[备份]算法模板大集锦

一、介绍

这是一篇赶工赶出来并且随时会更新的备份文章，里面汇集了我曾学过的所有高级（也就是太长了我记不住）算法的模板。大部分直接从以前的文章里蒯过来，所以对于任意一份模板，都说不定将来再次翻阅的时候忍受不了当时的格式/命名/写法等等而进行修改。

二、目录

1、网络流Dinic算法

2、Tarjan算法

3、倍增LCA

4、AC自动机

5、主席树

6、BKDRHash

三、正文

1、网络流Dinic算法

#include <cstdio>
#include <cstring>

#define MAXN 205
#define MAXM 205
#define INF 0x3f3f3f3f

int m, n, u, v, f, q[MAXN * MAXN], h[MAXN], d[MAXN], o = 1, ans;

struct Edge {
    int v, next, f;
} e[MAXM << 1];

int min(int a, int b) {
    return a < b ? a : b;
}

void add(int u, int v, int f) {
    o++, e[o] = (Edge) {v, h[u], f}, h[u] = o;
}

bool BFS() {
    int head = 1, tail = 2;
    q[1] = 1, d[1] = 1;
    while (head != tail) {
        int o = q[head];
        for (int x = h[o]; x; x = e[x].next) {
            int v = e[x].v;
            if (!d[v] && e[x].f > 0) d[v] = d[o] + 1, q[tail++] = v;
        }
        head++;
    }
    return d[n] != 0;
}

int DFS(int o, int mif) {
    int res = 0;
    if (mif <= 0 || o == n) return mif;
    for (int x = h[o]; x; x = e[x].next) {
        int v = e[x].v;
        if (d[v] == d[o] + 1) {
            int of = DFS(v, min(mif, e[x].f));
            e[x].f -= of, e[x ^ 1].f += of, mif -= of, res += of;
            if (!mif) break;
        }
    }
    return res;
}

int main() {
    scanf("%d %d", &m, &n);
    for (int i = 1; i <= m; i++) scanf("%d %d %d", &u, &v, &f), add(u, v, f), add(v, u, 0);
    while (BFS()) ans += DFS(1, INF), memset(d, 0, sizeof(d)); 
    printf("%d", ans);
    return 0;
}

2、Tarjan算法

#include <cstdio>

#define MAXN 500005
#define MAXM 500005

int n, m, u[MAXN], v[MAXN], tw[MAXN], ts, p, to, tb[MAXN], th[MAXN];
int w[MAXN], b[MAXN], s, h[MAXN], o, lik[MAXN];
int dfn[MAXN], low[MAXN], ins[MAXN], st[MAXN], tot, t, tim;
int f[MAXN], ans;

struct Edge {
    int v, next;
} e[MAXM], te[MAXM];

int min(int a, int b) {
    return a < b ? a : b; 
}

int max(int a, int b) {
    return a > b ? a : b; 
}

void add(int u, int v, int t) {
    if (t) to++, te[to] = (Edge) {v, th[u]}, th[u] = to;
    else o++, e[o] = (Edge) {v, h[u]}, h[u] = o;
}

void init() {
    scanf("%d %d", &n, &m);
    for (int i = 1; i <= m; i++) scanf("%d %d", &u[i], &v[i]), add(u[i], v[i], 1);
    for (int i = 1; i <= n; i++) scanf("%d", &tw[i]);
    scanf("%d %d", &ts, &p);
    for (int i = 1; i <= p; i++) scanf("%d", &o), tb[o] = 1;
}

void tarjan(int o) {
    dfn[o] = low[o] = ++tim, ins[o] = 1, st[++t] = o;
    for (int x = th[o]; x; x = te[x].next) {
        int v = te[x].v;
        if (!dfn[v]) tarjan(v), low[o] = min(low[v], low[o]);
        else if (ins[v] && dfn[v] < low[o]) low[o] = dfn[v];
    }
    if (dfn[o] == low[o]) {
        int x; tot++;
        do x = st[t--], ins[x] = 0, lik[x] = tot; while (x != o); 
    }
}

void rebuild() {
    for (int i = 1; i <= m; i++) if (lik[u[i]] != lik[v[i]]) add(lik[u[i]], lik[v[i]], 0);
    for (int i = 1; i <= n; i++) {
        w[lik[i]] += tw[i]; 
        if (i == ts) s = lik[i];
        if (tb[i]) b[lik[i]] = 1;
    }
    f[s] = w[s];
}

void DFS(int o) {
    if (b[o]) ans = max(ans, f[o]);
    for (int x = h[o]; x; x = e[x].next) {
        int v = e[x].v;
        if (f[o] + w[v] > f[v]) f[v] = f[o] + w[v], DFS(v);
    }
}

int main() {
    init();
    for (int i = 1; i <= n; i++) if (!dfn[i]) tarjan(i);
    rebuild();
    DFS(s); 
    printf("%d", ans);
    return 0;
}

3、倍增LCA

void prep() {
    for (int i = 1; i <= n; i++) p[i][0] = fa[i];
    for (int j = 1; (1 << j) <= n; j++)
        for (int i = 1; i <= n; i++) 
            if (p[i][j - 1]) p[i][j] = p[p[i][j - 1]][j - 1];
}

int lca_h() {
    if (d[x] < d[y]) swap(x, y);
    while (d[x] != d[y]) {
        int o = 1;
        while (d[p[x][o]] > d[y]) o++;
        x = p[x][o - 1];
    }
    while (x != y) {
        int o = 1;
        while (p[x][o] != p[y][o]) o++; 
        x = p[x][o - 1], y = p[y][o - 1];
    }
    return x;
}

4、AC自动机

#include <cstdio>
#include <cstring>

#define MAXM 1000005

int T, n, tot, q[MAXM], ls, l, r;
char s[55], ch[MAXM];

struct Tree {
    int a[26], x, f;
} t[MAXM];

void insert() {
    int o = r;
    for (int i = 0; i < ls; i++) {
        int x = s[i] - 'a';
        if (!t[o].a[x]) t[o].a[x] = ++tot;
        o = t[o].a[x];
    }
    t[o].x++;
}

void getf() {
    int head = 1, tail = 2;
    q[1] = r;
    while (head != tail) {
        int o = q[head];
        for (int i = 0; i <= 25; i++) {
            int v = t[o].a[i];
            if (!v) continue;
            if (o == r) t[v].f = r;
            else {
                int of = t[o].f;
                while (of) {
                    if (t[of].a[i]) {
                        t[v].f = t[of].a[i];
                        break;
                    }
                    of = t[of].f;
                }
                if (!of) t[v].f = r;
            }
            q[tail++] = v; 
        }
        head++;
    }
}

int find() {
    int ans = 0, x = r;
    for (int i = 0; i < l; i++) {
        int o = ch[i] - 'a';
        while (!t[x].a[o] && x != r) x = t[x].f;
        x = t[x].a[o] ? t[x].a[o] : r;
        int y = x;
        while (t[y].x) ans += t[y].x, t[y].x = 0, y = t[y].f;
    }
    return ans;
}

int main() {
    scanf("%d", &T);
    for (int i = 1; i <= T; i++) {
        scanf("%d", &n), r = ++tot;
        for (int j = 1; j <= n; j++) scanf("%s", s), ls = strlen(s), insert();
        getf();
        for (int j = r + 1; j <= tot; j++) if (!t[j].f) t[j].f = r;
        scanf("%s", ch), l = strlen(ch);
        printf("%d
", find());
    }
    return 0;
}

5、主席树

#include <cstdio>
#include <algorithm>
using namespace std;

#define MAXN 100005

int T, n, m, l, r, k, tot, root[MAXN], b[MAXN], lik[MAXN];

struct num {
    int w, n, r;
} a[MAXN];

struct cmpw {
    bool operator () (num a, num b) {
        return a.w < b.w;
    }
} cw;

struct cmpn {
    bool operator () (num a, num b) {
        return a.n < b.n;
    }
} cn;

struct Tree {
    int l, r, w;
} t[MAXN * 20];

void chg() {
    sort(a + 1, a + n + 1, cw);
    for (int i = 1; i <= n; i++) a[i].r = i;
    sort(a + 1, a + n + 1, cn);
    for (int i = 1; i <= n; i++) b[i] = a[i].r, lik[b[i]] = a[i].w;
}

void build(int o, int l, int r, int w, int x) {
    t[o] = t[x], t[o].w++;
    if (l == r) return;
    int m = (l + r) >> 1;
    if (w <= m) build(t[o].l = ++tot, l, m, w, t[x].l);
    else build(t[o].r = ++tot, m + 1, r, w, t[x].r);
}

int query(int rl, int rr, int l, int r, int k) {
    if (l == r) return l;
    int w = t[t[rr].l].w - t[t[rl].l].w, m = (l + r) >> 1;
    return w >= k ? query(t[rl].l, t[rr].l, l, m, k) : query(t[rl].r, t[rr].r, m + 1, r, k - w);
}

int main() {
    scanf("%d", &T);
    for (int j = 1; j <= T; j++) {
        root[0] = 0, tot = 0;
        scanf("%d %d", &n, &m);
        for (int i = 1; i <= n; i++) scanf("%d", &a[i].w), a[i].n = i;
        chg();
        for (int i = 1; i <= n; i++) 
            build(root[i] = ++tot, 1, n, b[i], root[i - 1]);
        for (int i = 1; i <= m; i++) {
            scanf("%d %d %d", &l, &r, &k);
            printf("%d
", lik[query(root[l - 1], root[r], 1, n, k)]);
        }
    }
    return 0; 
}

6、BKDRHash

#define x 131
#define MOD 1000000007
int h[MAXN]; char a[MAXN];
void getHash() {
　　int len = strlen(a);
　　for (int i = 0; i <= len - 1; i++) h[i] = (h[i - 1] * x + a[i]) % MOD;
}