2017 国庆湖南 Day1

Posted 2020-10-11 日拱一卒 功不唐捐

卡特兰数

#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;

int f[1001];

int main()
{
    freopen("stack.in","r",stdin);
    freopen("stack.out","w",stdout);
    int n;
    scanf("%d",&n);
    f[0]=1; f[1]=1;
    for(int i=2;i<=n;i++)
        for(int j=1;j<=i;j++)
            f[i]=(f[i]+f[j-1]*f[i-j])%7;
    printf("%d",f[n]);
}

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没看到取模的高精

#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;

struct node
{
    int len,a[1001];
    
    node()
    {
        len=0;
        memset(a,0,sizeof(a));
    }
    
    void operator = (int k)
    {
        a[1]=k; len=1;
    }
    
    void operator = (node b) 
    {
        len=b.len;
        for(int i=1;i<=len;i++) a[i]=b.a[i];
    }
    
    node operator * (int b)
    {
        node tmp;
        for(int i=1;i<=len;i++) tmp.a[i]=a[i]*b;
        for(int i=1;i<=len;i++) tmp.a[i+1]+=tmp.a[i]/10,tmp.a[i]%=10;
        tmp.len=tmp.a[len+1] ? len+1 : len;
        while(tmp.a[tmp.len]>=10) tmp.a[++tmp.len]=tmp.a[tmp.len-1]/10,tmp.a[tmp.len-1]%=10;
        return tmp;
    }  
    
    node operator / (int b)
    {
        node tmp,an;
        for(int i=len,j=1;i;i--,j++)  tmp.a[j]=a[i];
        int x=0;
        for(int i=1;i<=len;i++)
        {
            x=x*10+tmp.a[i];
            if(x>=b)
            {
                an.a[i]=x/b;
                x-=an.a[i]*b;
            }
        }
        int L=0;
        for(int i=1;i<=len;i++)
            if(an.a[i])
            {
                for(int j=len,k=1;j>=i;j--,L++,k++) tmp.a[k]=an.a[j]; 
                break;
            }
        tmp.len=L;
        return tmp;
    }
    
    void print()
    {
        for(int i=len;i;i--) printf("%d",a[i]);
    }
    
}f[1001];

int main()
{
    int n;
    scanf("%d",&n);
    f[0]=1; f[1]=1;
    for(int i=2;i<=n;i++) f[i]=f[i-1]*(4*i-2)/(i+1);
    f[n].print();
}

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加权并查集

#include<cstdio>

using namespace std;

#define N 30001

int fa[N],under[N],siz[N];

int find(int i)
{
    if(i!=fa[i])
    {
        int f=find(fa[i]);
        under[i]+=under[fa[i]];
        return fa[i]=f;
    }
    return i;
}

void unionn(int x,int y)
{
    int X=find(x),Y=find(y);
    under[X]+=siz[Y];
    siz[Y]+=siz[X];
    fa[X]=Y;
}

int main()
{
    freopen("cube.in","r",stdin);
    freopen("cube.out","w",stdout);
    int n,m;
    scanf("%d",&n); m=n;
    for(int i=1;i<=n;i++) fa[i]=i,siz[i]=1;
    char s[3]; int x,y;
    while(m--)
    {
        scanf("%s",s);
        if(s[0]==\'M\')
        {
            scanf("%d%d",&x,&y);
            unionn(x,y);
        }
        else 
        {
            scanf("%d",&x);
            find(x);
            printf("%d\\n",under[x]);
        }
    }
}

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区间DP

 

#include <cstdio>
#include <algorithm>
#include <iostream>
#include <cstring>

using namespace std;

const int N = 200 + 5;

int dp[N][N];
int n; 
char s[N];
int num[N], col[N], tot;

int main() {
    freopen("zuma.in", "r", stdin);
    freopen("zuma.out", "w", stdout);

    scanf("%s", s + 1);
    n = strlen(s + 1);
    int now = s[1] - \'0\', cnt = 1;
    for (int i = 2; i <= n; i ++) 
    {
        if (s[i] - \'0\' == now) 
        {
            cnt ++;
        } 
        else
         {
            num[++ tot] = cnt;
            col[tot] = now;
            cnt = 1;
            now = s[i] - \'0\';
        }
    }
    num[++ tot] = cnt;
    col[tot] = now;
    
    for (int i = 1; i <= tot; i ++) dp[i][i] = 3 - num[i];
    
    for (int len = 2; len <= tot; len ++) 
    {
        for (int i = 1, j = i + len - 1; j <= tot; i ++, j ++) 
        {
            dp[i][j] = 10000;
            if (col[i] == col[j]) 
            {
                dp[i][j] = min(dp[i][j], dp[i + 1][j - 1] + (num[i] + num[j] < 3 ? 1 : 0));
                for (int k = i + 1; k < j; k ++) 
                    if (col[k] == col[i]) dp[i][j] = min(dp[i][j], dp[i + 1][k - 1] + dp[k + 1][j - 1]);
            }
            for (int k = i; k < j; k ++)    dp[i][j] = min(dp[i][j], dp[i][k] + dp[k + 1][j]);
        }
    }
    printf("%d\\n", dp[1][tot]);
    return 0;
}

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75分大爆搜

#include<cstdio>
#include<cstring>

#define N 201

using namespace std;

int n,len;

int l,r,tot;

char s[N];
int col[N];

int ans=1000001;

void find(int x)
{
    l=x-1; r=x+1; tot=0;
    if(col[x]!=-1) tot++;
    while(col[x]==-1 && x>1) x--;
    if(x && col[x]!=-1)
    {
        while(col[l]==col[x] || col[l]==-1)
        {
            if(!l) break;
            if(col[l]==col[x]) tot++;
            l--;
            if(!l) break;
        }
    }
    if(col[x]==-1 || !x)
        while(col[x]==-1 && x<len) x++;
    while(col[r]==col[x] || col[r]==-1)
    {
        if(r==len+1) break;
        if(col[r]==col[x]) tot++;
        r++;
        if(r==len+1) break;
    }
}

void dfs(int sum,int last)
{
    if(sum>=ans) return;
    if(sum>len*3) return;
    if(!n) { ans=sum; return; }
    int m[N]; bool f; int tmp=n;
    for(int i=1;i<=len;i++) m[i]=col[i];
    for(int i=last;i<=len;i++)
        if(col[i]!=-1)
        {
            f=false;
            find(i);
            if(tot>=2) f=true;
            n-=tot;
            for(int j=l+1;j<i;j++) col[j]=-1;
            for(int j=r-1;j>=i;j--) col[j]=-1;
            while(n)
            {
                find(i);
                if(tot>=3)
                {
                    n-=tot;
                    for(int j=l+1;j<i;j++) col[j]=-1;
                    for(int j=r-1;j>=i;j--) col[j]=-1;
                }
                else break;
            }
            if(f) dfs(sum+1,i+1);
            else dfs(sum+2,i+1);
            n=tmp;
            for(int j=1;j<=len;j++) col[j]=m[j];
        }
}

int main()
{
    freopen("zuma.in","r",stdin);
    freopen("zuma.out","w",stdout);
    scanf("%s",s+1);
    len=strlen(s+1); n=len;
    for(int i=1;i<=len;i++) col[i]=s[i]==\'1\';
    dfs(0,1);
    printf("%d",ans);
}

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