【BZOJ4538】【HNOI2016】网络
2018-03-21 19:31
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【题目链接】
点击打开链接
【思路要点】
对树进行DFS序标号,令节点\(i\)的DFS序为\(dfn_i\),\(i\)子树内的节点DFS序范围为\([dfn_i,rit_i]\)。
对于路径\((a,b)\),节点\(x\)不影响\((a,b)\)的条件是满足以下之一:
1、\(dfn_{lca(a,b)}\in(dfn_x,rit_x]\)。
2、\(dfn_a\notin[dfn_x,rit_x]\)且\(dfn_b\notin[dfn_x,rit_x]\)。
1可以用线段树+堆维护,2可以用KDTree维护。
时间复杂度\(O(M*\sqrt{N})\),空间复杂度\(O(N+M)\)。
由于常数较大,BZOJ上这份代码会TLE,但该代码在DBZOJ上已经测试通过。
【代码】
点击打开链接
【思路要点】
对树进行DFS序标号,令节点\(i\)的DFS序为\(dfn_i\),\(i\)子树内的节点DFS序范围为\([dfn_i,rit_i]\)。
对于路径\((a,b)\),节点\(x\)不影响\((a,b)\)的条件是满足以下之一:
1、\(dfn_{lca(a,b)}\in(dfn_x,rit_x]\)。
2、\(dfn_a\notin[dfn_x,rit_x]\)且\(dfn_b\notin[dfn_x,rit_x]\)。
1可以用线段树+堆维护,2可以用KDTree维护。
时间复杂度\(O(M*\sqrt{N})\),空间复杂度\(O(N+M)\)。
由于常数较大,BZOJ上这份代码会TLE,但该代码在DBZOJ上已经测试通过。
【代码】
#include<bits/stdc++.h> using namespace std; const int MAXN = 200005; const int MAXLOG = 20; template <typename T> void chkmax(T &x, T y) {x = max(x, y); } template <typename T> void chkmin(T &x, T y) {x = min(x, y); } template <typename T> void read(T &x) { x = 0; int f = 1; char c = getchar(); for (; !isdigit(c); c = getchar()) if (c == '-') f = -f; for (; isdigit(c); c = getchar()) x = x * 10 + c - '0'; x *= f; } template <typename T> void write(T x) { if (x < 0) x = -x, putchar('-'); if (x > 9) write(x / 10); putchar(x % 10 + '0'); } template <typename T> void writeln(T x) { write(x); puts(""); } struct Heap { priority_queue <int> Heap, Del; void push(int x) {Heap.push(x); } void pop(int x) {Del.push(x); } int query() { while (!Heap.empty() && !Del.empty() && Heap.top() == Del.top()) { Heap.pop(); Del.pop(); } if (Heap.empty()) return -1; else return Heap.top(); } }; struct SegmentTree { struct Node { int lc, rc; int Max; } a[MAXN * 2]; Heap b[MAXN]; int root, size, n; void update(int root) { a[root].Max = max(a[a[root].lc].Max, a[a[root].rc].Max); } void build(int &root, int l, int r) { root = ++size; a[root].Max = -1; if (l == r) return; int mid = (l + r) / 2; build(a[root].lc, l, mid); build(a[root].rc, mid + 1, r); } void init(int x) { n = x; root = size = 0; build(root, 1, n); } void update(int root, int l, int r, int pos) { if (l == r) { a[root].Max = b[l].query(); return; } int mid = (l + r) / 2; if (mid >= pos) update(a[root].lc, l, mid, pos); else update(a[root].rc, mid + 1, r, pos); update(root); } void push(int x, int val) { b[x].push(val); update(root, 1, n, x); } void pop(int x, int val) { b[x].pop(val); update(root, 1, n, x); } int query(int root, int l, int r, int ql, int qr) { if (l == ql && r == qr) return a[root].Max; int mid = (l + r) / 2, ans = -1; if (mid >= ql) chkmax(ans, query(a[root].lc, l, mid, ql, min(mid, qr))); if (mid + 1 <= qr) chkmax(ans, query(a[root].rc, mid + 1, r, max(mid + 1, ql), qr)); return ans; } int query(int l, int r) { if (l > r) return -1; else return query(root, 1, n, l, r); } } ST; int n, m, timer; int dfn[MAXN], rit[MAXN]; int depth[MAXN], father[MAXN][MAXLOG]; vector <int> a[MAXN]; void work(int pos, int fa) { dfn[pos] = ++timer; father[pos][0] = fa; depth[pos] = depth[fa] + 1; for (int i = 1; i < MAXLOG; i++) father[pos][i] = father[father[pos][i - 1]][i - 1]; for (unsigned i = 0; i < a[pos].size(); i++) if (a[pos][i] != fa) work(a[pos][i], pos); rit[pos] = timer; } int lca(int x, int y) { if (depth[x] < depth[y]) swap(x, y); for (int i = MAXLOG - 1; i >= 0; i--) if (depth[father[x][i]] >= depth[y]) x = father[x][i]; if (x == y) return x; for (int i = MAXLOG - 1; i >= 0; i--) if (father[x][i] != father[y][i]) { x = father[x][i]; y = father[y][i]; } return father[x][0]; } struct point {int x, y; }; bool mode; bool operator < (point a, point b) { if (mode) { if (a.x == b.x) return a.y < b.y; else return a.x < b.x; } else { if (a.y == b.y) return a.x < b.x; else return a.y < b.y; } } struct info {point pos; int home; }; bool operator < (info a, info b) {return a.pos < b.pos; } struct KDTree { struct Node { int lc, rc, fa; int index, Max; point pos, l, r; } a[MAXN]; int root, tot, size, pos[MAXN]; info tmp[MAXN]; void updaterange(int root) { a[root].l = a[root].r = a[root].pos; int lc = a[root].lc, rc = a[root].rc; if (lc) { chkmin(a[root].l.x, a[lc].l.x); chkmin(a[root].l.y, a[lc].l.y); chkmax(a[root].r.x, a[lc].r.x); chkmax(a[root].r.y, a[lc].r.y); } if (rc) { chkmin(a[root].l.x, a[rc].l.x); chkmin(a[root].l.y, a[rc].l.y); chkmax(a[root].r.x, a[rc].r.x); chkmax(a[root].r.y, a[rc].r.y); } } void build(int &root, int l, int r, bool now) { root = ++size; a[root].index = a[root].Max = -1; int mid = (l + r) / 2; mode = now; nth_element(tmp + l, tmp + mid, tmp + r + 1); a[root].pos = tmp[mid].pos; pos[tmp[mid].home] = root; if (mid > l) { build(a[root].lc, l, mid - 1, now ^ true); a[a[root].lc].fa = root; } if (mid < r) { build(a[root].rc, mid + 1, r, now ^ true); a[a[root].rc].fa = root; } updaterange(root); } void add(int x, int y, int home) {tmp[++tot] = (info) {(point) {x, y}, home}; } void init() { size = root = 0; build(root, 1, tot, 0); } void updateMax(int root) { a[root].Max = a[root].index; if (a[root].lc) chkmax(a[root].Max, a[a[root].lc].Max); if (a[root].rc) chkmax(a[root].Max, a[a[root].rc].Max); } void modify(int home, int val) { int now = pos[home]; a[now].index = val; updateMax(now); while (now != root) { now = a[now].fa; updateMax(now); } } int query(int root, point ql, point qr) { if (root == 0 || a[root].Max == -1) return -1; if (ql.x <= a[root].l.x && ql.y <= a[root].l.y && qr.x >= a[root].r.x && qr.y >= a[root].r.y) return a[root].Max; if (ql.x > a[root].r.x || ql.y > a[root].r.y || qr.x < a[root].l.x || qr.y < a[root].l.y) return -1; int ans = -1; if (a[root].pos.x >= ql.x && a[root].pos.x <= qr.x && a[root].pos.y >= ql.y && a[root].pos.y <= qr.y) ans = a[root].index; chkmax(ans, query(a[root].lc, ql, qr)); chkmax(ans, query(a[root].rc, ql, qr)); return ans; } int query(int lx, int rx, int ly, int ry) { return query(root, (point) {lx, ly}, (point) {rx, ry}); } } KDT; int type[MAXN], x[MAXN], y[MAXN], z[MAXN]; int main() { read(n), read(m); for (int i = 1; i <= n - 1; i++) { int x, y; scanf("%d%d", &x, &y); a[x].push_back(y); a[y].push_back(x); } work(1, 0); for (int i = 1; i <= m; i++) { read(type[i]), read(x[i]); if (type[i] == 0) { read(y[i]), read(z[i]); KDT.add(dfn[x[i]], dfn[y[i]], i); } } KDT.init(); ST.init(n); for (int i = 1; i <= m; i++) { if (type[i] == 0) { int Lca = lca(x[i], y[i]); ST.push(dfn[Lca], z[i]); KDT.modify(i, z[i]); } if (type[i] == 1) { int j = x[i], Lca = lca(x[j], y[j]); ST.pop(dfn[Lca], z[j]); KDT.modify(j, -1); } if (type[i] == 2) { int tmp = x[i]; int ans = ST.query(dfn[tmp] + 1, rit[tmp]); chkmax(ans, KDT.query(1, dfn[tmp] - 1, rit[tmp] + 1, n)); chkmax(ans, KDT.query(1, dfn[tmp] - 1, 1, dfn[tmp] - 1)); chkmax(ans, KDT.query(rit[tmp] + 1, n, 1, dfn[tmp] - 1)); chkmax(ans, KDT.query(rit[tmp] + 1, n, rit[tmp] + 1, n)); writeln(ans); } } return 0; }
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