BZOJ 3631 松鼠的新家 - 树链剖分 / 树上差分

传送门

分析：

树链剖分：x->y，将x到y的路径加一，并将x端点的答案-1，最后统计答案。

树上差分：x->y，x+1，y+1，lca-1，fa[lca]-1,并将x打上标记，最后统计前缀和时将打上标记的点-1.

两种方法最后都要将终点答案-1.

code

差分

#include<bits/stdc++.h>
using namespace std;
namespace IO {
	template<typename T>
	inline void read(T &x) {
		T i = 0, f = 1;
		char ch = getchar();
		for(; (ch < '0' || ch > '9') && ch != '-'; ch = getchar());
		if(ch == '-') f = -1, ch = getchar();
		for(; ch >= '0' && ch <= '9'; ch = getchar()) i = (i << 3) + (i << 1) + (ch - '0');
		x = i * f;
	}
	template<typename T>
	inline void wr(T x) {
		if(x < 0) putchar('-'), x = -x;
		if(x > 9) wr(x / 10);
		putchar(x % 10 + '0');
	}
} using namespace IO;

const int N = 3e5 + 5;
int n, a[N], ans[N];
vector<int> G[N];
int sum[N];
bool mark[N];

namespace Tree{int idx[N];}
namespace Tree{
	int dep[N], son[N], top[N], pos[N], sze[N], tot, fa[N];
	inline void dfs1(int u, int f){
		fa[u] = f;
		dep[u] = dep[f] + 1;
		for(int e = G[u].size() - 1; e >= 0; e--){
			int v = G[u][e];
			if(v == f) continue;
			dfs1(v, u);
			sze[u] += sze[v];
			if(sze[v] > sze[son[u]] || !son[u]) son[u] = v;
		}
	}
	inline void dfs2(int u, int f){
		if(son[u]){
			pos[son[u]] = ++tot;
			idx[tot] = son[u];
			top[son[u]] = top[u];
			dfs2(son[u], u);
		}
		for(int e = G[u].size() - 1; e >= 0; e--){
			int v = G[u][e];
			if(v == f || v == son[u]) continue;
			pos[v] = ++tot;
			idx[tot] = v;
			top[v] = v;
			dfs2(v, u);
		}
	}
	inline void splitTree(){
		dfs1(a[1], 0);
		tot = 1, top[a[1]] = a[1], pos[a[1]] = 1, idx[1] = a[1];
		dfs2(a[1], 0);
	}
	inline int getLca(int u, int v){
		while(top[u] != top[v]){
			if(dep[top[u]] < dep[top[v]]) swap(u, v);
			u = fa[top[u]];
		}
		return dep[u] < dep[v] ? u : v;
	}
}

inline void getSum(int u, int f){
	for(int e = G[u].size() - 1; e >= 0; e--){
		int v = G[u][e];
		if(v == f) continue;
		getSum(v, u);
		sum[u] += sum[v];
	}
}

int main() {
	freopen("h.in", "r" ,stdin);
	read(n);
	for(int i = 1; i <= n; i++) read(a[i]);
	for(int i = 1; i < n; i++){
		int x, y; read(x), read(y);
		G[x].push_back(y), G[y].push_back(x);
	}
	Tree::splitTree();
//	dfs(a[1], 0);

	sum[a[1]]++;
	for(int i = 1; i < n; i++){
		sum[a[i]]++, sum[a[i + 1]]++;
		int lca = Tree::getLca(a[i], a[i + 1]);
		mark[a[i]] = true;
		sum[lca]--, sum[Tree::fa[lca]]--;
	}
	getSum(a[1], 0);
	for(int i = 1; i <= n; i++) wr(sum[i] - (i == a[n] ? 1 : 0) - (mark[i] ? 1 : 0)), putchar('\n');
	return 0;
}

树链剖分

#include<bits/stdc++.h>
using namespace std;
namespace IO {
	template<typename T>
	inline void read(T &x) {
		T i = 0, f = 1;
		char ch = getchar();
		for(; (ch < '0' || ch > '9') && ch != '-'; ch = getchar());
		if(ch == '-') f = -1, ch = getchar();
		for(; ch >= '0' && ch <= '9'; ch = getchar()) i = (i << 3) + (i << 1) + (ch - '0');
		x = i * f;
	}
	template<typename T>
	inline void wr(T x) {
		if(x < 0) putchar('-'), x = -x;
		if(x > 9) wr(x / 10);
		putchar(x % 10 + '0');
	}
} using namespace IO;

const int N = 3e5 + 5;
int n, a[N], ans[N];
vector<int> G[N];

namespace Tree{int idx[N];}

namespace Seg{
	int tree[N << 2], tag[N << 2];
	inline void upt(int k){
		tree[k] = tree[k << 1] + tree[k << 1 | 1];
	}
	inline void add(int k, int v, int l, int r){
		tree[k] += (r - l + 1) * v;
		tag[k] += v;
	}
	inline void modify(int k, int l, int r, int x, int y, int v){
		if(x <= l && r <= y){
			add(k, v, l, r);
			return;
		}
		int mid = l + r >> 1, lc = k << 1, rc = k << 1 | 1;
		if(x <= mid) modify(lc, l, mid, x, y, v);
		if(y > mid) modify(rc, mid + 1, r, x, y, v);
		upt(k);
	}
	inline void pushDown(int k, int l, int r){
		int mid = l + r >> 1;
		if(tag[k]){
			add(k << 1, tag[k], l, mid);
			add(k << 1 | 1, tag[k], mid + 1, r);
			tag[k] = 0;
		}
	}
	inline void getAns(int k, int l, int r){
		if(l == r){
			ans[Tree::idx[l]] += tree[k];
			return;
		}
		int mid = l + r >> 1;
		pushDown(k, l, r);
		getAns(k << 1, l, mid);
		getAns(k << 1 | 1, mid + 1, r);
	}
}

namespace Tree{
	int dep[N], son[N], top[N], pos[N], sze[N], tot, fa[N];
	inline void dfs1(int u, int f){
		fa[u] = f;
		dep[u] = dep[f] + 1;
		for(int e = G[u].size() - 1; e >= 0; e--){
			int v = G[u][e];
			if(v == f) continue;
			dfs1(v, u);
			sze[u] += sze[v];
			if(sze[v] > sze[son[u]] || !son[u]) son[u] = v;
		}
	}
	inline void dfs2(int u, int f){
		if(son[u]){
			pos[son[u]] = ++tot;
			idx[tot] = son[u];
			top[son[u]] = top[u];
			dfs2(son[u], u);
		}
		for(int e = G[u].size() - 1; e >= 0; e--){
			int v = G[u][e];
			if(v == f || v == son[u]) continue;
			pos[v] = ++tot;
			idx[tot] = v;
			top[v] = v;
			dfs2(v, u);
		}
	}
	inline void splitTree(){
		dfs1(a[1], 0);
		tot = 1, top[a[1]] = a[1], pos[a[1]] = 1, idx[1] = a[1];
		dfs2(a[1], 0);
	}
	inline void pathModify(int u, int v){
		while(top[u] != top[v]){
			if(dep[top[u]] < dep[top[v]]) swap(u, v);
			Seg::modify(1, 1, n, pos[top[u]], pos[u], 1);
			u = fa[top[u]];
		}
		if(dep[u] > dep[v]) swap(u, v);
		Seg::modify(1, 1, n, pos[u], pos[v], 1);
	}
}

inline void dfs(int u, int f){
	cout<<u<<" ";
	for(int e = G[u].size() - 1; e >= 0; e--){
		int v = G[u][e];
		if(v == f) continue;
		dfs(v, u);
	}
	cout<<endl;
}

int main() {
	freopen("h.in", "r" ,stdin);
	read(n);
	for(int i = 1; i <= n; i++) read(a[i]);
	for(int i = 1; i < n; i++){
		int x, y; read(x), read(y);
		G[x].push_back(y), G[y].push_back(x);
	}
	Tree::splitTree();
//	dfs(a[1], 0);

	ans[a[1]] = 1;
	for(int i = 1; i < n; i++) Tree::pathModify(a[i], a[i + 1]), ans[a[i]]--;
	Seg::getAns(1, 1, n);
	for(int i = 1; i <= n; i++) wr(ans[i] - (i == a[n] ? 1 : 0)), putchar('\n');
	return 0;
}