BZOJ 4034 [HAOI2015]树上操作（树链剖分）

题目链接  BZOJ4034

这道题树链剖分其实就可以了。

单点更新没问题。

相当于更新

[f[x], f[x]]这个区间。

f[x]表示树链剖分之后每个点的新的标号。

区间更新的话类似DFS序，求出所对应的区间。

也就是[f[x], f[x] + size[x] - 1]。

给这个区间加上a即可。

询问的时候有两种方法，一个是直接套模板。

还有一种方法是，因为是查询x到1的权值和，

所以跟着top[x]走就可以了。

第一种方法：

#include <bits/stdc++.h>

using namespace std;

#define rep(i, a, b)    for (int i(a); i <= (b); ++i)
#define dec(i, a, b)    for (int i(a); i >= (b); --i)
#define lson        	i << 1, L, mid
#define rson       	i << 1 | 1, mid + 1, R

typedef long long LL;

const int N = 300010;

LL a[N], sum[N << 2], lazy[N << 2], y;
int f[N], fp[N], son[N], deep[N], father[N], sz[N], top[N];
int x, tot, n, m, op;
vector <int> v[N];

void dfs1(int x, int fa, int dep){
	deep[x] = dep;
	father[x] = fa;
	son[x] = 0;
	sz[x] = 1;
	int ct = (int)v[x].size();
	rep(i, 0, ct - 1){
		int u = v[x][i];
		if (u == fa) continue;
		dfs1(u, x, dep + 1);
		sz[x] += sz[u];
		if (sz[son[x]] < sz[u]) son[x] = u;
	}
}

void dfs2(int x, int tp){
	top[x] = tp;
	f[x] = ++tot;
	fp[f[x]] = x;
	if (son[x]) dfs2(son[x], tp);
	int ct = (int)v[x].size();
	rep(i, 0, ct - 1){
		int u = v[x][i];
		if (u == father[x] || u == son[x]) continue;
		dfs2(u, u);
	}
}

inline void pushup(int i){
	sum[i] = sum[i << 1] + sum[i << 1 | 1];
}

inline void pushdown(int i, int L, int R){
	int mid = (L + R) >> 1;
	lazy[i << 1] += lazy[i];
	sum[i << 1]  += lazy[i] * (mid - L + 1);
	lazy[i << 1 | 1] += lazy[i];
	sum[i << 1 | 1] += lazy[i] * (R - mid);
	lazy[i] = 0;
}

void build(int i, int L, int R){
	if (L == R){ sum[i] = a[fp[L]]; return; }
	int mid = (L + R) >> 1;
	build(lson);
	build(rson);
	pushup(i);
}

void update(int i, int L, int R, int l, int r, LL val){
	if (l == L && R == r){
		sum[i]  += val * (R - L + 1);
		lazy[i] += val;
		return ;
	}

	if (lazy[i]) pushdown(i, L, R);

	int mid = (L + R) >> 1;
	if (r <= mid) update(lson, l, r, val);
	else if (l > mid) update(rson, l, r, val);
	else{
		update(lson, l, mid, val);
		update(rson, mid + 1, r, val);
	}

	pushup(i);
}

LL query_sum(int i, int L, int R, int l, int r){
	pushdown(i, L, R);
	if (L == l && R == r) return sum[i];
	int mid = (L + R) >> 1;
	if (r <= mid) return query_sum(lson, l, r);
	else if (l > mid) return query_sum(rson, l, r);
	else return query_sum(lson, l, mid) + query_sum(rson, mid + 1, r);
}

LL find_sum(int x, int y){
	int f1 = top[x], f2 = top[y];
	LL ret = 0;
	for (; f1 != f2; ){
		if (deep[f1] < deep[f2]) swap(f1, f2), swap(x, y);
		ret += query_sum(1, 1, n, f[f1], f[x]);
		x = father[f1], f1 = top[x];
	}

	if (x == y) return ret + query_sum(1, 1, n, f[x], f[y]);
	if (deep[x] > deep[y]) swap(x, y);
	return ret + query_sum(1, 1, n, f[x], f[y]);
}

int main(){

	scanf("%d%d", &n, &m);
	rep(i, 1, n) scanf("%lld", a + i);
	rep(i, 2, n){
		int x, y;
		scanf("%d%d", &x, &y);
		v[x].push_back(y);
		v[y].push_back(x);
	}

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

	build(1, 1, n);

	while (m--){
		scanf("%d", &op);
		if (op == 1){
			scanf("%d%lld", &x, &y);
			update(1, 1, n, f[x], f[x], y);
		}

		else if (op == 2){
			scanf("%d%lld", &x, &y);
			update(1, 1, n, f[x], f[x] + sz[x] - 1, y);
		}

		else{
			scanf("%d", &x);
			printf("%lld\n", find_sum(x, 1));
		}
	}

	return 0;
}

第二种方法：

#include <bits/stdc++.h>

using namespace std;

#define rep(i, a, b)    for (int i(a); i <= (b); ++i)
#define dec(i, a, b)    for (int i(a); i >= (b); --i)
#define lson        	i << 1, L, mid
#define rson        	i << 1 | 1, mid + 1, R

typedef long long LL;

const int N = 300010;

LL a[N], sum[N << 2], lazy[N << 2], y;
int f[N], fp[N], son[N], deep[N], father[N], sz[N], top[N];
int x, tot, n, m, op;
vector <int> v[N];

void dfs1(int x, int fa, int dep){
	deep[x] = dep;
	father[x] = fa;
	son[x] = 0;
	sz[x] = 1;
	int ct = (int)v[x].size();
	rep(i, 0, ct - 1){
		int u = v[x][i];
		if (u == fa) continue;
		dfs1(u, x, dep + 1);
		sz[x] += sz[u];
		if (sz[son[x]] < sz[u]) son[x] = u;
	}
}

void dfs2(int x, int tp){
	top[x] = tp;
	f[x] = ++tot;
	fp[f[x]] = x;
	if (son[x]) dfs2(son[x], tp);
	int ct = (int)v[x].size();
	rep(i, 0, ct - 1){
		int u = v[x][i];
		if (u == father[x] || u == son[x]) continue;
		dfs2(u, u);
	}
}

inline void pushup(int i){ sum[i] = sum[i << 1] + sum[i << 1 | 1]; }

inline void pushdown(int i, int L, int R){
	sum[i] += lazy[i] * (R - L + 1);
	lazy[i << 1] += lazy[i];
	lazy[i << 1 | 1] += lazy[i];
	lazy[i] = 0;
}

void build(int i, int L, int R){
	if (L == R){ sum[i] = a[fp[L]]; return; }
	int mid = (L + R) >> 1;
	build(lson);
	build(rson);
	pushup(i);
}

void update(int i, int L, int R, int l, int r, LL val){
	if (l == L && R == r){
		lazy[i] += val;
		return ;
	}

	int mid = (L + R) >> 1;
	if (r <= mid) update(lson, l, r, val);
	else if (l > mid) update(rson, l, r, val);
	else{
		update(lson, l, mid, val);
		update(rson, mid + 1, r, val);
	}

	pushdown(i << 1, L, mid);
	pushdown(i << 1 | 1, mid + 1, R);
	pushup(i);
}

LL query_sum(int i, int L, int R, int l, int r){
	pushdown(i, L, R);
	if (L == l && R == r) return sum[i];
	int mid = (L + R) >> 1;
	if (r <= mid) return query_sum(lson, l, r);
	else if (l > mid) return query_sum(rson, l, r);
	else return query_sum(lson, l, mid) + query_sum(rson, mid + 1, r);
}

int main(){

	scanf("%d%d", &n, &m);
	rep(i, 1, n) scanf("%lld", a + i);
	rep(i, 2, n){
		int x, y;
		scanf("%d%d", &x, &y);
		v[x].push_back(y);
		v[y].push_back(x);
	}

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

	build(1, 1, n);

	while (m--){
		scanf("%d", &op);
		if (op == 1){
			scanf("%d%lld", &x, &y);
			update(1, 1, n, f[x], f[x], y);
		}

		else if (op == 2){
			scanf("%d%lld", &x, &y);
			update(1, 1, n, f[x], f[x] + sz[x] - 1, y);
		}

		else{
			scanf("%d", &x);
			LL ans = 0;
			for (int i = x; i; i = father[top[i]])
				ans += query_sum(1, 1, n, f[top[i]], f[i]);
			printf("%lld\n", ans);
		}
	}

	return 0;
}