noip模板复习

自己敲模板还是有很多容易错的地方

写在注释里面了

LCA

#include<bits/stdc++.h>
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

const int N = 5e5 + ; //以后MAXN改成N。因为MAXM和MAXN不容易区分
const int M = ;
struct Edge{ int to, next; } e[N << ];
int head[N], tot, n, m, s;
int d[N], f[N][M + ]; //注意这里一定一定是M+10 

void AddEdge(int from, int to)
{
    e[tot] = Edge{to, head[from]};
    head[from] = tot++;
}

void dfs(int u, int fa) //dfs的作用是初始化f数组和d数组
{
    for(int i = head[u]; ~i; i = e[i].next)
    {
        int v = e[i].to;
        if(v == fa) continue;
        d[v] = d[u] + ;
        f[v][] = u;
        dfs(v, u);
    }
}

void init()
{
    f[s][] = s; //注意这里一定是自己的父亲为自己
    dfs(s, -);
    _for(j, , M) //注意这里是到M，不是N
        _for(i, , n)
            f[i][j] = f[f[i][j-]][j-];
}

int lca(int u, int v)
{
    if(d[u] < d[v]) swap(u, v); //u和v不要写反
    for(int j = M; j >= ; j--) //逆序
        if(d[f[u][j]] >= d[v]) //这里注意是深度的比较，u往上跳的深度和v本身的深度
            u = f[u][j];
    if(u == v) return u;
    for(int j = M; j >= ; j--)
        if(f[u][j] != f[v][j])
            u = f[u][j], v = f[v][j];
    return f[u][];
}

int main()
{
    memset(head, -, sizeof(head)); tot = ;
    scanf("%d%d%d", &n, &m, &s);
    REP(i, , n)
    {
        int u, v;
        scanf("%d%d", &u, &v);
        AddEdge(u, v); AddEdge(v, u);
    }

    init(); //主函数里面不要忘了写
    _for(i, , m)
    {
        int u, v;
        scanf("%d%d", &u, &v);
        printf("%d\n", lca(u, v));
    }

    return ;
}

线段树

#include<bits/stdc++.h>
#define ls (k << 1)
#define rs (k << 1 | 1)
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

typedef long long ll; //根据题目
const int N = 2e5 + ;
struct Segment_Tree
{
    int l, r;
    ll w, f;
    int m() { return (l + r) >> ; }
    int len() { return r - l + ; };
}t[N * ];
int n, q;

inline void deal(int k, ll p)
{
    t[k].f += p;
    t[k].w += p * t[k].len();
}

inline int up(int k)
{
    t[k].w = t[ls].w + t[rs].w;
}

inline void down(int k)
{
    deal(ls, t[k].f);
    deal(rs, t[k].f);
    t[k].f = ;
}

void build(int k, int l, int r)
{
    t[k] = Segment_Tree{l, r, , };
    if(l == r) { scanf("%lld", &t[k].w); return; }
    int m = t[k].m();
    build(ls, l, m);
    build(rs, m + , r);
    up(k);
}

void add(int k, int x, ll p)
{
    if(t[k].l == t[k].r) //注意这里一定是这么写，不能写t[k].l == x，这是错的
    {
        t[k].w += p;
        return;
    }
    if(t[k].f) down(k);
    int m = t[k].m();
    if(x <= m) add(ls, x, p);
    else add(rs, x, p);
    up(k);
}

void change(int k, int L, int R, ll p)
{
    if(L <= t[k].l && t[k].r <= R) { deal(k, p); return; }
    if(t[k].f) down(k);
    int m = t[k].m();
    if(L <= m) change(ls, L, R, p);
    if(R > m) change(rs, L, R, p);
    up(k);
}

ll query(int k, int L, int R)
{
    if(L <= t[k].l && t[k].r <= R) return t[k].w;
    if(t[k].f) down(k);
    int m = t[k].m(); ll res = ;
    if(L <= m) res += query(ls, L, R);
    if(R > m) res += query(rs, L, R);
    return res;
}

int main()
{
    scanf("%d", &n);
    build(, , n);
    scanf("%d", &q);
    while(q--)
    {
        int op, x, y; ll z;
        scanf("%d", &op);
        if(op == )
        {
            scanf("%d%d%lld", &x, &y, &z);
            change(, x, y, z);
        }
        else
        {
            scanf("%d%d", &x, &y);
            printf("%lld\n", query(, x, y));
        }
    }
    return ;
}

KMP

#include<bits/stdc++.h>
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

const int N = 1e6 + ;
char a[N], b[N];
int next[N], lena, lenb;

void get_next()
{
    next[] = ; int j = ; //注意这里从0开始。因为一开始匹配了0个
    _for(i, , lenb) //这里的i从2开始
    {
        while(j && b[j + ] != b[i]) j = next[j];
        if(b[j + ] == b[i]) j++;
        next[i] = j;
    }
} 

int main()
{
    scanf("%s%s", a + , b + );
    lena = strlen(a + ); lenb = strlen(b + );
    get_next();
    int j = ;
    _for(i, , lena) //这里的i从1开始
    {
        while(j && b[j + ] != a[i]) j = next[j];
        if(b[j + ] == a[i]) j++;
        if(j == lenb) { printf("%d %d\n", i - lenb + , i); return ; }
    }
    puts("NO");
    return ;
} 

同余方程

#include<bits/stdc++.h>
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

typedef long long ll;//如果考到数论题一定要开longlong！！！！！！！！
void exgcd(ll a, ll b, ll& d, ll& x, ll& y)
{
    if(!b) { d = a; x = ; y = ; return; }
    else { exgcd(b, a % b, d, y, x); y -= x * (a / b); }
} 

int main()
{
    ll a, b, m;
    scanf("%lld%lld%lld", &a, &b, &m);
    ll A, B, K, d, x, y;
    A = a, B = -m, K = b;
    exgcd(A, B, d, x, y);
    if(K % d) { puts("no solution!"); return ; }
    x *= K / d; int mod = abs(B / d);
    printf("%lld\n", (x % mod + mod) % mod);
    return ;
} 

同余方程组

#include<bits/stdc++.h>
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

typedef long long ll;
void exgcd(ll a, ll b, ll& d, ll& x, ll& y)
{
    if(!b) { d = a; x = ; y = ; return; }
    else { exgcd(b, a % b, d, y, x); y -= x * (a / b); }
} 

int main()
{
    int n;
    ll b1, b2, m1, m2;
    scanf("%d%lld%lld", &n, &b1, &m1);
    REP(i, , n)
    {
        scanf("%lld%lld", &b2, &m2);
        ll A, B, K, d, x, y;
        A = m1, B = -m2, K = b2 - b1; //推出什么写什么
        exgcd(A, B, d, x, y);
        if(K % d) { puts("no solution!"); return ; }

        x *= K / d; int mod = abs(B / d); //注意这里加abs
        x = (x % mod + mod) % mod;
        b1 = b1 + m1 * x;
        m1 = m1 * m2 / abs(d); //加abs
    }
    printf("%lld\n", b1);
    return ;
} 

欧拉函数

#include<bits/stdc++.h>
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

typedef long long ll;
ll euler(ll x)
{
    ll res = x; //注意区分res和x。x是用来取出因数的
    for(int i = ; i * i <= x; i++)
        if(x % i == )
        {
            res = res / i * (i - ); //先除后乘比较保险，可以这么做是因为i是res的因数
            while(x % i == ) x /= i;
        }
    if(x > ) res = res / x * (x - );
    return res;
}

int main()
{
    int n;
    scanf("%d", &n);
    _for(i, , n)
    {
        ll x; scanf("%lld", &x);
        printf("%lld\n", euler(x));
     }
    return ;
} 

//线性求法
const int N = 1e6 + ;
int euler[N];
void get_euler()
{
    REP(i, , N) euler[i] = i;
    REP(i, , N) //注意这里i从2开始。
        if(euler[i] == i)
            for(int j = i; j < N; j += i)
                euler[j] = euler[j] / i * (i - );
} 

线性筛素数

#include<bits/stdc++.h>
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

const int N = 2e7 + ;
bool is_prime[N];
vector<int> prime;

void get_prime()
{
    memset(is_prime, true, sizeof(is_prime));
    is_prime[] = is_prime[] = false;
    REP(i, , N) //切记不能越界
    {
        if(is_prime[i]) prime.push_back(i);
        REP(j, , prime.size())
        {
            if(i * prime[j] >= N) break; //切记不能越界
            is_prime[i * prime[j]] = false;
            if(i % prime[j] == ) break;
        }
    }
} 

int main()
{
    get_prime();
    int n;
    scanf("%d", &n);
    _for(i, , n)
    {
        int x; scanf("%d", &x);
        printf("%d\n", prime[x-]);
     }
    return ;
} 

组合数

const int N = 1e3 + ;
int c[N][N];
void init()
{
    REP(i, , N) //从0开始
    {
        c[i][] = ;
        _for(j, , i)
            c[i][j] = c[i-][j] + c[i-][j-];
    }
}

卡特兰数

f[] = ;
REP(i, , N) f[i] = f[i-] * ( * i - ) / (i + );