1216: 斐波那契数列

From:  合工宣OJ      http://xcacm.hfut.edu.cn/problem.php?id=1216

时间限制: 1 Sec  内存限制: 128 MB

题目描述 Fibonacci数列，定义如下： f(1)=f(2)=1 f(n)=f(n-1)+f(n-2) n>=3 计算第n项Fibonacci数值。

输入

输入第一行为一个整数n（1<=n<=10000）。

输出

输出对应的f(n)。

样例输入

1 2 3 4 5

样例输出

1 1 2 3 5

本题需要用到大整数，unsign long long已经明显装不下了，c++没有内置封装好的大整数（而JAVA是有的），需要自己定义大整数，大整数的模板很好找到，然而很多功能需要根据实际需要删减，本题只需重载加减符号，然而为用的方便此处未作删减。菲波那切递推公式已经给出，只需循环将每一个情况存在大整数开出的数组里，用时调用即可。原先把#define MAX_L 3000 开到了10000 结果出现内存超限，改合适一些内存会降低很多。 代码如下：

#include<string>
#include<iostream>
#include<iosfwd>
#include<cmath>
#include<cstring>
#include<stdlib.h>
#include<stdio.h>
#include<cstring>
#define MAX_L 3000 
using namespace std;
class bign                           //定义大整数
{
public:
        int len, s[MAX_L];
        bign();
        bign(const char*);
        bign(int);
        bool sign;
        string toStr() const;
        friend istream& operator>>(istream &,bign &);
        friend ostream& operator<<(ostream &,bign &);
        bign operator=(const char*);
        bign operator=(int);
        bign operator=(const string);
        bool operator>(const bign &) const;
        bool operator>=(const bign &) const;
        bool operator<(const bign &) const;
        bool operator<=(const bign &) const;
        bool operator==(const bign &) const;
        bool operator!=(const bign &) const;
        bign operator+(const bign &) const;
        bign operator++();
        bign operator++(int);
        bign operator+=(const bign&);
        bign operator-(const bign &) const;
        bign operator--();
        bign operator--(int);
        bign operator-=(const bign&);
        bign operator*(const bign &)const;
        bign operator*(const int num)const;
        bign operator*=(const bign&);
        bign operator/(const bign&)const;
        bign operator/=(const bign&);
        bign operator%(const bign&)const;
        void clean();
        ~bign();
};
#define max(a,b) a>b ? a : b
#define min(a,b) a<b ? a : b
bign::bign()
{
    memset(s, 0, sizeof(s));
    len = 1;
    sign = 1;
}
bign::bign(const char *num)
{
    *this = num;
}
bign::bign(int num)
{
    *this = num;
}
string bign::toStr() const
{
    string res;
    res = "";
    for (int i = 0; i < len; i++)
        res = (char)(s[i] + '0') + res;
    if (res == "")
        res = "0";
    if (!sign&&res != "0")
        res = "-" + res;
    return res;
}
istream &operator>>(istream &in, bign &num)
{
    string str;
    in>>str;
    num=str;
    return in;
}
ostream &operator<<(ostream &out, bign &num)
{
    out<<num.toStr();
    return out;
}
bign bign::operator=(const char *num)
{
    memset(s, 0, sizeof(s));
    char a[MAX_L] = "";
    if (num[0] != '-')
        strcpy(a, num);
    else
        for (int i = 1; i < strlen(num); i++)
            a[i - 1] = num[i];
    sign = !(num[0] == '-');
    len = strlen(a);
    for (int i = 0; i < strlen(a); i++)
        s[i] = a[len - i - 1] - 48;
    return *this;
}
bign bign::operator=(int num)
{
    if (num < 0)
        sign = 0, num = -num;
    else
        sign = 1;
    char temp[MAX_L];
    sprintf(temp, "%d", num);
    *this = temp;
    return *this;
}
bign bign::operator=(const string num)
{
    const char *tmp;
    tmp = num.c_str();
    *this = tmp;
    return *this;
}
bool bign::operator<(const bign &num) const
{
    if (sign^num.sign)
        return num.sign;
    if (len != num.len)
        return len < num.len;
    for (int i = len - 1; i >= 0; i--)
        if (s[i] != num.s[i])
            return sign ? (s[i] < num.s[i]) : (!(s[i] < num.s[i]));
    return !sign;
}
bool bign::operator>(const bign&num)const
{
    return num < *this;
}
bool bign::operator<=(const bign&num)const
{
    return !(*this>num);
}
bool bign::operator>=(const bign&num)const
{
    return !(*this<num);
}
bool bign::operator!=(const bign&num)const
{
    return *this > num || *this < num;
}
bool bign::operator==(const bign&num)const
{
    return !(num != *this);
}
bign bign::operator+(const bign &num) const
{
    if (sign^num.sign)
    {
        bign tmp = sign ? num : *this;
        tmp.sign = 1;
        return sign ? *this - tmp : num - tmp;
    }
    bign result;
    result.len = 0;
    int temp = 0;
    for (int i = 0; temp || i < (max(len, num.len)); i++)
    {
        int t = s[i] + num.s[i] + temp;
        result.s[result.len++] = t % 10;
        temp = t / 10;
    }
    result.sign = sign;
    return result;
}
bign bign::operator++()
{
    *this = *this + 1;
    return *this;
}
bign bign::operator++(int)
{
    bign old = *this;
    ++(*this);
    return old;
}
bign bign::operator+=(const bign &num)
{
    *this = *this + num;
    return *this;
}
bign bign::operator-(const bign &num) const
{
    bign b=num,a=*this;
    if (!num.sign && !sign)
    {
        b.sign=1;
        a.sign=1;
        return b-a;
    }
    if (!b.sign)
    {
        b.sign=1;
        return a+b;
    }
    if (!a.sign)
    {
        a.sign=1;
        b=bign(0)-(a+b);
        return b;
    }
    if (a<b)
    {
        bign c=(b-a);
        c.sign=false;
        return c;
    }
    bign result;
    result.len = 0;
    for (int i = 0, g = 0; i < a.len; i++)
    {
        int x = a.s[i] - g;
        if (i < b.len) x -= b.s[i];
        if (x >= 0) g = 0;
        else
        {
            g = 1;
            x += 10;
        }
        result.s[result.len++] = x;
    }
    result.clean();
    return result;
}
bign bign::operator * (const bign &num)const
{
    bign result;
    result.len = len + num.len;

    for (int i = 0; i < len; i++)
        for (int j = 0; j < num.len; j++)
            result.s[i + j] += s[i] * num.s[j];

    for (int i = 0; i < result.len; i++)
    {
        result.s[i + 1] += result.s[i] / 10;
        result.s[i] %= 10;
    }
    result.clean();
    result.sign = !(sign^num.sign);
    return result;
}
bign bign::operator*(const int num)const
{
    bign x = num;
    bign z = *this;
    return x*z;
}
bign bign::operator*=(const bign&num)
{
    *this = *this * num;
    return *this;
}
bign bign::operator /(const bign&num)const
{
    bign ans;
    ans.len = len - num.len + 1;
    if (ans.len < 0)
    {
        ans.len = 1;
        return ans;
    }

    bign divisor = *this, divid = num;
    divisor.sign = divid.sign = 1;
    int k = ans.len - 1;
    int j = len - 1;
    while (k >= 0)
    {
        while (divisor.s[j] == 0) j--;
        if (k > j) k = j;
        char z[MAX_L];
        memset(z, 0, sizeof(z));
        for (int i = j; i >= k; i--)
            z[j - i] = divisor.s[i] + '0';
        bign dividend = z;
        if (dividend < divid) { k--; continue; }
        int key = 0;
        while (divid*key <= dividend) key++;
        key--;
        ans.s[k] = key;
        bign temp = divid*key;
        for (int i = 0; i < k; i++)
            temp = temp * 10;
        divisor = divisor - temp;
        k--;
    }
    ans.clean();
    ans.sign = !(sign^num.sign);
    return ans;
}
bign bign::operator/=(const bign&num)
{
    *this = *this / num;
    return *this;
}
bign bign::operator%(const bign& num)const
{
    bign a = *this, b = num;
    a.sign = b.sign = 1;
    bign result, temp = a / b*b;
    result = a - temp;
    result.sign = sign;
    return result;
}
void bign::clean()
{
    if (len == 0) len++;
    while (len > 1 && s[len - 1] == '\0')
        len--;
}
bign::~bign() {}

bign f[10002];             //大整数数组

int main()
{
    int a,i;
    f[4]=3;f[1]=1;f[2]=1;f[3]=2;
    for(i=5;i<=10000;i++)
    {
        f[i]=f[i-1]+f[i-2];
    }
   while(cin>>a)
   {
        cout<<f[a]<<endl;
   }
   return 0;
}
/**************************************************************
    Problem: 1216
    User: 2014217052
    Language: C++
    Result: 正确
    Time:864 ms
    Memory:118808 kb
****************************************************************/