【BZOJ2243】[SDOI2011]染色【树链剖分】【线段树】

【题目链接】

很容易想到树剖，然后主要是线段树。

sum记录一段区间内的颜色子段个数，lx和rx分别记录左端点和右端点的颜色是什么。

然后就差不多了。

注意树剖爬的时候也得注意节点颜色。

/* Pigonometry */#include <cstdio>#include <algorithm>using namespace std;const int maxn = 100005, maxm = maxn;int n, m, head[maxn], cnt, w[maxn];struct _edge {int v, next;} g[maxm << 1];inline int iread() {int f = 1, x = 0; char ch = getchar();for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';return f * x;}inline void add(int u, int v) {g[cnt] = (_edge){v, head[u]};head[u] = cnt++;}int son[maxn], size[maxn], top[maxn], pre[maxn], dfn[maxn], depth[maxn], clo;inline void dfs1(int x) {size[x] = 1; son[x] = 0;for(int i = head[x]; ~i; i = g[i].next) if(g[i].v ^ pre[x]) {pre[g[i].v] = x;depth[g[i].v] = depth[x] + 1;dfs1(g[i].v);size[x] += size[g[i].v];if(size[g[i].v] > size[son[x]]) son[x] = g[i].v;}}inline void dfs2(int x, int tp) {top[x] = tp; dfn[x] = ++clo;if(son[x]) dfs2(son[x], tp);for(int i = head[x]; ~i; i = g[i].next) if(g[i].v ^ pre[x] && g[i].v ^ son[x])dfs2(g[i].v, g[i].v);}int val[maxn], sum[maxn << 2], lx[maxn << 2], rx[maxn << 2], setv[maxn << 2];inline void pushup(int p) {sum[p] = sum[p << 1] + sum[p << 1 | 1] - (rx[p << 1] == lx[p << 1 | 1]);lx[p] = lx[p << 1];rx[p] = rx[p << 1 | 1];}inline void pushdown(int p) {if(setv[p]) {lx[p << 1] = rx[p << 1] = lx[p << 1 | 1] = rx[p << 1 | 1] = setv[p << 1] = setv[p << 1 | 1] = setv[p];sum[p << 1] = sum[p << 1 | 1] = 1;setv[p] = 0;}}inline void build(int p, int l, int r) {if(l == r) {sum[p] = 1;lx[p] = rx[p] = val[l];return;}int mid = l + r >> 1;build(p << 1, l, mid); build(p << 1 | 1, mid + 1, r);pushup(p);}int LX, RX;inline int query(int p, int l, int r, int x, int y) {if(l == x) LX = lx[p];if(r == y) RX = rx[p];if(x <= l && r <= y) return sum[p];int mid = l + r >> 1, ans = 0, x1 = 0, x2 = 0;pushdown(p);if(x <= mid) ans += query(p << 1, l, mid, x, y), x1 = rx[p << 1];if(y > mid) ans += query(p << 1 | 1, mid + 1, r, x, y), x2 = lx[p << 1 | 1];return ans - (x1 == x2 && x1 != 0);}inline void change(int p, int l, int r, int x, int y, int c) {if(x <= l && r <= y) {sum[p] = 1;lx[p] = rx[p] = setv[p] = c;return;}int mid = l + r >> 1;pushdown(p);if(x <= mid) change(p << 1, l, mid, x, y, c);if(y > mid) change(p << 1 | 1, mid + 1, r, x, y, c);pushup(p);}inline int querychain(int u, int v) {int topu = top[u], topv = top[v], ans = 0;int ux = 0, vx = 0; LX = RX = 0;for(; topu != topv; topu = top[u = pre[topu]]) {if(depth[topu] < depth[topv]) swap(topu, topv), swap(u, v), swap(ux, vx);ans += query(1, 1, clo, dfn[topu], dfn[u]) - (RX == ux);ux = LX;}if(depth[u] < depth[v]) swap(u, v), swap(ux, vx);ans += query(1, 1, clo, dfn[v], dfn[u]) - (ux == RX) - (vx == LX);return ans;}inline void changechain(int u, int v, int c) {int topu = top[u], topv = top[v], ans = 0;for(; topu != topv; topu = top[u = pre[topu]]) {if(depth[topu] < depth[topv]) swap(topu, topv), swap(u, v);change(1, 1, clo, dfn[topu], dfn[u], c);}if(depth[u] < depth[v]) swap(u, v);change(1, 1, clo, dfn[v], dfn[u], c);}int main() {n = iread(); m = iread();for(int i = 1; i <= n; i++) w[i] = iread() + 1, head[i] = -1; cnt = 0;for(int i = 1; i < n; i++) {int u = iread(), v = iread();add(u, v); add(v, u);}depth[1] = 1;dfs1(1); dfs2(1, 1);for(int i = 1; i <= n; i++) val[dfn[i]] = w[i];build(1, 1, clo);while(m--) {char ch = getchar(); for(; ch != 'Q' && ch != 'C'; ch = getchar());if(ch == 'Q') {int u = iread(), v = iread();printf("%d\n", querychain(u, v));}else if(ch == 'C') {int u = iread(), v = iread(), c = iread(); c++;changechain(u, v, c);}}return 0;}

附mkdata和暴力。

#include <cstdio>#include <cstdlib>#include <algorithm>#include <ctime>inline int rd(int x) {return rand() % x + 1;}int main() {freopen("orz.in", "w", stdout);srand(time(0));int n = 10000, m = 10000, c = 10000;printf("%d %d\n", n, m);for(int i = 1; i <= n; i++) printf("%d ", rd(c));printf("\n");for(int i = 1; i < n; i++) {printf("%d %d\n", rd(i), i + 1);}for(int i = 1; i <= m; i++) {int opt = rd(2);if(opt == 1) printf("Q %d %d\n", rd(n), rd(n));else printf("C %d %d %d\n", rd(n), rd(n), rd(c));}return 0;}

#include <cstdio>#include <algorithm>using namespace std;const int maxn = 100005, maxm = 100005;int n, m, head[maxn], cnt, pre[maxn], val[maxn], depth[maxn];struct _edge {int v, next;} g[maxm << 1];inline int iread() {int f = 1, x = 0; char ch = getchar();for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';return f * x;}inline void add(int u, int v) {g[cnt] = (_edge){v, head[u]};head[u] = cnt++;}inline void dfs(int x) {for(int i = head[x]; ~i; i = g[i].next) if(g[i].v ^ pre[x]) {pre[g[i].v] = x;depth[g[i].v] = depth[x] + 1;dfs(g[i].v);}}inline int query(int u, int v) {int ans = 1;if(depth[u] < depth[v]) swap(u, v);for(; depth[u] != depth[v]; u = pre[u]) {if(val[u] != val[pre[u]]) ans++;}for(; u != v; u = pre[u], v = pre[v]) {if(val[u] != val[pre[u]]) ans++;if(val[v] != val[pre[v]]) ans++;}return ans;}inline void change(int u, int v, int c) {if(depth[u] < depth[v]) swap(u, v);for(; depth[u] != depth[v]; u = pre[u]) val[u] = c;for(; u != v; u = pre[u], v = pre[v]) val[u] = val[v] = c;val[u] = val[v] = c;}int main() {freopen("orz.in", "r", stdin); freopen("orz.ans", "w", stdout);n = iread(); m = iread();for(int i = 1; i <= n; i++) head[i] = -1, val[i] = iread(); cnt = 0;for(int i = 1; i < n; i++) {int u = iread(), v = iread();add(u, v); add(v, u);}depth[1] = 1;dfs(1);while(m--) {char ch = getchar(); for(; ch != 'Q' && ch != 'C'; ch = getchar());if(ch == 'Q') {int u = iread(), v = iread();printf("%d\n", query(u, v));}else if(ch == 'C') {int u = iread(), v = iread(), c = iread();change(u, v, c);}}return 0;}

话说随机数据这个暴力跑的飞快。