轻重链剖分
// time : 20210103
// test on https://www.luogu.com.cn/problem/P3384
#include <cstdio>
#include <cstring>
#include <string>
#include <iostream>
#include <algorithm>
#define M 100001
inline void read(int &T) {
int x = 0; bool f = 0; char c = getchar();
while (c < '0' || c > '9') { if (c == '-') f = !f; c = getchar(); }
while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
T = f ? -x : x;
}
int n, m, r, p, a[M], dfn[M], pre[M], size[M];
namespace Seg {
#define lson now << 1
#define rson now << 1 | 1
struct Node {
int l, r, w, lazy;
}tree[M << 2];
void build(int l, int r, int now) {
tree[now].l = l, tree[now].r = r;
if (tree[now].l == tree[now].r) {
tree[now].w = a[pre[l]]; return;
}
int mid = (tree[now].l + tree[now].r) >> 1;
build(l, mid, lson), build(mid + 1, r, rson);
tree[now].w = (tree[lson].w + tree[rson].w) % p;
}
void pushdown(int now) {
if (tree[now].l == tree[now].r) return;
tree[lson].lazy = (tree[lson].lazy + tree[now].lazy) % p;
tree[rson].lazy = (tree[rson].lazy + tree[now].lazy) % p;
tree[lson].w = (tree[lson].w + 1ll * (tree[lson].r - tree[lson].l + 1) * tree[now].lazy % p) % p;
tree[rson].w = (tree[rson].w + 1ll * (tree[rson].r - tree[rson].l + 1) * tree[now].lazy % p) % p;
tree[now].lazy = 0; return;
}
void update(int x, int y, int k, int now) {
if (tree[now].l >= x && tree[now].r <= y) {
tree[now].w = (tree[now].w + 1ll * (tree[now].r - tree[now].l + 1) * k % p) % p;
tree[now].lazy = (tree[now].lazy + k) % p; return;
}
if (tree[now].lazy) pushdown(now);
int mid = (tree[now].l + tree[now].r) >> 1;
if (x <= mid) update(x, y, k, lson);
if (y > mid) update(x, y, k, rson);
tree[now].w = (tree[lson].w + tree[rson].w) % p;
}
int query(int x, int y, int now) {
if (tree[now].l >= x && tree[now].r <= y) return tree[now].w;
if (tree[now].lazy) pushdown(now);
int mid = (tree[now].l + tree[now].r) >> 1, ans = 0;
if (x <= mid) ans = (ans + query(x, y, lson)) % p;
if (y > mid) ans = (ans + query(x, y, rson)) % p;
return ans;
}
}
namespace Cut {
int pthn, dep[M], head[M];
int cnt, fa[M], son[M], top[M];
struct Edge {
int nxt, to;
}pth[M << 1];
void add(int frm, int to) {
pth[++pthn].to = to, pth[pthn].nxt = head[frm];
head[frm] = pthn;
}
void dfs1(int u, int father) {
fa[u] = father, dep[u] = dep[father] + 1, size[u] = 1;
for (int i = head[u]; i; i = pth[i].nxt) {
int v = pth[i].to;
if (v != father) {
dfs1(v, u), size[u] += size[v];
if (size[v] > size[son[u]]) son[u] = v;
}
}
}
void dfs2(int u, int tp) {
dfn[u] = ++cnt, pre[cnt] = u, top[u] = tp;
if (son[u]) dfs2(son[u], tp);
for (int i = head[u]; i; i = pth[i].nxt) {
int v = pth[i].to;
if (v != fa[u] && v != son[u]) dfs2(v, v);
}
}
void change(int x, int y, int k) {
while (top[x] != top[y]) {
if (dep[top[x]] < dep[top[y]]) std::swap(x, y);
Seg::update(dfn[top[x]], dfn[x], k, 1);
x = fa[top[x]];
}
if (dfn[x] > dfn[y]) std::swap(x, y);
Seg::update(dfn[x], dfn[y], k, 1);
}
int ask(int x, int y) {
int ans = 0;
while (top[x] != top[y]) {
if (dep[top[x]] < dep[top[y]]) std::swap(x, y);
ans = (ans + Seg::query(dfn[top[x]], dfn[x], 1)) % p;
x = fa[top[x]];
}
if (dfn[x] > dfn[y]) std::swap(x, y);
ans = (ans + Seg::query(dfn[x], dfn[y], 1)) % p;
return ans;
}
}
int main() {
read(n), read(m), read(r), read(p);
for (int i = 1; i <= n; ++i) read(a[i]);
for (int i = 1, u, v; i < n; ++i) {
read(u), read(v);
Cut::add(u, v), Cut::add(v, u);
}
Cut::dfs1(r, 0), Cut::dfs2(r, r), Seg::build(1, n, 1);
for (int i = 1, opt, x, y, k; i <= m; ++i) {
read(opt), read(x);
if (opt == 1) { read(y), read(k), Cut::change(x, y, k); }
if (opt == 2) { read(y), printf("%d
", Cut::ask(x, y)); }
if (opt == 3) { read(y), Seg::update(dfn[x], dfn[x] + size[x] - 1, y, 1); }
if (opt == 4) { printf("%d
", Seg::query(dfn[x], dfn[x] + size[x] - 1, 1)); }
}
return 0;
}
线段树
// time : 20210103
// test on https://www.luogu.com.cn/problem/P3373
#include <cstdio>
#include <cstring>
#include <string>
#include <iostream>
#include <algorithm>
#define M 100001
#define lson now << 1
#define rson now << 1 | 1
inline void read(int &T) {
int x = 0; bool f = 0; char c = getchar();
while (c < '0' || c > '9') { if (c == '-') f = !f; c = getchar(); }
while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
T = f ? -x : x;
}
int n, m, p;
struct Node {
int l, r, w, add, mul;
}tree[M << 2];
void build(int l, int r, int now) {
tree[now].l = l, tree[now].r = r;
tree[now].add = 0, tree[now].mul = 1;
if (tree[now].l == tree[now].r) {
read(tree[now].w); return;
}
int mid = (tree[now].l + tree[now].r) >> 1;
build(l, mid, lson), build(mid + 1, r, rson);
tree[now].w = (tree[lson].w + tree[rson].w) % p;
}
void pushdown(int now) {
if (tree[now].l == tree[now].r) return;
tree[lson].mul = 1ll * tree[lson].mul * tree[now].mul % p;
tree[rson].mul = 1ll * tree[rson].mul * tree[now].mul % p;
tree[lson].add = (1ll * tree[lson].add * tree[now].mul % p + tree[now].add) % p;
tree[rson].add = (1ll * tree[rson].add * tree[now].mul % p + tree[now].add) % p;
tree[lson].w = (1ll * tree[lson].w * tree[now].mul % p + 1ll * (tree[lson].r - tree[lson].l + 1) * tree[now].add % p) % p;
tree[rson].w = (1ll * tree[rson].w * tree[now].mul % p + 1ll * (tree[rson].r - tree[rson].l + 1) * tree[now].add % p) % p;
tree[now].mul = 1, tree[now].add = 0;
}
void update1(int x, int y, int k, int now) {
if (tree[now].l >= x && tree[now].r <= y) {
tree[now].w = 1ll * tree[now].w * k % p;
tree[now].mul = 1ll * tree[now].mul * k % p;
tree[now].add = 1ll * tree[now].add * k % p;
return;
}
if (tree[now].mul != 1 || tree[now].add) pushdown(now);
int mid = (tree[now].l + tree[now].r) >> 1;
if (x <= mid) update1(x, y, k, lson);
if (y > mid) update1(x, y, k, rson);
tree[now].w = (tree[lson].w + tree[rson].w) % p;
}
void update2(int x, int y, int k, int now) {
if (tree[now].l >= x && tree[now].r <= y) {
tree[now].w = (tree[now].w + 1ll * (tree[now].r - tree[now].l + 1) * k % p) % p;
tree[now].add = (tree[now].add + k) % p; return;
}
if (tree[now].mul != 1 || tree[now].add) pushdown(now);
int mid = (tree[now].l + tree[now].r) >> 1;
if (x <= mid) update2(x, y, k, lson);
if (y > mid) update2(x, y, k, rson);
tree[now].w = (tree[lson].w + tree[rson].w) % p;
}
int query(int x, int y, int now) {
if (tree[now].l >= x && tree[now].r <= y) return tree[now].w;
if (tree[now].mul != 1 || tree[now].add) pushdown(now);
int mid = (tree[now].l + tree[now].r) >> 1, ans = 0;
if (x <= mid) ans = (ans + query(x, y, lson)) % p;
if (y > mid) ans = (ans + query(x, y, rson)) % p;
return ans;
}
int main() {
read(n), read(m), read(p);
build(1, n, 1);
for (int i = 1, opt, x, y, k; i <= m; ++i) {
read(opt), read(x), read(y);
if (opt == 1) { read(k), update1(x, y, k, 1); }
if (opt == 2) { read(k), update2(x, y, k, 1); }
if (opt == 3) printf("%d
", query(x, y, 1));
}
return 0;
}
树状数组
// time : 20210103
// test on https://www.luogu.com.cn/problem/P3374
// test on https://www.luogu.com.cn/problem/P3368
#include <cstdio>
#include <cstring>
#include <string>
#include <iostream>
#include <algorithm>
#define M 500001
#define lowbit(x) x & (-x)
inline void read(int &T) {
int x = 0; bool f = 0; char c = getchar();
while (c < '0' || c > '9') { if (c == '-') f = !f; c = getchar(); }
while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
T = f ? -x : x;
}
int n, m;
struct Bit {
int c[M];
void add(int x, int k) {
while (x <= n) { c[x] += k, x += lowbit(x); }
}
int ask(int x, int ans = 0) {
while (x > 0) { ans += c[x], x -= lowbit(x); }
return ans;
}
}b;
int main() {
read(n), read(m);
//bit1
for (int i = 1, x; i <= n; ++i) {
read(x), b.add(i, x);
}
for (int i = 1, opt, x, y; i <= m; ++i) {
read(opt), read(x), read(y);
if (opt == 1) b.add(x, y);
else printf("%d
", b.ask(y) - b.ask(x - 1));
}
//bit2
for (int i = 1, last = 0, x; i <= n; ++i, last = x) {
read(x), b.add(i, x - last);
}
for (int i = 1, opt, x, y, k; i <= m; ++i) {
read(opt), read(x);
if (opt == 1) {
read(y), read(k);
b.add(x, k), b.add(y + 1, -k);
}
else printf("%d
", b.ask(x));
}
return 0;
}
缩点（tarjan）
// time : 20210103
// test on https://www.luogu.com.cn/problem/P3387
#include <cstdio>
#include <cstring>
#include <string>
#include <iostream>
#include <algorithm>
#include <queue>
#define M 100001
int min(int a, int b) { return a < b ? a : b; }
int max(int a, int b) { return a > b ? a : b; }
inline void read(int &T) {
int x = 0; bool f = 0; char c = getchar();
while (c < '0' || c > '9') { if (c == '-') f = !f; c = getchar(); }
while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
T = f ? -x : x;
}
bool vis[M];
std::queue<int> q;
int n, m, ans, a[M], x[M], y[M], f[M], pthn, head[M];
int c, t, sc, b[M], s[M], dfn[M], low[M], num[M], ideg[M];
struct Edge {
int nxt, to;
}pth[M];
void add(int frm, int to) {
pth[++pthn].to = to, pth[pthn].nxt = head[frm];
head[frm] = pthn;
}
void format() {
memset(head, 0, sizeof head);
for (int i = 1; i <= pthn; ++i) {
pth[i].nxt = pth[i].to = 0;
}
pthn = 0;
}
void tarjan(int u) {
low[u] = dfn[u] = ++c;
vis[u] = true, s[++sc] = u;
for (int i = head[u]; i; i = pth[i].nxt) {
int v = pth[i].to;
if (!dfn[v]) {
tarjan(v);
low[u] = min(low[u], low[v]);
}
else if (vis[v]) low[u] = min(low[u], dfn[v]);
}
if (low[u] == dfn[u]) {
int now = s[sc--]; num[now] = ++t;
b[t] += a[now], vis[now] = false;
while (now != u) {
now = s[sc--], num[now] = t;
b[t] += a[now], vis[now] = false;
}
}
}
int main() {
read(n), read(m);
for (int i = 1; i <= n; ++i) read(a[i]);
for (int i = 1; i <= m; ++i) {
read(x[i]), read(y[i]);
add(x[i], y[i]);
}
for (int i = 1; i <= n; ++i) {
if (!dfn[i]) tarjan(i);
}
format();
for (int i = 1; i <= m; ++i) {
if (num[x[i]] != num[y[i]]) {
add(num[x[i]], num[y[i]]);
++ideg[num[y[i]]];
}
}
for (int i = 1; i <= t; ++i) {
if (!ideg[i]) q.push(i), f[i] = b[i];
}
while (!q.empty()) {
int u = q.front(); q.pop();
ans = max(ans, f[u]);
for (int i = head[u]; i; i = pth[i].nxt) {
int v = pth[i].to; --ideg[v];
f[v] = max(f[v], f[u] + b[v]);
if (!ideg[v]) q.push(v);
}
}
std::cout << ans << '
';
return 0;
}
回滚莫队（不删除莫队）
// time : 20200103
// test on https://www.luogu.com.cn/problem/P5906
#include <cmath>
#include <cstdio>
#include <cstring>
#include <string>
#include <iostream>
#include <algorithm>
#define M 200001
int min(int a, int b) { return a < b ? a : b; }
int max(int a, int b) { return a > b ? a : b; }
inline void read(int &T) {
int x = 0; bool f = 0; char c = getchar();
while (c < '0' || c > '9') { if (c == '-') f = !f; c = getchar(); }
while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
T = f ? -x : x;
}
int n, m, a[M], fir[M], las[M];
int sqrn, num[M], ans[M], fir_[M];
struct query {
int x, y, id;
friend bool operator < (query q1, query q2) {
if (num[q1.x] == num[q2.x]) return q1.y < q2.y;
else return num[q1.x] < num[q2.x];
}
}q[M];
struct lsh {
int w, id;
friend bool operator < (lsh l1, lsh l2) {
return l1.w < l2.w;
}
}b[M];
int main() {
read(n), sqrn = sqrt(n);
for (int i = 1; i <= n; ++i) {
read(a[i]);
b[i].id = i, b[i].w = a[i];
num[i] = (i - 1) / sqrn + 1;
}
std::sort(b + 1, b + n + 1);
for (int i = 1, now = 0; i <= n; ++i) {
if (b[i].w != b[i - 1].w) ++now;
a[b[i].id] = now;
}
read(m);
for (int i = 1; i <= m; ++i) {
read(q[i].x), read(q[i].y);
q[i].id = i;
}
std::sort(q + 1, q + m + 1);
int l = 1, r = 0, now = 0, lasb = 0;
for (int i = 1; i <= m; ++i) {
if (num[q[i].x] == num[q[i].y]) {
int temp = 0;
for (int j = q[i].x; j <= q[i].y; ++j) {
if (!fir_[a[j]]) fir_[a[j]] = j;
else temp = max(temp, j - fir_[a[j]]);
}
for (int j = q[i].x; j <= q[i].y; ++j) fir_[a[j]] = 0;
ans[q[i].id] = temp; continue;
}
if (lasb != num[q[i].x]) {
int stop = min(num[q[i].x] * sqrn, n );
memset(fir, 0, sizeof fir), memset(las, 0, sizeof las);
l = stop + 1, r = stop, now = 0, lasb = num[q[i].x];
}
while (r < q[i].y) {
++r;
if (!fir[a[r]]) fir[a[r]] = las[a[r]] = r;
else {
las[a[r]] = r;
now = max(now, r - fir[a[r]]);
}
}
int l_ = l, temp = now;
while (l_ > q[i].x) {
--l_;
if (!las[a[l_]] && !fir[a[l_]]) las[a[l_]] = l_;
else temp = max(temp, las[a[l_]] - l_);
}
ans[q[i].id] = temp;
while (l_ < l) {
if (!fir[a[l_]]) las[a[l_]] = 0;
++l_;
}
}
for (int i = 1; i <= m; ++i) printf("%d
", ans[i]);
return 0;
}
单调栈
// time : 20200103
// test on https://www.luogu.com.cn/problem/P5788
#include <cstdio>
#include <cstring>
#include <string>
#include <iostream>
#include <algorithm>
#include <stack>
#define M 3000001
inline void read(int &T) {
int x = 0; bool f = 0; char c = getchar();
while (c < '0' || c > '9') { if (c == '-') f = !f; c = getchar(); }
while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
T = f ? -x : x;
}
std::stack<int> s;
int n, a[M], ans[M];
int main() {
read(n);
for (int i = 1; i <= n; ++i) read(a[i]);
for (int i = 1; i <= n; ++i) {
while (!s.empty() && a[s.top()] < a[i]) {
ans[s.top()] = i; s.pop();
}
s.push(i);
}
for (int i = 1; i <= n; ++i) printf("%d ", ans[i]);
return 0;
}
单调队列
// time : 20200103
// test on https://www.luogu.com.cn/problem/P1886
#include <cstdio>
#include <cstring>
#include <string>
#include <iostream>
#include <algorithm>
#include <queue>
#define M 1000001
inline void read(int &T) {
int x = 0; bool f = 0; char c = getchar();
while (c < '0' || c > '9') { if (c == '-') f = !f; c = getchar(); }
while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
T = f ? -x : x;
}
std::deque<int> q1, q2;
int n, k, a[M], min[M], max[M];
int main() {
read(n), read(k);
for (int i = 1; i <= n; ++i) read(a[i]);
for (int i = 1; i <= n; ++i) {
while (!q1.empty() && q1.front() < i - k + 1) q1.pop_front();
while (!q2.empty() && q2.front() < i - k + 1) q2.pop_front();
while (!q1.empty() && a[q1.back()] >= a[i]) q1.pop_back();
while (!q2.empty() && a[q2.back()] <= a[i]) q2.pop_back();
q1.push_back(i), q2.push_back(i);
min[i] = a[q1.front()], max[i] = a[q2.front()];
}
for (int i = k; i <= n; ++i) printf("%d ", min[i]);
puts("");
for (int i = k; i <= n; ++i) printf("%d ", max[i]);
return 0;
}
Trie
// time : 20210109
// test on https://www.luogu.com.cn/problem/P2580
#include <cstdio>
#include <cstring>
#include <string>
#include <iostream>
#include <algorithm>
#define M 500001
int n, m;
std::string s;
struct Trie {
int ender[M];
int cnt, node[M][27];
void clear() {
cnt = 0;
memset(node, 0, sizeof node);
memset(ender, 0, sizeof ender);
}
void ins() {
int len = s.length(), now = 0;
for (int i = 0; i < len; ++i) {
if (!node[now][s[i] - 'a']) node[now][s[i] - 'a'] = ++cnt;
now = node[now][s[i] - 'a'];
}
ender[now] = true;
}
void find() {
int len = s.length(), now = 0;
for (int i = 0 ; i < len; ++i) {
if (node[now][s[i] - 'a']) now = node[now][s[i] - 'a'];
else { puts("WRONG"); return; }
}
++ender[now];
if (ender[now] > 2) puts("REPEAT");
else puts("OK");
}
}t;
int main() {
scanf("%d", &n); t.clear();
for (int i = 1; i <= n; ++i) { std::cin >> s; t.ins(); }
scanf("%d", &m);
for (int i = 1; i <= m; ++i) { std::cin >> s; t.find(); }
return 0;
}
倍增求LCA
// time : 20210110
// test on https://www.luogu.com.cn/problem/P3379
#include <cstdio>
#include <cstring>
#include <string>
#include <iostream>
#include <algorithm>
#define M 500001
inline void read(int &T) {
int x = 0; bool f = 0; char c = getchar();
while (c < '0' || c > '9') { if (c == '-') f = !f; c = getchar(); }
while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); }
T = f ? -x : x;
}
int n, m, s, pthn, head[M];
int lg[M], dep[M], fa[M][21];
struct Edge {
int nxt, to;
}pth[M << 1];
void add(int frm, int to) {
pth[++pthn].to = to, pth[pthn].nxt = head[frm];
head[frm] = pthn;
}
void dfs(int u, int father) {
fa[u][0] = father, dep[u] = dep[father] + 1;
for (int i = head[u]; i; i = pth[i].nxt) {
int x = pth[i].to;
if (x != father) dfs(x, u);
}
}
int lca(int x, int y) {
if (dep[x] < dep[y]) std::swap(x, y);
while (dep[x] > dep[y]) {
x = fa[x][lg[dep[x] - dep[y]] - 1];
}
if (x == y) return x;
for (int k = lg[dep[x]] - 1; k >= 0; --k) {
if (fa[x][k] != fa[y][k]) {
x = fa[x][k];
y = fa[y][k];
}
}
return fa[x][0];
}
int main() {
read(n), read(m), read(s);
for (int i = 1, u, v; i < n; ++i) {
read(u), read(v);
add(u, v), add(v, u);
}
for (int i = 1; i <= n; ++i) {
lg[i] = lg[i - 1] + ((1 << lg[i - 1]) == i);
}
dfs(s, 0);
for (int j = 1; (1 << j) <= n; ++j) {
for (int i = 1; i <= n; ++i) {
fa[i][j] = fa[fa[i][j - 1]][j - 1];
}
}
for (int i = 1, x, y; i <= m; ++i) {
read(x), read(y);
printf("%d
", lca(x, y));
}
return 0;
}