树链剖分+区间染色

因为是一颗树不是森林，所以应该用树剖就行，但是LCT好像也能写。。

直接用线段树维护树上的节点，注意pushdown还有询问的时候要考虑区间相交的地方，也就是左孩子右边和有孩子的左边，如果两个颜色相同就-1

树上询问的时候也是一样，跨越轻链的时候也要看一下相接的地方颜色是不是一样。。w

#include <bits/stdc++.h>

#define INF 0x3f3f3f3f

#define full(a, b) memset(a, b, sizeof a)

using namespace std;

typedef long long ll;

inline int lowbit(int x){ return x & (-x); }

inline int read(){

    int X = 0, w = 0; char ch = 0;

    while(!isdigit(ch)) { w |= ch == '-'; ch = getchar(); }

    while(isdigit(ch)) X = (X << 3) + (X << 1) + (ch ^ 48), ch = getchar();

    return w ? -X : X;

}

inline int gcd(int a, int b){ return a % b ? gcd(b, a % b) : b; }

inline int lcm(int a, int b){ return a / gcd(a, b) * b; }

template<typename T>

inline T max(T x, T y, T z){ return max(max(x, y), z); }

template<typename T>

inline T min(T x, T y, T z){ return min(min(x, y), z); }

template<typename A, typename B, typename C>

inline A fpow(A x, B p, C lyd){

    A ans = 1;

    for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;

    return ans;

}

const int N = 100005;

int n, m, cnt, dfn, head[N], size[N], depth[N], p[N], son[N], top[N], val[N], w[N], id[N];

int tree[N<<2], lc[N<<2], rc[N<<2], c[N<<2];

struct Edge { int v, next; } edge[N<<1];

void addEdge(int a, int b){

    edge[cnt].v = b, edge[cnt].next = head[a], head[a] = cnt ++;

}

void dfs1(int s, int fa){

    depth[s] = depth[fa] + 1;

    p[s] = fa;

    size[s] = 1;

    int child = -1;

    for(int i = head[s]; i != -1; i = edge[i].next){

        int u = edge[i].v;

        if(u == fa) continue;

        dfs1(u, s);

        size[s] += size[u];

        if(size[u] > child) child = size[u], son[s] = u;

    }

}

void dfs2(int s, int tp){

    id[s] = ++dfn;

    w[id[s]] = val[s];

    top[s] = tp;

    if(son[s] != -1) dfs2(son[s], tp);

    for(int i = head[s]; i != -1; i = edge[i].next){

        int u = edge[i].v;

        if(u == p[s] || u == son[s]) continue;

        dfs2(u, u);

    }

}

void push_up(int rt){

    int l = rt << 1, r = rt << 1 | 1;

    tree[rt] = tree[l] + tree[r];

    lc[rt] = lc[l], rc[rt] = rc[r];

    if(rc[l] == lc[r]) tree[rt] --;

}

void push_down(int rt){

    //printf("c[%d] = %d\n", rt, c[rt]);

    if(c[rt] != -1){

        int ls = rt << 1, rs = rt << 1 | 1;

        c[ls] = c[rs] = c[rt];

        tree[ls] = tree[rs] = 1;

        lc[ls] = rc[ls] = lc[rs] = rc[rs] = c[rt];

        c[rt] = -1;

    }

}

void buildTree(int rt, int l, int r){

    if(l == r){

        tree[rt] = 1, c[rt] = -1, lc[rt] = rc[rt] = w[l];

        return;

    }

    int mid = (l + r) >> 1;

    buildTree(rt << 1, l, mid);

    buildTree(rt << 1 | 1, mid + 1, r);

    push_up(rt);

}

void modify(int rt, int l, int r, int ml ,int mr, int tot){

    if(l == ml && r == mr){

        c[rt] = tot, tree[rt] = 1, lc[rt] = rc[rt] = tot;

        return;

    }

    push_down(rt);

    int mid = (l + r) >> 1;

    if(ml > mid) modify(rt << 1 | 1, mid + 1, r, ml, mr, tot);

    else if(mr <= mid) modify(rt << 1, l, mid, ml, mr, tot);

    else modify(rt << 1, l, mid, ml, mid, tot), modify(rt << 1 | 1, mid + 1, r, mid + 1, mr, tot);

    push_up(rt);

}

int query(int rt, int l, int r, int ql, int qr){

    if(l == ql && r == qr){

        return tree[rt];

    }

    push_down(rt);

    int mid = (l + r) >> 1;

    if(ql > mid) return query(rt << 1 | 1, mid + 1, r, ql, qr);

    else if(qr <= mid) return query(rt << 1, l, mid, ql, qr);

    else{

        int ls = query(rt << 1, l, mid, ql, mid);

        int rs = query(rt << 1 | 1, mid + 1, r, mid + 1, qr);

        return rc[rt << 1] == lc[rt << 1 | 1] ? ls + rs - 1 : ls + rs;

    }

}

int color(int rt, int l, int r, int index){

    if(l == r) return lc[rt];

    push_down(rt);

    int mid = (l + r) >> 1;

    if(index > mid) return color(rt << 1 | 1, mid + 1, r, index);

    return color(rt << 1, l, mid, index);

}

void treeModify(int x, int y, int tot){

    while(top[x] != top[y]){

        if(depth[top[x]] < depth[top[y]]) swap(x, y);

        modify(1, 1, n, id[top[x]], id[x], tot);

        x = p[top[x]];

    }

    if(depth[x] > depth[y]) swap(x, y);

    modify(1, 1, n, id[x], id[y], tot);

}

int treeQuery(int x, int y){

    int ret = 0;

    while(top[x] != top[y]){

        if(depth[top[x]] < depth[top[y]]) swap(x, y);

        ret += query(1, 1, n, id[top[x]], id[x]);

        if(color(1, 1, n, id[top[x]]) == color(1, 1, n, id[p[top[x]]])) ret --;

        x = p[top[x]];

    }

    if(depth[x] > depth[y]) swap(x, y);

    ret += query(1, 1, n, id[x], id[y]);

    return ret;

}

int main(){

    full(head, -1), full(son, -1), full(c, -1);

    n = read(), m = read();

    for(int i = 1; i <= n; i ++) val[i] = read();

    for(int i = 0; i < n - 1; i ++){

        int u = read(), v = read();

        addEdge(u, v), addEdge(v, u);

    }

    dfs1(1, 0), dfs2(1, 1);

    buildTree(1, 1, n);

    while(m --){

        char opt[10]; scanf("%s", opt);

        int a = read(), b = read();

        if(opt[0] == 'C'){

            int c = read();

            treeModify(a, b, c);

        }

        else if(opt[0] == 'Q'){

            printf("%d\n", treeQuery(a, b));

        }

    }

    return 0;

}

于是我换了个LCT的做法

交换区间的时候注意把lc和rc也换下，其他的没啥区别。

但是我在link的时候加了个pushup，然后莫名WA。。难道不能加的吗qwq，就算左右子树为0，pushup也不会改变什么啊。。。

#include <bits/stdc++.h>

#define INF 0x3f3f3f3f

#define full(a, b) memset(a, b, sizeof a)

using namespace std;

typedef long long ll;

inline int lowbit(int x){ return x & (-x); }

inline int read(){

    int X = 0, w = 0; char ch = 0;

    while(!isdigit(ch)) { w |= ch == '-'; ch = getchar(); }

    while(isdigit(ch)) X = (X << 3) + (X << 1) + (ch ^ 48), ch = getchar();

    return w ? -X : X;

}

inline int gcd(int a, int b){ return a % b ? gcd(b, a % b) : b; }

inline int lcm(int a, int b){ return a / gcd(a, b) * b; }

template<typename T>

inline T max(T x, T y, T z){ return max(max(x, y), z); }

template<typename T>

inline T min(T x, T y, T z){ return min(min(x, y), z); }

template<typename A, typename B, typename C>

inline A fpow(A x, B p, C lyd){

    A ans = 1;

    for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;

    return ans;

}

const int N = 100005;

int n, m, tot, ch[N][2], c[N], lc[N], rc[N], val[N], rev[N], sum[N], fa[N], st[N];

void newNode(int v){

    ++tot, c[tot] = -1, lc[tot] = rc[tot] = val[tot] = v;

    sum[tot] = 1, rev[tot] = ch[tot][0] = ch[tot][1] = fa[tot] = 0;

}

void reverse(int x){

    rev[x] ^= 1;

    swap(ch[x][0], ch[x][1]);

    swap(lc[x], rc[x]);

}

void pushtag(int x, int e){

    val[x] = lc[x] = rc[x] = e;

    sum[x] = 1, c[x] = e;

}

void push_up(int x){

    int l = ch[x][0], r = ch[x][1];

    lc[x] = l ? lc[l] : val[x];

    rc[x] = r ? rc[r] : val[x];

    if(l && r) sum[x] = sum[l] + sum[r] + 1 - (rc[l] == val[x]) - (lc[r] == val[x]);

    else if(l) sum[x] = sum[l] + 1 - (rc[l] == val[x]);

    else if(r) sum[x] = sum[r] + 1 - (lc[r] == val[x]);

    else sum[x] = 1;

}

void push_down(int x){

    if(rev[x]){

        int l = ch[x][0], r = ch[x][1];

        if(l) reverse(l);

        if(r) reverse(r);

        rev[x] ^= 1;

    }

    if(c[x] != -1){

        int l = ch[x][0], r = ch[x][1];

        if(l) pushtag(l, c[x]);

        if(r) pushtag(r, c[x]);

        c[x] = -1;

    }

}

bool isRoot(int x){

    return (ch[fa[x]][0] != x && ch[fa[x]][1] != x);

}

void rotate(int x){

    int y = fa[x], z = fa[y], p = (ch[y][1] == x) ^ 1;

    push_down(y), push_down(x);

    ch[y][p^1] = ch[x][p], fa[ch[x][p]] = y;

    if(!isRoot(y)) ch[z][ch[z][1] == y] = x;

    fa[x] = z, fa[y] = x, ch[x][p] = y;

    push_up(y), push_up(x);

}

void splay(int x){

    int pos = 0; st[++pos] = x;

    for(int i = x; !isRoot(i); i = fa[i]) st[++pos] = fa[i];

    while(pos) push_down(st[pos--]);

    while(!isRoot(x)){

        int y = fa[x], z = fa[y];

        if(!isRoot(y)){

            (ch[y][0] == x) ^ (ch[z][0] == y) ? rotate(x) : rotate(y);

        }

        rotate(x);

    }

    push_up(x);

}

void access(int x){

    for(int p = 0; x; p = x, x = fa[x])

        splay(x), ch[x][1] = p, push_up(x);

}

void makeRoot(int x){

    access(x), splay(x), reverse(x);

}

void link(int x, int y){

    makeRoot(x), fa[x] = y;//push_up(y);

}

void split(int x, int y){

    makeRoot(x), access(y), splay(y);

}

int main(){

    full(c, -1);

    n = read(), m = read();

    for(int i = 1; i <= n; i ++){

        int v = read();

        newNode(v);

    }

    for(int i = 0; i < n - 1; i ++){

        int u = read(), v = read();

        link(u, v);

    }

    while(m --){

        char opt[10]; scanf("%s", opt);

        int a = read(), b = read();

        if(opt[0] == 'C'){

            int i = read();

            split(a, b);

            pushtag(b, i);

        }

        else if(opt[0] == 'Q'){

            split(a, b);

            printf("%d\n", sum[b]);

        }

    }

    return 0;

}