BZOJ4034 [HAOI2015]T2 【DFS序+线段树】
题目大意:有一棵$n$个点的树,$q$次操作,每个点有点权,1号点为根。
1. 修改点权。
2. 修改子树内所有点的点权。
3. 询问点到根路径点权和。
*4. 修改一个点到根路径上的点点权和。
*5. 询问子树内的点权。
$n \leq 100000, q \leq 100000$
【题解】
记录DFS序,记录进栈以及出栈,进栈为正,出栈为负。
维护线段树。
1. 修改点权:单点修改
2. 修改子树内所有点的点权:区间修改
3. 询问点到根路径点权和:区间查询
*4. 修改一个点到根路径上的点点权和:区间修改
*5. 询问子树内的点权:区间查询正值(线段树多维护一个正值和)
本题只涉及前3个操作。本题也可以用树链剖分解决。
# include <stdio.h> using namespace std; int n, m, val[100010]; const int root = 1; int head[100010], to[200010], next[200010], tot=0; int seq[600010], sn=0, in[100010], out[100010]; bool io[600010]; inline void add(int u, int v) { ++tot; next[tot]=head[u]; head[u]=tot; to[tot]=v; } inline void dfs(int x, int fa) { ++sn; in[x] = sn; seq[sn] = val[x]; io[sn] = 1; for (int i=head[x]; i; i=next[i]) { if(to[i] == fa) continue; dfs(to[i], x); } ++sn; out[x] = sn; seq[sn] = -val[x]; io[sn] = 0; } typedef long long ll; int lc[2400010], rc[2400010]; ll w[2400010], lazy[2400010]; int flag[2400010]; inline void pushdown(int x) { if(!lazy[x]) return; w[x<<1] += lazy[x] * flag[x<<1]; w[x<<1|1] += lazy[x] * flag[x<<1|1]; lazy[x<<1] += lazy[x]; lazy[x<<1|1] += lazy[x]; lazy[x] = 0; } inline void build(int x, int l, int r) { lc[x] = l, rc[x] = r; w[x] = lazy[x] = 0; if(l == r) { w[x] = (ll)seq[l]; if(io[l]) flag[x] = 1; else flag[x] = -1; return ; } int mid = l+r>>1; build(x<<1, l, mid); build(x<<1|1, mid+1, r); w[x] = w[x<<1] + w[x<<1|1]; flag[x] = flag[x<<1] + flag[x<<1|1]; } inline void change(int x, int L, int R, ll delta) { int l = lc[x], r = rc[x]; if(L <= l && r <= R) { w[x] = w[x] + flag[x] * delta; lazy[x] += delta; return ; } pushdown(x); int mid = l+r >> 1; if(L > mid) change(x<<1|1, L, R, delta); else if(R <= mid) change(x<<1, L, R, delta); else { change(x<<1, L, mid, delta); change(x<<1|1, mid+1, R, delta); } w[x] = w[x<<1] + w[x<<1|1]; } inline ll query(int x, int L, int R) { int l = lc[x], r = rc[x]; if(L <= l && r <= R) return w[x]; pushdown(x); int mid = l+r >> 1; if(L > mid) return query(x<<1|1, L, R); else if(R <= mid) return query(x<<1, L, R); else return query(x<<1, L, mid) + query(x<<1|1, mid+1, R); } int main() { scanf("%d%d", &n, &m); for (int i=1; i<=n; ++i) scanf("%d", &val[i]); for (int i=1, u, v; i<n; ++i) { scanf("%d%d", &u, &v); add(u, v); add(v, u); } dfs(root, 0); //for (int i=1; i<=sn; ++i) printf("%d ", seq[i]); //printf("\n"); //for (int i=1; i<=n; ++i) printf("%d ", in[i]); //printf("\n"); //for (int i=1; i<=n; ++i) printf("%d ", out[i]); //printf("\n"); build(1, 1, sn); for (int i=1; i<=m; ++i) { int opt; scanf("%d", &opt); if(opt == 1) { int x, del; scanf("%d%d", &x, &del); change(1, in[x], in[x], (ll)del); change(1, out[x], out[x], (ll)del); } else if(opt == 2) { int x, del; scanf("%d%d", &x, &del); change(1, in[x], out[x], (ll)del); } else if(opt == 3) { int x; scanf("%d", &x); printf("%lld\n", query(1, 1, in[x])); } } return 0; }
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