You are given a tree (an acyclic undirected connected graph) with N nodes. The tree nodes are numbered from 1 to N. In the start, the color of any node in the tree is white.node
We will ask you to perfrom some instructions of the following form:c++
In the first line there are two integers N and Q.數組
In the next N-1 lines describe the edges in the tree: a line with two integers a bdenotes an edge between a and b.測試
The next Q lines contain instructions "0 i" or "1 v" (1 ≤ i, v ≤ N).ui
For each "1 v" operation, write one integer representing its result.spa
9 8 1 2 1 3 2 4 2 9 5 9 7 9 8 9 6 8 1 3 0 8 1 6 1 7 0 2 1 9 0 2 1 9
-1 8 -1 2 -1
There are 12 real input files.code
For 1/3 of the test cases, N=5000, Q=400000.orm
For 1/3 of the test cases, N=10000, Q=300000.ip
For 1/3 of the test cases, N=100000, Q=100000.input
樹鏈剖分後,用線段樹或者樹狀數組維護區間和,找距離1最近的黑點即找區間和大於零的最小的左端點,對於線段樹查詢,咱們優先訪問左兒子便可,對於樹狀數組能夠套二分查詢深度最小的點
二分+樹狀數組
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10; typedef long long ll; vector<int> G[N]; int n, m; int fa[N]; int son[N]; int sze[N]; int dep[N]; void dfs1(int u, int f) { sze[u] = 1; fa[u] = f; son[u] = 0; dep[u] = dep[f] + 1; for (int i = 0; i < G[u].size(); i++) { int v = G[u][i]; if (v == f) continue; dfs1(v, u); sze[u] += sze[v]; if (sze[v] > sze[son[u]]) son[u] = v; } } int top[N]; int cnt; int pos[N]; int mp[N]; void dfs2(int u, int f, int t) { top[u] = t; pos[u] = ++cnt; mp[cnt] = u; if (son[u]) dfs2(son[u], u, t); for (int i = 0; i < G[u].size(); i++) { int v = G[u][i]; if (v == f || v == son[u]) continue; dfs2(v, u, v); } } int a[N]; int d[N]; void update(int x, int v) { for (int i = x; i <= n; i += i & (-i)) d[i] += v; } int query(int x) { int ans = 0; for (int i = x; i; i -= i & (-i)) ans += d[i]; return ans; } int calcans(int u) { int ans = 0; int res = -1; while (top[u] != top[1]) { if (query(pos[u]) - query(pos[top[u]] - 1) > 0) { int l = pos[top[u]], r = pos[u]; int tl = l; while (l <= r) { int mid = (l + r) >> 1; if (query(mid) - query(tl - 1) > 0) { r = mid - 1; ans = mid; } else l = mid + 1; } if (ans) res = mp[ans]; } u = fa[top[u]]; } if (query(pos[u]) - query(pos[1] - 1) > 0) { int l = pos[1], r = pos[u]; while (l <= r) { int mid = (l + r) >> 1; if (query(mid) > 0) { r = mid - 1; ans = mid; } else l = mid + 1; } if (ans) res = mp[ans]; } return res; } int main() { //freopen("in.txt", "r", stdin); //freopen("out.txt", "w", stdout); scanf("%d%d", &n, &m); for (int i = 1; i <= n; i++) { G[i].clear(); } memset(d, 0, sizeof(d)); memset(sze, 0, sizeof(sze)); memset(a, 0, sizeof(a)); for (int i = 1; i < n; i++) { int u, v; scanf("%d%d", &u, &v); G[u].push_back(v); G[v].push_back(u); } dep[0] = 0; dfs1(1, 0); cnt = 0; dfs2(1, 0, 1); int ch, k; for (int i = 1; i <= m; i++) { scanf("%d%d", &ch, &k); switch(ch) { case 1: printf("%d\n", calcans(k)); break; case 0: { if (a[k] == 0) { update(pos[k], 1); a[k] = 1; } else { update(pos[k], -1); a[k] = 0; } break; } } } return 0; }
線段樹
#include <bits/stdc++.h> #define lson (o << 1) #define rson (o << 1 | 1) using namespace std; const int N = 1e5 + 10; typedef long long ll; vector<int> G[N]; int n, m; int fa[N]; int son[N]; int sze[N]; int dep[N]; void dfs1(int u, int f) { sze[u] = 1; fa[u] = f; son[u] = 0; dep[u] = dep[f] + 1; for (int i = 0; i < G[u].size(); i++) { int v = G[u][i]; if (v == f) continue; dfs1(v, u); sze[u] += sze[v]; if (sze[v] > sze[son[u]]) son[u] = v; } } int top[N]; int cnt; int pos[N]; int mp[N]; void dfs2(int u, int f, int t) { top[u] = t; pos[u] = ++cnt; mp[cnt] = u; if (son[u]) dfs2(son[u], u, t); for (int i = 0; i < G[u].size(); i++) { int v = G[u][i]; if (v == f || v == son[u]) continue; dfs2(v, u, v); } } int a[N]; int sumv[N << 2]; void pushup(int o) { sumv[o] = sumv[lson] + sumv[rson]; } void update(int o, int l, int r, int pos) { if (l == r) { sumv[o] = !sumv[o]; return; } int mid = (l + r) >> 1; if (pos <= mid) update(lson, l, mid, pos); else update(rson, mid + 1, r, pos); pushup(o); } int query(int o, int l, int r, int ql, int qr) { if (sumv[o] == 0) return 0; if (l == r) return l; int mid = (l + r) >> 1; int ans = 0; if (ql <= mid) ans = query(lson, l, mid, ql, qr); if (ans) return ans; if (qr > mid) ans = query(rson, mid + 1, r, ql, qr); return ans; } int calcans(int u) { int ans; int res = -1; while (1) { ans = query(1, 1, n, pos[top[u]], pos[u]); if (ans) res = mp[ans]; if (u == 1 || top[u] == 1) break; u = fa[top[u]]; } return res; } int main() { //freopen("in.txt", "r", stdin); //freopen("out.txt", "w", stdout); scanf("%d%d", &n, &m); for (int i = 1; i <= n; i++) { G[i].clear(); } memset(sumv, 0, sizeof(sumv)); memset(sze, 0, sizeof(sze)); memset(a, 0, sizeof(a)); for (int i = 1; i < n; i++) { int u, v; scanf("%d%d", &u, &v); G[u].push_back(v); G[v].push_back(u); } dep[0] = 0; dfs1(1, 0); cnt = 0; dfs2(1, 0, 1); int ch, k; for (int i = 1; i <= m; i++) { scanf("%d%d", &ch, &k); switch(ch) { case 1: printf("%d\n", calcans(k)); break; case 0: { update(1, 1, n, pos[k]); break; } } } return 0; }
給定一棵有n個節點的無根樹和m個操做,操做有2類:
一、將節點a到節點b路徑上全部點都染成顏色c;
二、詢問節點a到節點b路徑上的顏色段數量(連續相同顏色被認爲是同一段),
如「112221」由3段組成:「11」、「222」和「1」。
請你寫一個程序依次完成這m個操做。
第一行包含2個整數n和m,分別表示節點數和操做數;
第二行包含n個正整數表示n個節點的初始顏色
下面 行每行包含兩個整數x和y,表示x和y之間有一條無向邊。
下面 行每行描述一個操做:
「C a b c」表示這是一個染色操做,把節點a到節點b路徑上全部點(包括a和b)都染成顏色c;
「Q a b」表示這是一個詢問操做,詢問節點a到節點b(包括a和b)路徑上的顏色段數量。
對於每一個詢問操做,輸出一行答案。
6 5 2 2 1 2 1 1 1 2 1 3 2 4 2 5 2 6 Q 3 5 C 2 1 1 Q 3 5 C 5 1 2 Q 3 5
3 1 2
數N<=10^5,操做數M<=10^5,全部的顏色C爲整數且在[0, 10^9]之間。
樹剖後用線段樹維護每一個區間的顏色段數,和左端點右端點的顏色是什麼,合併時判斷顏色是否同樣便可
#include <bits/stdc++.h> #define lson (o << 1) #define rson (o << 1 | 1) using namespace std; const int N = 1e5 + 10; typedef long long ll; vector<int> G[N]; const ll inf = 1e9; int n; ll val[N]; int fa[N]; int son[N]; int sze[N]; int dep[N]; void dfs1(int u, int f) { sze[u] = 1; fa[u] = f; son[u] = 0; dep[u] = dep[f] + 1; for (int i = 0; i < G[u].size(); i++) { int v = G[u][i]; if (v == f) continue; dfs1(v, u); sze[u] += sze[v]; if (sze[v] > sze[son[u]]) son[u] = v; } } int top[N]; int cnt; int pos[N]; int a[N]; void dfs2(int u, int f, int t) { top[u] = t; pos[u] = ++cnt; a[cnt] = val[u]; if (son[u]) dfs2(son[u], u, t); for (int i = 0; i < G[u].size(); i++) { int v = G[u][i]; if (v == f || v == son[u]) continue; dfs2(v, u, v); } } ll sumv[N << 2]; ll cov[N << 2]; ll L[N << 2]; ll R[N << 2]; void pushup(int o) { L[o] = L[lson]; R[o] = R[rson]; if (R[lson] == L[rson]) { sumv[o] = sumv[lson] + sumv[rson] - 1; } else sumv[o] = sumv[lson] + sumv[rson]; } void pushdown(int o, int l, int r) { if (cov[o]) { cov[lson] = cov[rson] = cov[o]; sumv[lson] = sumv[rson] = 1; L[lson] = R[lson] = cov[o]; L[rson] = R[rson] = cov[o]; cov[o] = 0; } } void build(int o, int l, int r) { if (l == r) { sumv[o] = 1; cov[o] = 0; L[o] = R[o] = a[l]; return; } int mid = (l + r) >> 1; build(lson, l, mid); build(rson, mid + 1, r); pushup(o); } void update(int o, int l, int r, int ql, int qr, ll v) { if (ql <= l && r <= qr) { sumv[o] = 1; cov[o] = v; L[o] = R[o] = v; return; } int mid = (l + r) >> 1; pushdown(o, l, r); if (ql <= mid) update(lson, l, mid, ql, qr, v); if (qr > mid) update(rson, mid + 1, r, ql, qr, v); pushup(o); } ll query(int o, int l, int r, int ql, int qr) { if (ql == l && r == qr) { return sumv[o]; } int mid = (l + r) >> 1; pushdown(o, l, r); if (qr <= mid) return query(lson, l, mid, ql, qr); else if (ql > mid) return query(rson, mid + 1, r, ql, qr); else { ll res = query(lson, l, mid, ql, mid) + query(rson, mid + 1, r, mid + 1, qr); if (R[lson] == L[rson]) return res - 1; else return res; } } ll querycor(int o, int l, int r, int pos) { if (l == r) { return L[o]; } int mid = (l + r) >> 1; pushdown(o, l, r); if (pos <= mid) return querycor(lson, l, mid, pos); else return querycor(rson, mid + 1, r, pos); } ll calcsum(int u, int v) { ll ans = 0; while (top[u] != top[v]) { if (dep[top[u]] < dep[top[v]]) swap(u, v); ans += query(1, 1, n, pos[top[u]], pos[u]); int tmp = top[u]; u = fa[top[u]]; if (querycor(1, 1, n, pos[tmp]) == querycor(1, 1, n, pos[u])) ans--; } if (dep[u] < dep[v]) swap(u, v); ans += query(1, 1, n, pos[v], pos[u]); return ans; } void update1(int u, int v, ll val) { while (top[u] != top[v]) { if (dep[top[u]] < dep[top[v]]) swap(u, v); update(1, 1, n, pos[top[u]], pos[u], val); u = fa[top[u]]; } if (dep[u] < dep[v]) swap(u, v); update(1, 1, n, pos[v], pos[u], val); } int main() { //freopen("in.txt", "r", stdin); //freopen("out.txt", "w", stdout); scanf("%d", &n); int m; scanf("%d", &m); for (int i = 1; i <= n; i++) scanf("%lld", &val[i]); for (int i = 1; i < n; i++) { int u, v; scanf("%d%d", &u, &v); G[u].push_back(v); G[v].push_back(u); } dep[0] = 0; dfs1(1, 0); cnt = 0; dfs2(1, 0, 1); build(1, 1, n); char ch[10]; for (int i = 1; i <= m; i++) { scanf("%s", ch); int l, r, k; ll v; switch(ch[0]) { case 'Q': scanf("%d%d", &l, &r); printf("%lld\n", calcsum(l, r)); break; case 'C': { scanf("%d%d%lld", &l, &r, &v); update1(l, r, v); break; } } } return 0; }
Ray 樂忠於旅遊,此次他來到了T 城。T 城是一個水上城市,一共有 N 個景點,有些景點之間會用一座橋鏈接。爲了方便遊客到達每一個景點但又爲了節約成本,T 城的任意兩個景點之間有且只有一條路徑。換句話說, T 城中只有N − 1 座橋。Ray 發現,有些橋上能夠看到美麗的景色,讓人心情愉悅,但有些橋狹窄泥濘,使人煩躁。因而,他給每座橋定義一個愉悅度w,也就是說,Ray 通過這座橋會增長w 的愉悅度,這或許是正的也多是負的。有時,Ray 看待同一座橋的心情也會發生改變。如今,Ray 想讓你幫他計算從u 景點到v 景點能得到的總愉悅度。有時,他還想知道某段路上最美麗的橋所提供的最大愉悅度,或是某段路上最糟糕的一座橋提供的最低愉悅度。
輸入的第一行包含一個整數N,表示T 城中的景點個數。景點編號爲 0...N − 1。接下來N − 1 行,每行三個整數u、v 和w,表示有一條u 到v,使 Ray 愉悅度增長w 的橋。橋的編號爲1...N − 1。|w| <= 1000。輸入的第N + 1 行包含一個整數M,表示Ray 的操做數目。接下來有M 行,每行描述了一個操做,操做有以下五種形式: C i w,表示Ray 對於通過第i 座橋的愉悅度變成了w。 N u v,表示Ray 對於通過景點u 到v 的路徑上的每一座橋的愉悅度都變成原來的相反數。 SUM u v,表示詢問從景點u 到v 所得到的總愉悅度。 MAX u v,表示詢問從景點u 到v 的路徑上的全部橋中某一座橋所提供的最大愉悅度。 MIN u v,表示詢問從景點u 到v 的路徑上的全部橋中某一座橋所提供的最小愉悅度。測試數據保證,任意時刻,Ray 對於通過每一座橋的愉悅度的絕對值小於等於1000。
對於每個詢問(操做S、MAX 和MIN),輸出答案。
3 0 1 1 1 2 2 8 SUM 0 2 MAX 0 2 N 0 1 SUM 0 2 MIN 0 2 C 1 3 SUM 0 2 MAX 0 2
3 2 1 -1 5 3
一共有10 個數據,對於第i (1 <= i <= 10) 個數據, N = M = i * 2000。
本題給的是邊權,對於邊權咱們不太方便樹鏈剖分,咱們將每條邊的邊權給子節點,這樣根節點點權爲0,而後就能夠正常樹剖了,對於取區間相反數的操做,咱們就將最大值和最小值交換再取負數就能夠了,區間和直接取負數.
#include <bits/stdc++.h> #define lson (o << 1) #define rson (o << 1 | 1) using namespace std; const int N = 1e5 + 10; typedef long long ll; struct node { int v, w; node(int v = 0, int w = 0): v(v), w(w) {} }; vector<node> G[N]; const int inf = 1e9; int n; int val[N]; int fa[N]; int son[N]; int sze[N]; int dep[N]; void dfs1(int u, int f) { sze[u] = 1; fa[u] = f; son[u] = 0; dep[u] = dep[f] + 1; for (int i = 0; i < G[u].size(); i++) { int v = G[u][i].v; if (v == f) continue; val[v] = G[u][i].w; dfs1(v, u); sze[u] += sze[v]; if (sze[v] > sze[son[u]]) { son[u] = v; } } } int top[N]; int cnt; int pos[N]; int a[N]; void dfs2(int u, int f, int t) { top[u] = t; pos[u] = ++cnt; a[cnt] = val[u]; if (son[u]) dfs2(son[u], u, t); for (int i = 0; i < G[u].size(); i++) { int v = G[u][i].v; if (v == f || v == son[u]) continue; dfs2(v, u, v); } } int sumv[N << 2]; int maxv[N << 2]; int minv[N << 2]; void pushup(int o) { sumv[o] = sumv[lson] + sumv[rson]; maxv[o] = max(maxv[lson], maxv[rson]); minv[o] = min(minv[lson], minv[rson]); } int negv[N << 2]; void myswap(int x) { negv[x] ^= 1; swap(maxv[x], minv[x]); maxv[x] = -maxv[x]; minv[x] = -minv[x]; sumv[x] = -sumv[x]; } void pushdown(int o, int l, int r) { if (negv[o]) { myswap(lson); myswap(rson); negv[o] = 0; } } void build(int o, int l, int r) { if (l == r) { sumv[o] = maxv[o] = minv[o] = a[l]; return; } int mid = (l + r) >> 1; build(lson, l, mid); build(rson, mid + 1, r); pushup(o); } void update(int o, int l, int r, int pos, int v) { if (l == r) { sumv[o] = maxv[o] = minv[o] = v; return; } int mid = (l + r) >> 1; pushdown(o, l, r); if (pos <= mid) update(lson, l, mid, pos, v); else update(rson, mid + 1, r, pos, v); pushup(o); } void neg(int o, int l, int r, int ql, int qr) { if (ql > r || qr < l) return; if (ql <= l && r <= qr) { myswap(o); return; } int mid = (l + r) >> 1; pushdown(o, l, r); if (ql <= mid) neg(lson, l, mid, ql, qr); if (qr > mid) neg(rson, mid + 1, r, ql, qr); pushup(o); } int querysum(int o, int l, int r, int ql, int qr) { if (ql > r || qr < l) return 0; if (ql <= l && r <= qr) { return sumv[o]; } int mid = (l + r) >> 1; int ans = 0; pushdown(o, l, r); if (ql <= mid) ans += querysum(lson, l, mid, ql, qr); if (qr > mid) ans += querysum(rson, mid + 1, r, ql, qr); return ans; } int querymax(int o, int l, int r, int ql, int qr) { if (ql > r || qr < l) return -inf; if (ql <= l && r <= qr) { return maxv[o]; } int mid = (l + r) >> 1; int ans = -inf; pushdown(o, l, r); if (ql <= mid) ans = max(ans, querymax(lson, l, mid, ql, qr)); if (qr > mid) ans = max(ans, querymax(rson, mid + 1, r, ql, qr)); return ans; } int querymin(int o, int l, int r, int ql, int qr) { if (ql > r || qr < l) return inf; if (ql <= l && r <= qr) { return minv[o]; } int mid = (l + r) >> 1; pushdown(o, l, r); int ans = inf; if (ql <= mid) ans = min(ans, querymin(lson, l, mid, ql, qr)); if (qr > mid) ans = min(ans, querymin(rson, mid + 1, r, ql, qr)); return ans; } int csum(int u, int v) { int ans = 0; while (top[u] != top[v]) { if (dep[top[u]] < dep[top[v]]) swap(u, v); ans += querysum(1, 1, n, pos[top[u]], pos[u]); u = fa[top[u]]; } if (dep[u] < dep[v]) swap(u, v); ans += querysum(1, 1, n, pos[v] + 1, pos[u]); return ans; } int cmax(int u, int v) { int ans = -inf; while (top[u] != top[v]) { if (dep[top[u]] < dep[top[v]]) swap(u, v); ans = max(ans, querymax(1, 1, n, pos[top[u]], pos[u])); u = fa[top[u]]; } if (dep[u] < dep[v]) swap(u, v); ans = max(ans, querymax(1, 1, n, pos[v] + 1, pos[u])); return ans; } int cmin(int u, int v) { int ans = inf; while (top[u] != top[v]) { if (dep[top[u]] < dep[top[v]]) swap(u, v); ans = min(ans, querymin(1, 1, n, pos[top[u]], pos[u])); u = fa[top[u]]; } if (dep[u] < dep[v]) swap(u, v); ans = min(ans, querymin(1, 1, n, pos[v] + 1, pos[u])); return ans; } void update1(int u, int v) { while (top[u] != top[v]) { if (dep[top[u]] < dep[top[v]]) swap(u, v); neg(1, 1, n, pos[top[u]], pos[u]); u = fa[top[u]]; } if (dep[u] < dep[v]) swap(u, v); neg(1, 1, n, pos[v] + 1, pos[u]); } struct edge { int u, v; } edge[N]; int main() { //freopen("in.txt", "r", stdin); //freopen("out.txt", "w", stdout); scanf("%d", &n); val[1] = 0; for (int i = 1; i < n; i++) { int u, v, w; scanf("%d%d%d", &u, &v, &w); u++; v++; G[u].push_back(node(v, w)); G[v].push_back(node(u, w)); edge[i].u = u; edge[i].v = v; } dep[0] = 0; dfs1(1, 0); cnt = 0; dfs2(1, 0, 1); build(1, 1, n); int m; scanf("%d", &m); char ch[10]; for (int i = 1; i <= m; i++) { scanf("%s", ch); int x, y; scanf("%d%d", &x, &y); if (ch[0] == 'S') { x++, y++; printf("%d\n", csum(x, y)); } else if (ch[0] == 'C') { int v = dep[edge[x].u] < dep[edge[x].v] ? edge[x].v : edge[x].u; update(1, 1, n, pos[v], y); } else if (ch[0] == 'N') { x++; y++; update1(x, y); } else if (ch[1] == 'A') { x++; y++; printf("%d\n", cmax(x, y)); } else { x++; y++; printf("%d\n", cmin(x, y)); } } return 0; }
continue