BZOJ_2243 [SDOI2011]染色 【树链剖分+线段树】

一 　题目

　　[SDOI2011]染色

二　分析

　　感觉树链剖分的这些题真的蛮考验码力的，自己的码力还是不够啊！o(╯□╰)o

　　还是比较常规的树链剖分，但是一定记得这里的线段树在查询的时候一定要考虑链于链相邻的两个点。

　　一开始自己已经把很多坑都已经注意了，包括颜色可以为0，链的相邻点，但怎么就是不正确，还是要多刷题。

三　AC代码

/**************************************************************
    Problem: 2243
    User: Dybala21
    Language: C++
    Result: Accepted
    Time:6652 ms
    Memory:18580 kb
****************************************************************/
 
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e5 + 15;
int n, m;
int c[MAXN];
struct Edge
{
    int to, next;
}edge[MAXN<<1];
int head[MAXN], tot;
int e[MAXN][2];
int fa[MAXN], deep[MAXN], sz[MAXN], son[MAXN];
int p[MAXN], top[MAXN];
int pos;
 
void init()
{
    tot = 0, pos = 0;
    memset(head, -1, sizeof(head));
    memset(son, -1, sizeof(son));
}
void addedge(int u, int v)
{
    edge[tot].to = v;
    edge[tot].next = head[u];
    head[u] = tot++;  
}
void dfs1(int u, int pre, int d)
{
    fa[u] = pre;
    sz[u] = 1;
    deep[u] = d;
    for(int i = head[u]; i != -1; i = edge[i].next)
    {
        int v = edge[i].to;
        if(v != pre)
        {
            dfs1(v, u, d + 1);
            sz[u] += sz[v];
            if(son[u] == -1 || sz[v] > sz[son[u]])
                son[u] = v;
        }
    }
}
void dfs2(int u, int sp)
{
    p[u] = ++pos;
    top[u] = sp;
    if(son[u] != -1)
        dfs2(son[u], sp);
    else
        return;
    for(int i = head[u]; i != -1; i = edge[i].next)
    {
        int v = edge[i].to;
        if(v != fa[u] && v != son[u])
            dfs2(v, v);
    }
}
int lca(int x, int y)
{
    int f1 = top[x], f2 = top[y];
    while(f1 != f2)
    {
         
        if(deep[f1] < deep[f2])
        {
            swap(f1, f2);
            swap(x, y);
        }
        x = fa[f1];
        f1 = top[x];
    }
    if(deep[x] < deep[y])   swap(x, y);
    return y;
}
struct Node
{
    int l, r;
    int lc, rc;
    int lazy, sum;
}segTree[MAXN*3];
void pushdown(int rt)
{
    int tmp = segTree[rt].lazy;
    segTree[rt].lazy = -1;
    if(tmp == -1 || segTree[rt].l == segTree[rt].r)
        return;
    segTree[rt<<1].lc = segTree[rt<<1].rc = tmp;
    segTree[rt<<1|1].lc = segTree[rt<<1|1].rc = tmp;
    segTree[rt<<1].sum = segTree[rt<<1|1].sum = 1;
    segTree[rt<<1].lazy = segTree[rt<<1|1].lazy = tmp;
}
void maintain(int rt)
{
    segTree[rt].sum = segTree[rt<<1].sum + segTree[rt<<1|1].sum;
    if(segTree[rt<<1].rc == segTree[rt<<1|1].lc)
        segTree[rt].sum--;
    segTree[rt].lc = segTree[rt<<1].lc;
    segTree[rt].rc = segTree[rt<<1|1].rc;
}
void build(int rt, int l, int r)
{
    segTree[rt].l = l;
    segTree[rt].r = r;
    segTree[rt].lazy = -1;    
    segTree[rt].sum = 0;
    if(l == r)
        return;
    int mid = (l + r) >> 1;
    build(rt<<1, l, mid);
    build(rt<<1|1, mid + 1, r);
}
void update(int rt, int l, int r, int val)
{
    pushdown(rt);
    if(segTree[rt].l == l && segTree[rt].r == r)
    {
        segTree[rt].lazy = val;
        segTree[rt].lc = segTree[rt].rc = val;
        segTree[rt].sum = 1;
        return;
    }
    int mid = (segTree[rt].l + segTree[rt].r) >> 1;
    if(r <= mid)
        update(rt<<1, l, r, val);
    else if(l > mid)
        update(rt<<1|1, l, r, val);
    else
    {
        update(rt<<1, l, mid, val);
        update(rt<<1|1, mid+1, r, val);
    }
    maintain(rt);
}
void update(int x, int y, int val)
{
    while(top[x] != top[y])
    {
        if(deep[top[x]] < deep[top[y]])
            swap(x, y);
        update(1, p[top[x]], p[x], val);
        x = fa[top[x]];
    }
    if(deep[x] < deep[y])
        swap(x, y);
    update(1, p[y], p[x], val);
}
int query(int rt, int l, int r)
{
    pushdown(rt);
    if(segTree[rt].l == l && segTree[rt].r == r)
        return segTree[rt].sum;
    int mid = (segTree[rt].l + segTree[rt].r) >> 1;
    int ans = 0;
    if(r <= mid)
        ans += query(rt<<1, l, r);
    else if(l > mid)
        ans += query(rt<<1|1, l, r);
    else
    {
        ans += query(rt<<1, l, mid);
        ans += query(rt<<1|1, mid + 1, r);
        if(segTree[rt<<1].rc == segTree[rt<<1|1].lc)
            ans--;
    }
    return ans;
}
int find(int rt, int x)
{
    pushdown(rt);
    if(segTree[rt].l == segTree[rt].r)
        return segTree[rt].lc;
    int mid = (segTree[rt].l + segTree[rt].r) >> 1;
    if(x <= mid)
        return find(rt<<1, x);
    else
        return find(rt<<1|1, x);
}
int query(int x, int y)
{
    int res = 0;
    while(top[x] != top[y])
    {
        if(deep[top[x]] < deep[top[y]])
            swap(x, y);
        res += query(1, p[top[x]], p[x]);
        if(find(1, p[top[x]]) == find(1, p[fa[top[x]]]))
            res--;
        x = fa[top[x]];
    }
    if(deep[x] < deep[y])
        swap(x, y);
    res += query(1, p[y], p[x]);
    return res;
}
int main()
{
    //freopen("in.txt", "r", stdin);
    init();
    scanf("%d%d", &n, &m);
    for(int i = 1; i <= n; i++)
        scanf("%d", &c[i]);
    for(int i = 0; i < n - 1; i++)
    {
        scanf("%d%d", &e[i][0], &e[i][1]);
        addedge(e[i][0], e[i][1]);
        addedge(e[i][1], e[i][0]);
    }
    dfs1(1, 1, 1);
    dfs2(1, 1);
    build(1, 1, pos);
    for(int i = 1; i <= n; i++)
        update(1, p[i], p[i], c[i]);
    char op;
    int a, b, val;
    for(int i = 0; i < m; i++)
    {
        scanf(" %c %d %d", &op, &a, &b);
        if(op == 'Q')
        {
            printf("%d\n", query(a, b));
        }
        else
        {
            scanf("%d", &val);
            update(a, b, val);
        }
    }
    return 0;
}