Shino
Shino
Shino

Shino Channel

$ sudo echo Shino >> YourHeart

板子 (Ver.诗乃)

Shino Shino published on
Tarjan&Topo 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 void tarjan(int u) { dfn[u] = low[u] = ++tim; ins[u] = 1; stac[++top] = u; for(int v, i = h[u]; ~i; i = e[i].next) if(!dfn[(v = e[i].to)]) { tarjan(v); low[u] = min(low[u], low[v]); } else if(ins[v]) low[u] = min(low[u], low[v]); if(low[u] == dfn[u]) { int y; while(y = stac[top--]) { sd[y] = u; ins[y] = 0; if(u == y) break; p[u] += p[y]; } } } void topo() { queue <int> q; for(int i = 1; i <= n; ++i) if(sd[i] == i && !in[i]) q.push(i), dis[i] = p[i]; while(!q.empty()) { int u = q.front(); q.pop(); for(int v, i = h[u]; ~i; i = e[i].next) { v = e[i].to; dis[v] = max(dis[v], dis[u] + p[v]); --in[v]; if(!in[v]) q.push(v); } } int ans = 0; for(int i = 1; i <= n; ++i) ans = max(ans, dis[i]); printf("%d\n", ans); } ST 1 2 3 4 5 6 7 8 9 void ST_Build() { for(int j = 1; j <= 21; ++j) for(int i = 1; i + (1 << j) - 1 <= n; ++i) st[i][j] = max(st[i][j-1], st[i+(1<<(j-1))][j-1]); } int ST_query(int l, int r) { int k = lg2[r-l+1]; return max(st[l][k], st[r-(1<<k)+1][k]); } ST-BlackMagic 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 struct RMQ { #define L(x) ((x-1)*siz+1) #define R(x) std::min(n, x*siz+1) #define bl(x) ((x-1)/siz+1) const int MAXB = 2050, siz = 50; int prf[MAXN], suf[MAXN], n, st[MAXB][13], lg2[MAXN], a[MAXN]; void init(int *s, int _n, int k) { n = _n; for(int i = 1; i <= n; ++i) a[i] = s[i] % k, st[bl(i)][0] = min(st[bl(i)][0], a[i]); for(int i = 1; i <= bl(n); ++i) { prf[L(i)] = a[L(i)]; suf[R(i)] = a[R(i)]; for(int j = L(i)+1; j <= R(i); ++j) prf[j] = min(prf[j-1], a[j]); for(int j = R(i)-1; j >= L(i); --j) suf[j] = min(suf[j+1], a[j]); } for(int j = 1; j <= 12; ++j) for(int i = 1; i + (1 << j) - 1 <= bl(n); ++i) st[i][j] = min(st[i][j-1], st[i+(1<<(j-1))][j-1]); } int QST(int l, int r) { if(l > r) return 0; int k = lg2[r-l+1]; return min(st[l][k], st[r-(1<<k)+1][k]); } int query(int l, int r) { if(bl(l) == bl(r)) { int res = 0; for(int i = l; i <= r; ++i) res = max(res, a[i]); return res; } else return min(min(prf[r], suf[l]), QST(bl(l)+1, bl(r)-1)); } } ST; Manacher 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 void Manacher() { int mr = 0, mid; for(int i = 0; i < n; ++i) { p[i] = i < mr ? min(p[(mid << 1) - i], p[mid] + mid - i) : 1; for(; s[i-p[i]] == s[i+p[i]]; ++p[i]); if(p[i] + i > mr) mr = i + p[i], mid = i; } } int main() { scanf("%s", a); _n = strlen(a); s[0] = s[1] = '#'; n = 1; for(int i = 0; i < _n; ++i) s[++n] = a[i], s[++n] = '#'; s[++n] = 0; Manacher(); for(int i = 0; i < n; ++i) ans = max(ans, p[i]); printf("%d\n", ans-1); } 线性基 1 2 3 4 5 6 7 8 9 10 11 for(int i = 1; i <= n; ++i) { read(a); for(int j = 50; j >= 0; --j) { if((a >> j) & 1) { if(!p[j]) {p[j] = a; break;} a ^= p[j]; } } } for(int i = 50; i >= 0; --i) if(p[i]) ans = max(ans, ans ^ p[i]); 线性逆元 1 2 3 inv[1] = 1; for(int i = 2; i <= n; ++i) inv[i] = 1ll * (P - P / i) % P * inv[P % i] % P; 后缀数组 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 void getSA() { for(int i = 1; i <= n; ++i) ++c[x[i] = s[i]]; for(int i = 1; i <= m; ++i) c[i] += c[i-1]; for(int i = n; i >= 1; --i) sa[c[x[i]]--] = i; for(int k = 1; k <= n; k <<= 1) { int num = 0; for(int i = n - k + 1; i <= n; ++i) y[++num] = i; for(int i = 1; i <= n; ++i) if(sa[i] > k) y[++num] = sa[i] - k; memset(c, 0, sizeof c); for(int i = 1; i <= n; ++i) ++c[x[i]]; for(int i = 1; i <= m; ++i) c[i] += c[i-1]; for(int i = n; i >= 1; --i) sa[c[x[y[i]]]--] = y[i], y[i] = 0; swap(x, y); x[sa[1]] = 1; num = 0; for(int i = 1; i <= n; ++i) x[sa[i]] = (y[sa[i-1]] == y[sa[i]] && y[sa[i-1]+k] == y[sa[i]+k]) ? num : ++num; if(num == n) break; m = num; } } 点分治 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 void getroot(int u, int p, int S) { siz[u] = 1, f[u] = 0; for(int v, i = h[u]; ~i; i = e[i].next) if((v = e[i].to) != p && !vis[v]) getroot(v, u, S), siz[u] += siz[v], f[u] = max(f[u], siz[v]); f[u] = max(f[u], S - siz[u]); rt = f[u] < f[rt] ? u : rt; } void getdis(int u, int p) { stk[++top] = dis[u]; for(int v, i = h[u]; ~i; i = e[i].next) if((v = e[i].to) != p && !vis[v]) dis[v] = dis[u] + e[i].w, getdis(v, u); } void solve(int u, int w, int t) { top = 0, dis[u] = w, getdis(u, 0); for(int i = 1; i <= top; ++i) for(int j = 1; j <= top; ++j) if(i != j) ans[stk[i] + stk[j]] += t; } void devide(int u) { solve(u, 0, 1); vis[u] = 1; for(int v, i = h[u]; ~i; i = e[i].next) if(!vis[(v = e[i].to)]) { solve(v, e[i].w, -1), rt = 0, f[0] = n; getroot(v, u, siz[u]), devide(rt); } } 线段树 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 #define L(u) (u<<1) #define R(u) (u<<1|1) #define mid ((l+r)>>1) void PU(int u) {t[u] = (t[L(u)] + t[R(u)]) % P;} void ADD(int u, int l, int r, int k) { t[u] += (r - l + 1) * k % P; t[u] %= P; add[u] = (add[u] + k) % P; } void MUL(int u, int l, int r, int k) { t[u] = t[u] * k % P; add[u] = add[u] * k % P; mul[u] = mul[u] * k % P; } void PD(int u, int l, int r) { MUL(L(u), l, mid, mul[u]); MUL(R(u), mid+1, r, mul[u]); mul[u] = 1; ADD(L(u), l, mid, add[u]); ADD(R(u), mid+1, r, add[u]); add[u] = 0; } void build(int u, int l, int r) { mul[u] = 1; if(l == r) {t[u] = a[l]; return;} build(L(u), l, mid); build(R(u), mid+1, r); PU(u); } void MA(int u, int l, int r, int tl, int tr, int k) { if(tr < l || tl > r) return; if(tl <= l && r <= tr) {ADD(u, l, r, k); return;} PD(u, l, r); MA(L(u), l, mid, tl, tr, k); MA(R(u), mid+1, r, tl, tr, k); PU(u); } void MM(int u, int l, int r, int tl, int tr, int k) { if(tr < l || tl > r) return; if(tl <= l && r <= tr) {MUL(u, l, r, k); return;} PD(u, l, r); MM(L(u), l, mid, tl, tr, k); MM(R(u), mid+1, r, tl, tr, k); PU(u); } int Q(int u, int l, int r, int tl, int tr) { if(tr < l || tl > r) return 0; if(tl <= l && r <= tr) return t[u]; PD(u, l, r); return (Q(L(u), l, mid, tl, tr) + Q(R(u), mid+1, r, tl, tr)) % P; } 三分 1 2 3 4 5 while(fabs(r-l) >= eps) { double mid = (l + r) / 2; if(f(mid - eps) < f(mid + eps)) l = mid; else r = mid; } 树状数组 1 2 void U(int x, int k) {for(; x <= n; t[x] += k, x += x&-x);} int Q(int x) {int w = 0; for(; x; w += t[x], x -= x&-x); return w;} 高斯消元 1 2 3 4 5 6 7 8 9 10 11 12 13 for(int i = 1; i <= n; ++i) { int p = i; for(int j = i + 1; j <= n; ++j) if(fabs(a[j][i]) > fabs(a[p][i])) p = j; if(a[p][i] == 0) {puts("No Solution"); return 0;} for(int j = 1; j <= n+1; ++j) swap(a[i][j], a[p][j]); for(int j = 1; j <= n; ++j) { if(i == j) continue; double t = a[j][i] / a[i][i]; for(int k = i; k <= n+1; ++k) a[j][k] -= a[i][k] * t; } } for(int i = 1; i <= n; ++i) printf("%.2lf\n", a[i][n+1] / a[i][i]); 最小生成树&并查集 1 2 3 4 5 6 7 8 9 10 11 12 int findfa(int x) {return x == fa[x] ? x : fa[x] = findfa(fa[x]);} int main() { for(int i = 1; i <= n; ++i) fa[i] = i; sort(e+1, e+m+1); for(int i = 1; i <= m; ++i) { int x = findfa(e[i].u), y = findfa(e[i].v); if(x == y) continue; ans += e[i].w; ++cnt; if(cnt == n-1) break; fa[x] = y; } } DINIC 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 bool bfs() { memset(d, -1, sizeof d); queue <int> q; q.push(s); d[s] = 0; while(!q.empty()) { int u = q.front(); q.pop(); for(int v, i = h[u]; ~i; i = e[i].next) if(d[v = e[i].to] == -1 && e[i].w > 0) d[v] = d[u] + 1, q.push(v); } return d[t] != -1; } int dfs(int u, int f) { int r = 0; if(u == t) return f; for(int v, i = h[u]; ~i && r < f; i = e[i].next) if(d[(v = e[i].to)] == d[u] + 1 && e[i].w > 0) { int x = dfs(v, min(e[i].w, f-r)); e[i].w -= x; e[i^1].w += x; r += x; } if(!r) d[u] = -1; return r; } int dinic() { int x, ans = 0; while(bfs()) while(x = dfs(s, 1e9)) ans += x; return ans; } 线性筛 1 2 3 4 5 6 7 for(int i = 2; i <= n; ++i) { if(!notp[i]) p[++cntp] = i; for(int j = 1; 1ll*i*p[j] <= n && j <= cntp; ++j) { notp[i*p[j]] = 1; if(i % p[j] == 0) break; } } 左偏树 1 2 3 4 5 6 7 8 9 10 11 12 13 14 int F(int x) {return x == fa[x] ? x : fa[x] = F(fa[x]);} int Merge(int x, int y) { if(x*y == 0) return x+y; if(v[x] > v[y] || (v[x] == v[y] && x > y)) swap(x, y); R(x) = Merge(R(x), y); fa[R(x)] = fa[L(x)] = x; if(dis[R(x)] > dis[L(x)]) swap(L(x), R(x)); dis[x] = dis[R(x)] + 1; return x; } int Top(int x) {return del[x] ? -1 : v[x];} void Pop(int x) { if(del[x]) return; del[x] = 1; fa[L(x)] = L(x); fa[R(x)] = R(x); fa[x] = Merge(L(x), R(x)); } LCT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 bool nroot(int x) {return ch[fa[x]][0] == x || ch[fa[x]][1] == x;} void pushup(int x) {sumx[x] = sumx[ch[x][1]] ^ sumx[ch[x][0]] ^ val[x];} void pushr(int x) {swap(ch[x][1], ch[x][0]); rot[x] ^= 1;} void pushdown(int x) {if(rot[x]) {if(ch[x][0]) pushr(ch[x][0]); if(ch[x][1]) pushr(ch[x][1]); rot[x] = 0;}} void rotate(int x) { int y = fa[x], z = fa[y], k = (x == ch[y][1]); if(nroot(y)) ch[z][(y == ch[z][1])] = x; fa[x] = z; ch[y][k] = ch[x][k^1]; if(ch[x][k^1]) fa[ch[x][k^1]] = y; ch[x][k^1] = y; fa[y] = x; pushup(y); } void splay(int x) { int y = x, z = 0; st[++z] = y; while(nroot(y)) st[++z] = y = fa[y]; while(z) pushdown(st[z--]); for(int y; nroot(x); rotate(x)) if(nroot(y = fa[x])) rotate((y == ch[fa[y]][0]) ^ (x == ch[y][0]) ? x : y); pushup(x); } void access(int x) {for(int y = 0; x; x = fa[y = x]) splay(x), ch[x][1] = y, pushup(x);} void makeroot(int x) {access(x); splay(x); pushr(x);} int findroot(int x) {access(x); splay(x); for(; ch[x][0]; x = ch[x][0]) pushdown(x); splay(x); return x;} void spilit(int x, int y) {makeroot(x); access(y); splay(y);} void link(int x, int y) {makeroot(x); if(findroot(y) != x) fa[x] = y;} void cut(int x, int y) {makeroot(x); if(findroot(y) == x && fa[y] == x && !ch[y][0]) {fa[y] = ch[x][1] = 0; pushup(x);}} KMP 1 2 3 4 5 6 7 8 9 for(int i = 2, j = 0; i <= n; ++i) { while(j && s[i] != s[j+1]) j = nxt[j]; if(s[j+1] == s[i]) ++j; nxt[i] = j; } for(int i = 1, j = 0; i <= m; ++i) { while(j > 0 && t[i] != s[j+1]) j = nxt[j]; if(s[j+1] == t[i]) ++j; if(j == n) printf("%d\n", i-n+1); } SAM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 struct SoumAsuMire { int ch[MAXN][26], fa[MAXN], last, cnt, len[MAXN]; void insert(int c) { int p = last, np = ++cnt; last = np; len[np] = len[p] + 1; for(; p && !ch[p][c]; ch[p][c] = np, p = fa[p]); if(!p) fa[np] = 1; else { int q = ch[p][c]; if(len[q] == len[p] + 1) fa[np] = q; else { int nq = ++cnt; len[nq] = len[p] + 1; memcpy(ch[nq], ch[q], sizeof ch[q]); fa[nq] = fa[q]; fa[q] = fa[np] = nq; for(; p && ch[p][c] == q; ch[p][c] = nq, p = fa[p]); } } } void build(char *s) { int n = strlen(s+1); last = 1; for(int i = 1; i <= n; ++i) insert(s[i] - 'a'); } int getans() { int ans = 0; for(int i = 2; i <= cnt; ++i) ans += len[i] - len[fa[i]]; return ans; } } SAM; LCA(ST) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 void dfsRMQ(int u, int p) { st[++idx][0] = u; dfn[u] = idx; dep[u] = dep[p] + 1; for(int v, i = h[u]; ~i; i = e[i].next) if((v = e[i].to) != p) dfsRMQ(v, u), st[++idx][0] = u; } void LCAinit() { for(int i = 2; i <= (n << 1); ++i) lg2[i] = lg2[i>>1] + 1; dep[1] = 1; dfsRMQ(rt, 0); for(int j = 1; j < 20; ++j) for(int i = 1; i + (1 << j) <= (n << 1); ++i) st[i][j] = Min(st[i][j-1], st[i+(1<<(j-1))][j-1]); } int LCA(int x, int y) { x = dfn[x]; y = dfn[y]; if(x > y) swap(x, y); int k = lg2[y-x+1]; return Min(st[x][k], st[y-(1<<k)+1][k]); } mcmf 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 bool SPFA() { memset(d, 63, sizeof d); memset(vis, 0, sizeof vis); memset(flow, 63, sizeof flow); queue <int> q; q.push(s); d[s] = 0; vis[s] = 1; while(!q.empty()) { int u = q.front(); q.pop(); vis[u] = 0; for(int v, i = h[u]; ~i; i = e[i].next) if(d[v = e[i].to] > d[u] + e[i].c && e[i].f) { d[v] = d[u] + e[i].c; pos[v] = i; fa[v] = u; flow[v] = min(flow[u], e[i].f); if(!vis[v]) vis[v] = 1, q.push(v); } } return flow[s] != flow[t]; } void mcmf() { while(SPFA()) { mc += flow[t]; mf += flow[t] * d[t]; for(int u = t; u != s; u = fa[u]) e[pos[u]].f -= flow[t], e[pos[u]^1].f += flow[t]; } } AC自动机 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 #include <bits/stdc++.h> using namespace std; const int S = 2000050, T = 200050; struct Edge {int to, next;} e[T]; char s[S]; int n, h[T], cnt, ch[T][26], fail[T], match[T], siz[T], tot = 1, en; queue <int> q; void addedge(int u, int v) {e[en] = (Edge) {v, h[u]}; h[u] = en++;} void dfs(int u) { for(int v, i = h[u]; ~i; i = e[i].next) dfs(v = e[i].to), siz[u] += siz[v]; } int main() { scanf("%d", &n); memset(h, -1, sizeof h); for(int i = 1; i <= n; ++i) { scanf("%s", s); int u = 1, j; for(u = 1, j = 0; s[j]; ++j) { int c = s[j] - 'a'; if(!ch[u][c]) ch[u][c] = ++tot; u = ch[u][c]; } match[i] = u; } for(int i = 0; i < 26; ++i) ch[0][i] = 1; q.push(1); while(!q.empty()) { int u = q.front(); q.pop(); for(int i = 0; i < 26; ++i) if(ch[u][i]) { fail[ch[u][i]] = ch[fail[u]][i]; q.push(ch[u][i]); } else ch[u][i] = ch[fail[u]][i]; } scanf("%s", s); for(int u = 1, i = 0; s[i]; ++i) ++siz[u = ch[u][s[i]-'a']]; for(int i = 2; i <= tot; ++i) addedge(fail[i], i); dfs(1); for(int i = 1; i <= n; ++i) printf("%d\n", siz[match[i]]); puts(""); } dijkstra 1 2 3 4 5 6 7 8 9 10 11 12 13 void dijkstra() { memset(d, 0x3f, sizeof d); d[s] = 0; q.push((D) {s, 0}); while(!q.empty()) { int u = q.top().u; q.pop(); if(vis[u]) continue; vis[u] = 1; for(int v, i = h[u]; ~i; i = e[i].next) if(d[v = e[i].to] > d[u] + e[i].w) { d[v] = d[u] + e[i].w; if(!vis[v]) q.push((D) {v, d[v]}); } } } 树哈希 1 2 3 4 5 6 7 8 ull Hash(int u, int p) { ull q[MAXN], ans = X; int top = 0; for(int i = h[u]; ~i; i = e[i].next) if(e[i].to != p) q[++top] = Hash(e[i].to, u); sort(q+1, q+top+1); for(int i = 1; i <= top; ++i) ans = ans * P + q[i]; return ans * P + X + 1; } CDQ分治 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 struct BITS { int t[MAXN]; void U(int x, int k) {for(; x <= m; t[x] += k, x += x&-x);} int Q(int x) {int res = 0; for(; x; res += t[x], x -= x&-x); return res;} } T; void cdq(int l, int r) { if(l == r) return; int mid = (l + r) >> 1; cdq(l, mid); cdq(mid+1, r); sort(a+l, a+mid+1, cmpy); sort(a+mid+1, a+r+1, cmpy); int i = mid + 1, j = l; for(; i <= r; ++i) { for(; a[j].y <= a[i].y && j <= mid; ++j) T.U(a[j].z, a[j].w); a[i].ans += T.Q(a[i].z); } for(int k = l; k < j; ++k) T.U(a[k].z, -a[k].w); } int main() { read(_n); read(m); for(int i = 1; i <= _n; ++i) read(b[i].x), read(b[i].y), read(b[i].z); sort(b+1, b+_n+1, cmpx); for(int c = 0, i = 1; i <= _n; ++i) { ++c; if(b[i].x != b[i+1].x || b[i].y != b[i+1].y || b[i].z != b[i+1].z) a[++n] = b[i], a[n].w = c, c = 0; } cdq(1, n); for(int i = 1; i <= n; ++i) cnt[a[i].ans + a[i].w - 1] += a[i].w; for(int i = 0; i < _n; ++i) printf("%d\n", cnt[i]); } Lucas 1 2 3 4 5 6 7 8 int C(int n, int m) { if(m > n) return 0; return 1ll * fac[n] * power(fac[m], P-2) * power(fac[n-m], P-2); } int Lucas(int n, int m) { if(m == 0) return 1; return 1ll * C(n%P, m%P) * Lucas(n/P, m/P) % P; } 二分图 1 2 3 4 5 6 7 8 9 10 bool dfs(int u) { for(int v, i = h[u]; ~i; i = e[i].next) { if(vis[v = e[i].to] != tag) { vis[v] = tag; if(!match[v] || dfs(match[v])) { match[v] = u; return 1; } } } return 0; } 莫队二次离线 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 #include <bits/stdc++.h> using namespace std; const int MAXN = 100050; typedef long long lint; void read(int &x) { char ch; while(ch = getchar(), ch < '!'); x = ch - 48; while(ch = getchar(), ch > '!') x = (x << 3) + (x << 1) + ch - 48; } struct Qry {int l, r, id; lint ans;} q[MAXN]; struct T{int l, r, id;}; int n, m, a[MAXN], siz[MAXN], k, blsz, bl[MAXN], t[MAXN], pref[MAXN]; vector <int> buc; vector <T> v[MAXN]; lint ans[MAXN]; int cmp(Qry a, Qry b) {return bl[a.l] == bl[b.l] ? a.r < b.r : a.l < b.l;} int main() { read(n); read(m); read(k); blsz = sqrt(n); if(k > 14) {for(int i = 1; i <= m; ++i) puts("0"); return 0;} for(int i = 1; i <= n; ++i) read(a[i]); for(int i = 0; i < 16384; ++i) if((siz[i] = siz[(i>>1)] + (i&1)) == k) buc.push_back(i); for(int i = 1; i <= m; ++i) read(q[i].l), read(q[i].r), q[i].id = i; for(int i = 1; i <= n; ++i) bl[i] = (i-1) / blsz + 1; sort(q+1, q+m+1, cmp); for(int i = 1; i <= n; ++i) { for(int j = 0; j < buc.size(); ++j) ++t[a[i]^buc[j]]; pref[i] = t[a[i+1]]; } for(int L = 1, R = 0, i = 1; i <= m; ++i) { int l = q[i].l, r = q[i].r; if(L < l) v[R].push_back((T) {L, l-1, -i}); while(L < l) {q[i].ans += pref[L-1]; ++L;} if(L > l) v[R].push_back((T) {l, L-1, i}); while(L > l) {q[i].ans -= pref[L-2]; --L;} if(R < r) v[L-1].push_back((T) {R+1, r, -i}); while(R < r) {q[i].ans += pref[R]; ++R;} if(R > r) v[L-1].push_back((T) {r+1, R, i}); while(R > r) {q[i].ans -= pref[R-1]; --R;} } memset(t, 0, sizeof t); for(int l, r, id, i = 1; i <= n; ++i) { for(int j = 0; j < buc.size(); ++j) ++t[a[i]^buc[j]]; for(int o = 0; o < v[i].size(); ++o) { l = v[i][o].l; r = v[i][o].r; id = v[i][o].id; for(int j = l, tmp = 0; j <= r; ++j) { tmp = t[a[j]]; if(j <= i && !k) --tmp; if(id > 0) q[id].ans += tmp; else q[-id].ans -= tmp; } } } for(int i = 1; i <= m; ++i) q[i].ans += q[i-1].ans; for(int i = 1; i <= m; ++i) ans[q[i].id] = q[i].ans; for(int i = 1; i <= m; ++i) printf("%lld\n", ans[i]); } 莫比乌斯反演 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 void GetMu() { mu[1] = 1; for(int i = 2; i <= 10000000; ++i) { if(!vis[i]) p[++cnt] = i, mu[i] = -1; for(int j = 1; j <= cnt && p[j] * i <= 10000000; ++j) { vis[p[j]*i] = 1; if(i % p[j]) mu[p[j]*i] = -mu[i]; } } for(int i = 1; i <= cnt; ++i) for(int j = 1; j * p[i] <= 10000000; ++j) f[j*p[i]] += mu[j]; for(int i = 1; i <= 10000000; ++i) pref[i] = pref[i-1] + f[i]; } lint calc(int a, int b) { lint res = 0; if(a > b) swap(a, b); for(int l = 1, r = 0; l <= a; l = r + 1) { r = min(a/(a/l), b/(b/l)); res += (pref[r] - pref[l-1])*1ll*(a/l)*(b/l); } return res; } 树剖 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 void ADD(int u, int l, int r, int k) {t[u] = (t[u] + 1ll*k*(r-l+1)%P) % P; tag[u] = (tag[u] + k) % P;} void PD(int u, int l, int r) {ADD(L(u), l, mid, tag[u]); ADD(R(u), mid+1, r, tag[u]); tag[u] = 0;} void PU(int u) {t[u] = (t[L(u)] + t[R(u)]) % P;} void build(int u, int l, int r) { if(l == r) {t[u] = w[id[l]]; return; } build(L(u), l, mid); build(R(u), mid+1, r); PU(u); } void upd(int u, int l, int r, int tl, int tr, int k) { if(tr < l || tl > r) return; if(tl <= l && r <= tr) ADD(u, l, r, k); else PD(u, l, r), upd(L(u), l, mid, tl, tr, k), upd(R(u), mid+1, r, tl, tr, k), PU(u); } int qry(int u, int l, int r, int tl, int tr) { if(tr < l || tl > r) return 0; if(tl <= l && r <= tr) return t[u]; PD(u, l, r); return (qry(L(u), l, mid, tl, tr) + qry(R(u), mid+1, r, tl, tr)) % P; } void dfs1(int u, int p) { fa[u] = p; siz[u] = 1; dep[u] = dep[p] + 1; for(int v, i = h[u]; ~i; i = e[i].next) if((v = e[i].to) != p) { dfs1(v, u); siz[u] += siz[v]; if(siz[son[u]] < siz[v]) son[u] = v; } } void dfs2(int u, int p) { id[dfn[u] = ++idx] = u; top[u] = p; if(son[u]) dfs2(son[u], p); for(int v, i = h[u]; ~i; i = e[i].next) if((v = e[i].to) != fa[u] && v != son[u]) dfs2(v, v); } void addpath(int x, int y, int k) { for(; top[x] != top[y]; x = fa[top[x]]) { if(dep[top[x]] < dep[top[y]]) swap(x, y); upd(1, 1, n, dfn[top[x]], dfn[x], k); } if(dep[x] > dep[y]) swap(x, y); upd(1, 1, n, dfn[x], dfn[y], k); } int qrypath(int x, int y) { int res = 0; for(; top[x] != top[y]; x = fa[top[x]]) { if(dep[top[x]] < dep[top[y]]) swap(x, y); res = (res + qry(1, 1, n, dfn[top[x]], dfn[x])) % P; } if(dep[x] > dep[y]) swap(x, y); return (res + qry(1, 1, n, dfn[x], dfn[y])) % P; } void addroot(int x, int k) {upd(1, 1, n, dfn[x], dfn[x] + siz[x] - 1, k); } int qryroot(int x) {return qry(1, 1, n, dfn[x], dfn[x] + siz[x] - 1);} 主席树 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 struct JZM_T {int ch[2], v;} t[MAXN << 6]; int cnt, rt[MAXN << 6], o[MAXN], a[MAXN], n, m; void build(int &u, int l, int r) { t[u = ++cnt].v = 0; if(l != r) build(L(u), l, mid), build(R(u), mid+1, r); } void update(int &u, int v, int l, int r, int p, int k) { t[u = ++cnt] = t[v]; t[u].v += k; if(l != r) p <= mid ? update(L(u), L(v), l, mid, p, k) : update(R(u), R(v), mid+1, r, p, k); } int query(int tl, int tr, int l, int r, int k) { if(l == r) return o[l]; int s = t[L(tr)].v - t[L(tl)].v; return k <= s ? query(L(tl), L(tr), l, mid, k) : query(R(tl), R(tr), mid+1, r, k-s); } int main() { read(n); read(m); for(int i = 1; i <= n; ++i) read(a[i]), o[i] = a[i]; sort(o+1, o+n+1); int _n = unique(o+1, o+n+1)-o-1; build(rt[0], 1, _n); for(int i = 1; i <= n; ++i) update(rt[i], rt[i-1], 1, _n, lower_bound(o+1, o+_n+1, a[i])-o, 1); for(int l, r, k; m--; ) { read(l); read(r); read(k); printf("%d\n", query(rt[l-1], rt[r], 1, _n, k)); } } GCD-BlackMagic 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 int gcd(int a, int b) { int g = 1; for(int tmp, i = 0; i < 3; b /= tmp, g *= tmp, ++i) tmp = (k[a][i] > siz) ? (b % k[a][i] == 0 ? k[a][i] : 1) : _gcd[k[a][i]][b%k[a][i]]; return g; } int main() { k[1][0] = k[1][1] = k[1][2] = 1; notp[1] = 1; for(int i = 2; i <= V; ++i) { if(!notp[i]) p[++cnt] = i, k[i][2] = i, k[i][1] = k[i][0] = 1; for(int j = 1; p[j] * i <= V; ++j) { notp[i * p[j]] = 1; int *t = k[i*p[j]]; t[0] = k[i][0] * p[j]; t[1] = k[i][1]; t[2] = k[i][2]; if(t[1] < t[0]) swap(t[0], t[1]); if(t[2] < t[1]) swap(t[1], t[2]); if(i % p[j] == 0) break; } } for(int i = 1; i <= siz; ++i) _gcd[i][0] = _gcd[0][i] = i; for(int _max = 1; _max <= siz; ++_max) for(int i = 1; i <= _max; ++i) _gcd[i][_max] = _gcd[_max][i] = _gcd[_max % i][i]; FFT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 struct Complex { double x, y; Complex(double xx = 0, double yy = 0) {x = xx; y = yy;} Complex operator + (Complex &b) const {return Complex(x+b.x, y+b.y);} Complex operator - (Complex &b) const {return Complex(x-b.x, y-b.y);} Complex operator * (Complex &b) const {return Complex(x*b.x-y*b.y, y*b.x+x*b.y);} } a[MAXN], b[MAXN]; int r[MAXN], n, m, l, limit; void FFT (Complex *A, int t) { for(int i = 0; i < limit; ++i) if(i < r[i]) swap(A[i], A[r[i]]); for(int mid = 1; mid < limit; mid <<= 1) { Complex Wn = Complex(cos(Pi/mid), t * sin(Pi/mid)); for(int R = mid<<1, j = 0; j < limit; j += R) { Complex w = Complex(1, 0); for(int k = 0; k < mid; ++k, w = w * Wn) { Complex x = A[j+k], y = w*A[j+mid+k]; A[j+k] = x+y; A[j+mid+k] = x-y; } } } } int main() { n = read(); m = read(); for(int i = 0; i <= n; ++i) a[i].x = read(); for(int i = 0; i <= m; ++i) b[i].x = read(); for(limit = 1; limit <= n+m; limit <<= 1, ++l); for(int i = 0; i < limit; ++i) r[i] = (r[i>>1]>>1)|((i&1)<<(l-1)); FFT(a, 1); FFT(b, 1); for(int i = 0; i <= limit; ++i) a[i] = a[i]*b[i]; FFT(a, -1); for(int i = 0; i <= n+m; ++i) printf("%d ", (int)(a[i].x/limit+0.5)); puts(""); } 多项式 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 #include<bits/stdc++.h> #define ll long long #define FIO "loj150" using namespace std; const int N=1e5+5,MOD=998244353,P=19,INV2=MOD+1>>1; inline int add(int a,const int &b){if((a+=b)>=MOD)a-=MOD;return a;} inline int sub(int a,const int &b){if((a-=b)< 0)a+=MOD;return a;} inline int mul(const int &a,const int &b){return 1ll*a*b%MOD;} inline void inc(int &a,const int &b=1){a=add(a,b);} inline void dec(int &a,const int &b=1){a=sub(a,b);} inline void pro(int &a,const int &b){a=mul(a,b);} inline int qpow(int a,int b){int c=1;for(;b;b>>=1,pro(a,a))if(b&1)pro(c,a);return c;} int n,k,w[2][1<<P]; inline void pre(){ for(int i=1;i<1<<P;i<<=1){ w[0][i]=w[1][i]=1; int wn1=qpow(3,(MOD-1)/(i<<1)),wn0=qpow(wn1,MOD-2); for(int j=1;j<i;j++) w[0][i+j]=mul(w[0][i+j-1],wn0),w[1][i+j]=mul(w[1][i+j-1],wn1); } } #define poly vector<int> inline void read(poly &a,const int &n){ a.resize(n); for(int i=0;i<n;i++)scanf("%d",&a[i]); } inline void out(const poly &a){ for(int i=0,n=a.size();i<n;i++)printf("%d%c",a[i],i^n-1?' ':'\n'); } inline void clear(poly &a){ int n=a.size(); while(n>1&&!a[n-1])n--; a.resize(n); } inline poly operator +(poly a,const int &b){inc(a[0],b);return a;} inline poly operator +(const int &b,poly a){inc(a[0],b);return a;} inline poly operator -(poly a,const int &b){dec(a[0],b);return a;} inline poly operator -(const int &b,poly a){dec(a[0],b);return a;} inline poly operator +(poly a,const poly &b){ if(a.size()<b.size())a.resize(b.size()); for(int i=0,n=a.size();i<n;i++)inc(a[i],b[i]); return a; } inline poly operator -(poly a,const poly &b){ if(a.size()<b.size())a.resize(b.size()); for(int i=0,n=a.size();i<n;i++)dec(a[i],b[i]); return a; } inline void ntt(int *f,int opt,int l){ poly rev(l); for(int i=0;i<l;i++){rev[i]=(rev[i>>1]>>1)|((i&1)*(l>>1));if(i<rev[i])swap(f[i],f[rev[i]]);} for(int i=1;i<l;i<<=1) for(int j=0;j<l;j+=i<<1) for(int k=0;k<i;k++){ int x=f[j+k],y=mul(f[i+j+k],w[opt][i+k]); f[j+k]=add(x,y); f[i+j+k]=sub(x,y); } if(opt)for(int i=0,inv=qpow(l,MOD-2);i<l;i++)pro(f[i],inv); } inline poly operator *(poly a,poly b){ int n=a.size(),m=b.size(),l=1; while(l<n+m)l<<=1; a.resize(l);b.resize(l); ntt(&a[0],0,l);ntt(&b[0],0,l); for(int i=0;i<l;i++)pro(a[i],b[i]); ntt(&a[0],1,l); clear(a); return a; } inline poly& operator *=(poly &a,const poly b){return a=a*b;} inline poly operator *(poly a,const int &b){ for(int i=0,n=a.size();i<n;i++)pro(a[i],b); return a; } inline poly inv(const poly &a,const int &n){ if(n==1)return poly(1,qpow(a[0],MOD-2)); int l=1;while(l<=n<<1)l<<=1; poly b=inv(a,n+1>>1),c(l);b.resize(l); for(int i=0;i<n;i++)c[i]=a[i]; ntt(&b[0],0,l);ntt(&c[0],0,l); for(int i=0;i<l;i++)pro(b[i],sub(2,mul(b[i],c[i]))); ntt(&b[0],1,l); b.resize(n); clear(b); return b; } inline poly inv(const poly &a){return inv(a,a.size());} int B; #define pii pair<int,int> inline pii operator *(pii a,pii b){ return pii(add(mul(a.first,b.first),mul(mul(a.second,b.second),B)),add(mul(a.first,b.second),mul(a.second,b.first))); } inline pii qpow(pii a,int b){pii c=pii(1,0);for(;b;b>>=1,a=a*a)if(b&1)c=c*a;return c;} inline int remain(int x){ if(x<=1)return x; int a=mul(mul(rand(),rand()),rand()); while(qpow(B=sub(mul(a,a),x),MOD-1>>1)==1)a=mul(mul(rand(),rand()),rand()); pii A=pii(a,1),ans=qpow(A,MOD+1>>1); return min(ans.first,MOD-ans.first); } inline poly sqrt(const poly &a,const int &n){ if(n==1)return poly(1,remain(a[0])); int l=1;while(l<=n<<1)l<<=1; poly b=sqrt(a,n+1>>1),c(l),d; b.resize(n);d=inv(b)*INV2; b.resize(l);d.resize(l); for(int i=0;i<n;i++)c[i]=a[i]; ntt(&b[0],0,l);ntt(&c[0],0,l);ntt(&d[0],0,l); for(int i=0;i<l;i++)b[i]=mul(d[i],add(mul(b[i],b[i]),c[i])); ntt(&b[0],1,l); b.resize(n); clear(b); return b; } inline poly sqrt(const poly &a){return sqrt(a,a.size());} inline poly deri(poly a){ int n=a.size(); if(n==1)return poly(1,0); for(int i=0;i<n;i++)a[i]=mul(a[i+1],i+1); a.resize(n-1); return a; } inline poly inte(poly a){ int n=a.size(); a.resize(n+1); for(int i=n;i;i--)a[i]=mul(a[i-1],qpow(i,MOD-2)); a[0]=0; return a; } inline poly ln(const poly &a){ int n=a.size(); poly c=inv(a)*deri(a); c.resize(n-1); return inte(c); } inline poly exp(const poly &a,const int &n){ if(n==1)return poly(1,1); poly b=exp(a,n+1>>1),c; b.resize(n);c=ln(b); for(int i=0;i<n;i++)c[i]=sub(a[i],c[i]); inc(c[0]); b*=c; b.resize(n); return b; } inline poly exp(const poly &a){return exp(a,a.size());} inline poly qpow(poly a,const double &b){return exp(ln(a)*b);} poly a; int main(){ srand(19260817); pre(); scanf("%d%d",&n,&k); read(a,1+n); a=deri(qpow(1+ln(2+a-a[0]-exp(inte(inv(sqrt(a))))),k)); a.resize(n); out(a); return 0; } 珂朵莉树 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 //以防我忘了set迭代器怎么写 struct node { int l, r; mutable lint v; node(int L, int R = -1, lint V = 0) : l(L), r(R), v(V) {} bool operator < (const node &o) const { return l < o.l; } }; set <node> s; IT spilit (int pos) { IT it = s.lower_bound(node(pos)); if(it != s.end() && it->l == pos) return it; it--; int L = it -> l, R = it -> r; lint V = it->v; s.erase(it); s.insert(node(L, pos-1, V)); return s.insert(node(pos, R, V)).first; } void add(int l, int r, int val) { IT il = spilit(l), ir = spilit(r+1); for(; il != ir; il->v += val, il++); } void tp(int l, int r, int val = 0) { IT il = spilit(l), ir = spilit(r+1); s.erase(il, ir); s.insert(node(l, r, val)); }
Read More

线性代数与空间解析几何 女娲补天复习笔记

Shino Shino published on
矩阵及其初等变换 概念 同型矩阵：A与B都是m*n矩阵，则称A与B是同型矩阵。 负矩阵：A的每个元换成它的相反数，记为-A 数量矩阵：$kI，k∈R$ 反称矩阵：$A^T=-A$ Conclusions $(AB)T=BTA^T$ $(AB){-1}=B{-1}A^{-1}$ AB为对称矩阵$\iff AB=BA$ 行初等变换左乘初等矩阵，列初等变换右乘。 $(AT){-1}=(A^{-1})^T$ 行列式 Conclusions 若行列式某两行对应元成比例， 行列式为零。 $|A^{-1}|=\frac{1}{|A|}$ $|A^{\star}|=|A|^{n-1}$ 范德蒙德行列式结论：$\prod_{1≤j<i<n}(x_i-x_j)$ $A^{\star}A=|A|I$ A可逆$\iff R(A)=n \iff AX=0$只有零解$\iff AX=b$有唯一解 $R(A)=R(B) \iff $ A与B等价（A与B是同型矩阵） 几何空间 概念 自由向量：不考虑起点的向量 方向角：向量与坐标轴的夹角 方向余弦：方向角的余弦 平面束：经过直线$l$的全体平面称为过$l$的平面束 Conclusions $Prj_u(\vec{a}+\vec{b})=Prj_u\vec{a}+Prj_u\vec{b}$ $[\vec{a}\ \vec{b}\ \vec{c}]=0 \iff \vec{a}\ \vec{b}\ \vec{c}$共面 n维向量空间 概念 子空间：设$V$是$Rn$的一个非空子集合，则$V$是$Rn$的一个子空间的充分必要条件是$V$对于$R^n$的加法和数乘运算是封闭的。 所有向量$\vec{a_1}\ \vec{a_2}\ \vec{a_3}\ … \vec{a_n}$线性组合的集合用$L(\vec{a_1},\vec{a_2},…,\vec{a_n})$表示。 只含零向量的向量组的秩为0。 Conclusions $A=(\vec{a_1},\vec{a_2},…,\vec{a_n})$，则$\vec{a_1},\vec{a_2},…,\vec{a_n}$线性相关$\iff AX=0$有非零解$\iff R(A)<n\iff |A|=0$ $R(AB)≤min{R(A),R(B)}$ $R(A+B)≤R(A)+R(B)$ $max{R(A),R(B)}R[(A,B)]≤R(A)+R(B)$ $AX=0$的基础解系所含解向量个数为$n-R(A)$ $R(A)=n-1$则$R(A^{\star})=1$ 特征值与特征向量 概念 特征子空间：对于特征值$\lambda$的所有特征向量构成的子空间。 Conclusions $\lambda$是$A$的一个特征值，则$\frac{1}{\lambda}$是$A^{-1}$的一个特征值，特征向量相同。
Read More
0%