UVA 12333 大数，字典树

Posted 2020-09-29 树的种子

题意：给一个数字，看他最小是第几个菲波那切数列的前缀。

分析：

大数模板就是吊哦。

将菲波那切数列前500个数字放到字典树上。注意插入的时候不能像普通一样，只在尾节点处标记，而是一路标记下去。

#include <bits/stdc++.h>

using namespace std;

const int NV = 10000;
const int ra = 10;
int ten[4] = {1,ra,ra*ra,ra*ra*ra};
int radix = ra*ra*ra*ra;

struct integer
{
    int d[NV];
    integer()
    {
        *this=integer(0);
    }
    integer(int x)
    {
        for (int i=0; i<NV; i++) d[i]=0;
        if (!x) d[0]=1;
        while(x)
        {
            d[++d[0]]=x%radix;
            x/=radix;
        }
    }
    integer(long long x)
    {
        for (int i=0; i<NV; i++) d[i]=0;
        if (!x) d[0]=1;
        while(x)
        {
            d[++d[0]]=x%radix;
            x/=radix;
        }
    }
    integer(const char s[])
    {
        int len=strlen(s),i,j,k;
        d[0]=(len-1)/4+1;
        for (i=1; i<NV; i++) d[i]=0;
        for (i=len-1; i>=0; i--)
        {
            j=(len-i-1)/4+1;
            k=(len-i-1)%4;
            d[j]+=ten[k]*(s[i]-‘0‘);
        }
        while(d[0]>1&&d[d[0]]==0) d[0]--;
    }

    string tostring()
    {
        string s;
        int i,j,temp;
        for (i=3; i>=1; i--) if (d[d[0]]>=ten[i]) break;
        temp=d[d[0]];
        int cnt=0;
        for (j=i; j>=0; j--)
        {
            s+=(char) (temp/ten[j]+‘0‘);
            if(cnt++>41)return s;
            temp%=ten[j];
        }
        for (i=d[0]-1; i>0; i--)
        {
            temp=d[i];
            for (j=3; j>=0; j--)
            {
                s+=(char) (temp/ten[j]+‘0‘);
                if(cnt++>41)return s;
                temp%=ten[j];
            }
        }
        return s;
    }

    void output()
    {
        int k=d[0];
        printf("%d",d[k--]);
        while(k) printf("%04d",d[k--]);
        putchar(‘\n‘);
    }
} d,mid1[15];

bool operator <(const integer &a,const integer &b)
{
    if (a.d[0]!=b.d[0]) return a.d[0]<b.d[0];
    for (int i=a.d[0]; i>0; i--)
        if (a.d[i]!=b.d[i])
            return a.d[i]<b.d[i];
    return 0;
}

integer operator +(const integer &a,const integer &b)
{
    integer c;
    c.d[0]=max(a.d[0],b.d[0]);
    int i,x=0;
    for (i=1; i<=c.d[0]; i++)
    {
        x+=a.d[i]+b.d[i];
        c.d[i]=x%radix;
        x/=radix;
    }
    while(x)
    {
        c.d[++c.d[0]]=x%radix;
        x/=radix;
    }
    return c;
}
integer operator -(const integer &a,const integer &b)
{
    integer c;
    c.d[0]=a.d[0];
    int i,x=0;
    for (i=1; i<=c.d[0]; i++)
    {
        x+=radix+a.d[i]-b.d[i];
        c.d[i]=x%radix;
        x=x/radix-1;
    }
    while(c.d[0]>1&&c.d[c.d[0]]==0) c.d[0]--;
    return c;
}
integer operator *(const integer &a,const integer &b)
{
    integer c;
    c.d[0]=a.d[0]+b.d[0];
    int i,j,x=0;
    for (i=1; i<=a.d[0]; i++)
    {
        x=0;
        for (j=1; j<=b.d[0]; j++)
        {
            x=a.d[i]*b.d[j]+x+c.d[i+j-1];
            c.d[i+j-1]=x%radix;
            x/=radix;
        }
        c.d[i+b.d[0]]=x;
    }
    while(c.d[0]>1&&c.d[c.d[0]]==0) c.d[0]--;
    return c;
}

integer operator *(const integer &a,const long long &k)
{
    integer c;
    c.d[0]=a.d[0];
    int i;
    long long x=0;
    for (i=1; i<=a.d[0]; i++)
    {
        x+=a.d[i]*k;
        c.d[i]=x%radix;
        x/=radix;
    }
    while(x>0)
    {
        c.d[++c.d[0]]=x%radix;
        x/=radix;
    }
    while(c.d[0]>1&&c.d[c.d[0]]==0) c.d[0]--;
    return c;
}
long long rem;
integer operator /(const integer &a,const long long &k)
{
    integer c;
    c.d[0]=a.d[0];
    long long x=0;
    for (int i=a.d[0]; i>=1; i--)
    {
        x+=a.d[i];
        c.d[i]=x/k;
        x%=k;
        rem=x;
        x*=radix;
    }
    while(c.d[0]>1&&c.d[c.d[0]]==0) c.d[0]--;
    return c;
}

bool smaller(const integer &a,const integer &b,int delta)
{
    if (a.d[0]+delta!=b.d[0]) return a.d[0]+delta<b.d[0];
    for (int i=a.d[0]; i>0; i--)
        if (a.d[i]!=b.d[i+delta])
            return a.d[i]<b.d[i+delta];
    return 1;
}

void Minus(integer &a,const integer &b,int delta)
{
    int i,x=0;
    for (i=1; i<=a.d[0]-delta; i++)
    {
        x+=radix+a.d[i+delta]-b.d[i];
        a.d[i+delta]=x%radix;
        x=x/radix-1;
    }
    while(a.d[0]>1&&a.d[a.d[0]]==0) a.d[0]--;
}

integer operator /(const integer &a,const integer &b)
{
    integer c;
    d=a;
    int i,j,temp;
    mid1[0]=b;
    for (i=1; i<=13; i++) mid1[i]=mid1[i-1]*2;
    for (i=a.d[0]-b.d[0]; i>=0; i--)
    {
        temp=8192;
        for (j=13; j>=0; j--)
        {
            if (smaller(mid1[j],d,i))
            {
                Minus(d,mid1[j],i);
                c.d[i+1]+=temp;
            }
            temp/=2;
        }
    }
    c.d[0]=max(1,a.d[0]-b.d[0]+1);
    while(c.d[0]>1&&c.d[c.d[0]]==0) c.d[0]--;
    return c;
}

bool operator ==(const integer &a,const integer &b)
{
    if (a.d[0]!=b.d[0]) return 0;
    for (int i=1; i<=a.d[0]; i++)
        if (a.d[i]!=b.d[i])
            return 0;
    return 1;
}


const int maxnode = 5000000+5;
const int sigma_size = 11;

struct Trie {
    int ch[maxnode][sigma_size];
    int val[maxnode];

    int sz;
    Trie() {sz=1;memset(ch[0],0,sizeof(ch[0]));memset(val,0,sizeof(val));}
    int idx(char c) {return c - ‘0‘;}

    void insert(char *s, int v) {
        int u = 0, n = strlen(s);
        for (int i = 0; i < n; i++) {
            if(val[u]==0) val[u]=v;
            int c = idx(s[i]);
            if (!ch[u][c]) {
                memset(ch[sz], 0, sizeof(ch[sz]));
                ch[u][c] = sz++;
            }
            u = ch[u][c];

        }
        if(val[u]==0)  val[u] = v;
    }

    int values(char* s) {
        int u = 0,n = strlen(s);
        for(int i=0;i<n;i++) {
            int c = idx(s[i]);
            if(!ch[u][c]) return -1;
            u = ch[u][c];
        }
        //printf("%d\n",val[u]);
        return val[u];

    }

}sol;

void init() {
    integer a = 1,b = 1;
    char qwq[100] = "1";
    sol.insert(qwq,1);
    for(int i=2;i<100000;i++) {
        if(i%2) {
            a = a+b;
            strcpy(qwq,a.tostring().c_str());
        }
        else {
            b = a+b;
            strcpy(qwq,b.tostring().c_str());
        }
        sol.insert(qwq,i);
    }
}

int main()
{
    //freopen("in.txt","r",stdin);
    init();
    int t;
    scanf("%d",&t);

    int kase = 1;
    char st[55];
    while(t--) {
        scanf("%s",st);
        int ans = sol.values(st);
        if(ans==1) ans =0;
        printf("Case #%d: %d\n",kase++,ans);

    }
    return 0;
}

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