BZOJ 2243 染色
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;
}
