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并没有力气写完了T_T
【数学】
- 快速幂/快速乘
int Pow(int a, int b, int Mod){ int temp = 1, cmp = a; while (b) { if (b & 1) temp = temp * cmp % Mod; b >>= 1; cmp = cmp * cmp % Mod; } return temp;}int Mul(int a, int b, int Mod){ int temp = 1, cmp = a; while (b) { if (b & 1) temp = (temp + cmp) % Mod; b >>= 1; cmp = (cmp + cmp) % Mod; } return temp;}- 矩阵快速幂
struct Mart { int C[MartMax][MartMax]; int Mod; Mart operator * (const Mart &b) const { Mart ans; for (int i = 1; i <= MartMax; ++ i) for (int j = 1; j <= MartMax; ++ j) { unsigned long long temp = 0llu; for (int k = 1; k <= MartMax; ++ k) temp += C[i][k] * b.C[k][j]; ans.C[i][j] = temp % Mod; } return ans; }}E;Mart MartPow(Mart A, int b){ for (int i = 1; i <= MartMax; ++ i) E.C[i][i] = 1; while (b) { if (b & 1) E = E * A; b >>= 1; A = A * A; } return E;}- GCD
int gcd(int a, int b){ if (!a || !b) return a + b; for (int t = a % b; b; a = b, b = t, t = a % b); return b;}- 扩展欧几里得
void Ex_gcd(int a, int b, int &x, int &y){if (!b) { x = 1, y = 0; return; }Ex_gcd(b, a % b, y, x); y -= a / b * x;}
- 线性筛欧拉函数
void get_phi(){ phi[1] = 1; for (int i = 2; i <= N; ++ i) { if (!Mark[i]) { prime[++ tot] = i; phi[i] = i - 1; } for (int j = 1; j <= tot && i * prime[j] <= N; ++ j) { Mark[i * prime[j]] = 1; if (i % prime[j] == 0) { phi[i * prime[j]] = phi[i] * prime[j]; break; } else phi[i * prime[j]] = phi[i] * phi[prime[j]]; } }}- 高斯消元
typedef double Matrix[Nmax][Nmax];void Gauss(Matrix A, int N){ for (int i = 0; i < N; ++ i) { int r = i; for (int j = i + 1; j < N; ++ j) if (fabs(A[j][i]) > fabs(A[r][i])) r = j; if (r ^ i) for (int j = 0; j <= N; ++ j) swap(A[r][j], A[i][j]); for (int k = i + 1; k < N; ++ k) { double f = A[k][i] / A[i][i]; for (int j = i; j <= N; ++ j) A[k][j] -= f * A[i][j]; } for (int i = N - 1; ~i; -- i) { for (int j = i + 1; j < N; ++ j) A[i][N] -= A[j][N] * A[i][j]; A[i][N] /= A[i][i]; } 【图论】
- SPFA
int dis[Nmax];bool vis[Nmax];queue <int> q;int spfa(int S, int T){ memset(dis, 0x3f, sizeof(dis)); q.push(S); dis[S] = 0; while (q.size()) { int u = q.front(); q.pop(); vis[u] = 0; for (int i = head[u]; i; i = e[i].next) { int v = e[i].v; if (dis[v] > dis[u] + e[i].w) { dis[v] = dis[u] + e[i].w; if (!vis[v]) { vis[v] = 1; q.push(v); } } } } return dis[T];}- Dijkstra
typedef pair<int, int> node;priority_queue < node, vector<node>, greater<node> > q;int dis[Nmax];int dijkstra(int S, int T){ memset(dis, 0x3f, sizeof(dis)); q.push(node(0, S)); while (q.size()) { node temp = q.top(); q.pop(); int u = temp.second; if (temp.first != dis[u]) continue; for (int i = head[u]; i; i = e[i].next) { int v = e[i].v; if (dis[v] > dis[u] + e[i].w) { dis[v] = dis[u] + e[i].w; q.push(node(dis[v], v)); } } } return dis[T];}
- Floyd最小环
int map[Nmax][Nmax], dis[Nmax][Nmax];int floyd(){int MinCircle = inf;for (int k = 1; k <= N; ++ k) {for (int i = 1; i <= N; ++ i)for (int j = 1; j <= N; ++ j)MinCircle = min(MinCircle, dis[i][j] + map[i][k] + map[k][j]);for (int i = 1; i <= N; ++ i)for (int j = 1; j <= N; ++ j)dis[i][j] = min(dis[i][k] + dis[k][j]);}return MinCircle;}
- Kruskal
int f[Nmax];int find(int x) { return (x == f[x]) ? x : f[x] = find(f[x]); }bool cmp(ed &a, ed &b) { return a.w < b.w; }int kruskal(int N, int M){ for (int i = 1; i <= N; ++i) f[i] = i; sort(e + 1, e + M + 1, cmp); int ans = 0; for (int i = 1; i <= M; ++i) { int u = e[i].u, v = e[i].v; int fu = find(u), fv = find(v); if (fu == fv) continue; f[fu] = fv; ans += e[i].w; } return ans;}- Prim
int dis[Nmax], map[Nmax][Nmax], N;bool vis[Nmax];int prim(){ int sum = 0; for (int i = 1; i <= N; ++ i) dis[i] = map[1][i]; vis[1] = 1; for (int i = 1; i < N; ++ i) { int pos = -1, mmin = inf; for (int j = 1; j <= N; ++ i) { if (!vis[j] && dis[j] < mmin){ pos = j; mmin = dis[j]; } } if (pos == -1) break; vis[pos] = 1; sum += dis[pos]; for (int j = 1; j <= N; ++ i) dis[j] = map[pos][j]; } return sum;}- LCA
int dep[Nmax], d[Nmax];int f[Nmax][20];void dfs(int u, int fa, int w){ dep[u] = dep[fa] + 1, d[u] = d[fa] + w; f[u][0] = fa; for (int i = 1; (1 << i) <= dep[u]; ++ i) f[u][i] = f[f[u][i - 1]][i - 1]; for (int i = head[u]; i; i = e[i].next) { int v = e[i].v; if (v != fa) dfs(v, u, e[i].w); }}int LCA(int u, int v){ if (dep[u] < dep[v]) swap(u, v); int k = dep[u] - dep[v]; for (int i = 1; (1 << i) <= dep[u]; ++ i) if (k & (1 << i)) u = f[u][i]; if (u == v) return u; else for (int i = 19; ~i; -- i) if (f[u][i] != f[v][i]) { u = f[u][i]; v = f[v][i]; } return f[u][0];}- Tarjan强联通
int dfn[Nmax], low[Nmax];int belong[Nmax];int tot, scnt;stack <int> s;bool ins[Nmax];void dfs(int u){ dfn[u] = low[u] = ++ tot; s.push(u); ins[u] = 1; for (int i = head[u]; i; i = e[i].next) { int v = e[i].v; if (!dfn[v]) { dfs(v); low[u] = min(low[v], low[u]); } else if (ins[v]) low[u] = min(low[v], low[u]); } if (low[u] == dfn[u]) { ++ scnt; for ( ; ; ) { int v = s.top(); s.pop(); belong[v] = scnt; if (v == u) break; } }}- 匈牙利算法
int map[Nmax][Nmax];int cx, cy;int match[Nmax];bool Vis[Nmax];bool Match(int u){ for (int v = 1; v < cy; ++v) { if (!map[u][v] || Vis[v]) continue; Vis[v] = 1; if (match[v] == -1 || Match(match[v])) { match[v] = u; return 1; } } return 0;}int Hurngray(){ memset(match, -1, sizeof(match)); int res = 0; for (int i = 1; i <= cx; ++i) { memset(vis, 0, sizeof(vis)); res += Match(i); } return res;}- KM
int N;int w[Nmax][Nmax];int lx[Nmax], ly[Nmax], match[Nmax], slack[Nmax];bool visx[Nmax], visy[Nmax];bool dfs(int u){ visx[u] = 1; for (int v = 1; v <= N; ++ v) if(!visy[v]){ int t = lx[u] + ly[v] - w[u][v]; if (!t) { visy[v] = 1; if (match[v] == -1 || dfs(match[v])) { match[v] = u; return 1; } else if (slack[v] > t) slack[v] = t; } } return 0;}void adjust(){ int d = inf; for (int i = 1; i <= N; ++ i) if (!visy[i] && slack[i] < d) d = slack[i]; for (int i = 1; i <= N; ++ i) if (visx[i]) lx[i] -= d; for (int i = 1; i <= N; ++ i) if (visy[i]) ly[i] += d; else slack[i] -= d;}int KM(){ memset(match, -1, sizeof(match)); memset(ly, 0, sizeof(ly)); for (int i = 1; i <= N; ++ i) { lx[i] = -inf; for (int j = 1; j <= N; ++ j) if (w[i][j] > lx[i]) lx[i] = w[i][j]; } for (int i = 1; i <= N; ++ i) { for (int j = 1; j <= N; ++ j) slack[j] = inf; for ( ; ; ) { memset(visx, 0, sizeof(visx)); memset(visy, 0, sizeof(visy)); if (dfs(i)) break; else adjust(); } } int ans = 0; for (int i = 1; i <= N; ++ i) ans += w[match[i]][i]; return ans;}- Dinic
int S, T;queue <int> q;int dis[Nmax];bool bfs(){ memcpy(cur, head, sizeof(cur)); memset(dis, -1, sizeof(dis)); while (q.size()) q.pop(); q.push(S); dis[S] = 0; while (q.size()) { int u = q.front(); q.pop(); for (int i = head[u]; i; i = e[i].next) { int v = e[i].v; if (e[i].flow && dis[v] == -1) { dis[v] = dis[u] + 1; if (v == T) return 1; q.push(v); } } } return 0;}int dfs(int u, int maxf){ if (u == T || !maxf) return maxf; int flow = 0, f; for (int &i = cur[u]; i; i = e[i].next) { int v = e[i].v; if (dis[v] == dis[u] + 1 && (f = dfs(v, min(maxf, e[i].w))) > 0) { e[i].flow -= f; e[i ^ 1].flow -= f; flow += f; maxf -= f; if (!maxf) break; } } return flow;}int max_flow(){ int f = 0; while (bfs()) f += dfs(S, inf); return f;}- 费用流 （SPFA没力气写了 TAT）
int MinCostMaxFlow(){ int cost = 0; while (spfa()) { for (int i = T; i != S; i = e[pre[i] ^ 1].v) { e[pre[i]].flow -= deltaf; e[pre[i] ^ 1].flow += deltaf; } cost += deltaf * dis[T]; }}【数据结构】
- 树状数组
#define lowbit(x) (x & -x)namespace BIT { int sum[Nmax][2]; inline void Add(bool s, int pos, int c) { for (int i = pos; i <= N; i += lowbit(i)) sum[i][s] += c; } inline int Sum(bool s, int pos) { int res = 0; for (int i = pos; i; i -= lowbit(i)) res += sum[i][s]; return res; } inline void Modify(int l, int r, int c) { Add(0, l, c); Add(1, l, l * c); Add(0, r + 1, -c); Add(1, r + 1, -(r + 1) * c); } inline int Query(int l, int r) { int temp = (r + 1) * Sum(0, r) - Sum(1, r); temp -= l * Sum(0, l - 1) - Sum(1, l - 1); return temp; }}namespace Splay { struct node { node *c[2], *f; int w, size, mmin; int add, rev; inline bool right() { return f -> c[1] == this; } inline void setch(node *p, bool r) { c[r] = p; p -> f = this; } }; void build(node *p, int l, int r, int rank) { p -> w = p -> mmin = a[rank]; if (l ^ rank) { node *lch = NewNode(); p -> setch(lch, 0); build(lch, l, rank - 1, (l + rank - 1) << 1); } if (r ^ rank) { node *rch = NewNode(); p -> setch(rch, 1); build(rch, rank + 1, r, (rank + 1 + r) << 1); } pushup(p); } void rotate(node *p) { node *fa = p -> f; bool r = p -> right(); fa -> f -> setch(p, f -> right()); fa -> setch(p -> c[r ^ 1], r); p -> setch(fa, r ^ 1); pushup(fa); } void splay(node *p, node *father) { while (p -> f != father) { if (p -> f -> f == father) rotate(p); else { rotate(p -> right() == p -> f -> right() ? p -> fa : p); rotate(p); } } pushup(p); if (p -> f == null) root = p; } node *find(int rank) { for (node *p = root; ; ) { pushdown(p); int ls = p -> lc -> s; if (rank <= ls) p = p -> lc; else if (rank + 1 == ls) return p; else { rank -= ls + 1; p = p -> rc; } } } node *getrange(int l, int r) { -- l, ++ r; splay(find(l), null); splay(find(r), root); return root -> rc -> lc; } }【字符串】
- KMP
int next[Nmax];void KMP(char *str){ next[0] = next[1] = 0; int j = 0; for (int i = 2; str[i]; ++ i) { while (j && s[i] != s[j + 1]) j = next[j]; if (s[i] == s[j + 1]) ++ j; next[i] = j; }}- Manacher
int far = 0, ans = 0; for (int i = 1; s[i]; ++i) { int already = p[far] + far; p[i] = already > i ? min(already - i, p[(far << 1) - i]) : 1; while (s[i - p[i]] == s[i + p[i]]) ++p[i]; if (i + p[i] >= already) far = i; ans = max(ans, p[i] - 1); } - 扩展KMP
inline void e_kmp() { int j = 0, last = 1; for(; j < len && s[j] == s[j + 1]; ++j); p[0] = len; p[1] = j; for(int i = 2; i < len; ++i) { int itmax = p[i - last], already = max(0, last + p[last] - i); if(itmax < already) p[i] = itmax; else { p[i] = already; last = i; while(i + p[i] < len && s[i + p[i]] == s[p[i]]) ++p[i]; } } } 0 0
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