this.path[b]
        this.val[b] += v
    }
}

func (this *Right) queryChain(a int, b int) int {
    this.path = make(map[int]int)
    this.path[a] = math.MinInt64
    for a != this.fa[a] {
        this.path[this.fa[a]] = a
        a = this.fa[a]
    }
    ans := 0
    _, ok := this.path[b]
    for !ok {
        ans += this.val[b]
        b = this.fa[b]
    }
    ans += this.val[b]
    for this.path[b] != math.MinInt64 {
        b = this.path[b]
        ans += this.val[b]
    }
    return ans
}

左神java代码