Blog of RuSun

\begin {array}{c} \mathfrak {One Problem Is Difficult} \\\\ \mathfrak {Because You Don't Know} \\\\ \mathfrak {Why It Is Diffucult} \end {array}

P4092 [HEOI2016/TJOI2016]树

P4092 [HEOI2016/TJOI2016]树

题意:维护最近的有标记的祖先。树链剖分,维护最深的有标记的祖先,查询 $1…x$ 路径上最深的有标记的点即可。

一个常见的错误 modify(1, dfn[x], x); -> modify(1, x, x);

查看代码
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#include <cstdio>
using namespace std;
const int N = 1e5 + 10, M = 2e5 + 10;
int n, q, d[N], p[N], sz[N];
int idx, hd[N], nxt[M], edg[M];
int stmp, dfn[N], top[N], son[N];
struct Node
{
int pos;
int l, r;
} tr[N << 2];
void pushup(Node &x, Node l, Node r)
{
if (~l.pos && ~r.pos)
x.pos = (d[l.pos] > d[r.pos] ? l.pos : r.pos);
else if (~l.pos)
x.pos = l.pos;
else if (~r.pos)
x.pos = r.pos;
else
x.pos = -1;
}
void build(int x, int l, int r)
{
tr[x].l = l, tr[x].r = r;
if (l == r)
{
tr[x].pos = -1;
return;
}
int mid = l + r >> 1;
build(x << 1, l, mid);
build(x << 1 | 1, mid + 1, r);
pushup(tr[x], tr[x << 1], tr[x << 1 | 1]);
}
void modify(int x, int t, int k)
{
if (tr[x].l == tr[x].r)
{
tr[x].pos = k;
return;
}
int mid = tr[x].l + tr[x].r >> 1;
if (t <= mid)
modify(x << 1, t, k);
else
modify(x << 1 | 1, t, k);
pushup(tr[x], tr[x << 1], tr[x << 1 | 1]);
}
Node query(int x, int l, int r)
{
if (tr[x].l >= l && tr[x].r <= r)
return tr[x];
int mid = tr[x].l + tr[x].r >> 1;
if (r <= mid)
return query(x << 1, l, r);
if (l > mid)
return query(x << 1 | 1, l, r);
Node res;
pushup(res, query(x << 1, l, r), query(x << 1 | 1, l, r));
return res;
}
int QueryPath(int x)
{
while (top[x] != 1)
{
int t = query(1, dfn[top[x]], dfn[x]).pos;
if (~t)
return t;
x = p[top[x]];
}
int t = query(1, 1, dfn[x]).pos;
if (~t)
return t;
return 1;
}
void dfs1(int x)
{
sz[x] = 1;
son[x] = -1;
for (int i = hd[x]; ~i; i = nxt[i])
if (!d[edg[i]])
{
d[edg[i]] = d[x] + 1;
p[edg[i]] = x;
dfs1(edg[i]);
sz[x] += sz[edg[i]];
if (son[x] == -1 || sz[edg[i]] > sz[son[x]])
son[x] = edg[i];
}
}
void dfs2(int x, int t)
{
dfn[x] = ++stmp;
top[x] = t;
if (son[x] == -1)
return;
dfs2(son[x], t);
for (int i = hd[x]; ~i; i = nxt[i])
if (edg[i] != son[x] && edg[i] != p[x])
dfs2(edg[i], edg[i]);
}
void add(int a, int b)
{
nxt[++idx] = hd[a];
hd[a] = idx;
edg[idx] = b;
}
int main()
{
scanf("%d%d", &n, &q);
for (int i = 1; i <= n; i++)
hd[i] = -1;
for (int i = 1, a, b; i < n; i++)
{
scanf("%d%d", &a, &b);
add(a, b);
add(b, a);
}
d[1] = 1;
dfs1(1);
dfs2(1, 1);
build(1, 1, n);
for (char op[2]; q; q--)
{
scanf("%s", op);
if (op[0] == 'Q')
{
int x;
scanf("%d", &x);
printf("%d\n", QueryPath(x));
}
else if (op[0] == 'C')
{
int x;
scanf("%d", &x);
modify(1, dfn[x], x);
}
}
return 0;
}