Very simple problem

分析：使用的是构造新数字法进行不断构造，然后逼近每一位数字，然后使用c++徒手敲了240多行代码，竟然过了........................很有成就感。

代码如下：

===============================================================================================================================

#include<stdio.h>
#include<algorithm>
#include<vector>
#include<iostream>
#include<math.h>
#include<string.h>
using namespace std;

const int MAXN = 2007;

struct BigNum
{///数值保存从0位开始
    int Size;///数的位数
    int num[MAXN];///数值，逆序保存

    BigNum(){
        Size=1;
        memset(num, false, sizeof(num));
    }
    void Cin()
    {
        char s[MAXN];

        scanf("%s", s);
        Size = strlen(s);

        for(int i=Size-1; i>=0; i--)
            num[i] = s[Size-i-1] - '0';
    }
    bool operator <= (const BigNum &b)const
    {
        if(Size > b.Size)return false;
        if(Size < b.Size)return true;

        for(int i=Size-1; i>=0; i--)
        {
            if(num[i] > b.num[i])return false;
            if(num[i] < b.num[i])return true;
        }

        return true;
    }
    void operator = (const BigNum &b)
    {
        Size = b.Size;

        for(int i=0; i<b.Size; i++)
            num[i] = b.num[i];
    }
    void operator = (const int &b)
    {
        int tem = b;

        if(b == 0)
            Size = 1;
        else
            Size = (int)(log10(tem)+0.00001)+1;

        for(int i=0; i<Size; i++)
        {
            num[i] = tem % 10;
            tem /= 10;
        }
    }
    BigNum operator <<(const int &k)const
    {
        BigNum tmp;

        for(int i=Size-1; i>=0; i--)
        {
            tmp.num[i+k] = num[i];
        }
        tmp.Size = Size + k;

        tmp.CarryBit();

        return tmp;
    }
    BigNum operator * (const BigNum &b)const
    {
        BigNum res;

        res.Size = Size + b.Size - 1;

        for(int i=0; i<b.Size; i++)
        for(int j=0; j<Size; j++)
        {
            res.num[i+j] += num[j] * b.num[i];
        }

        res.CarryBit();

        return res;
    }
    BigNum operator * (const int &b)const
    {
        BigNum res;

        res.Size = Size;

        for(int i=0; i<Size; i++)
        {
            res.num[i] = num[i] * b;
        }

        res.CarryBit();

        return res;
    }
    BigNum operator + (const BigNum &b)const
    {
        BigNum res;
        res.Size = max(b.Size, Size);

        for(int i=0; i<res.Size; i++)
            res.num[i] = num[i] + b.num[i];
        res.CarryBit();

        return res;
    }
    BigNum operator + (const int &b)const
    {
        BigNum res;
        res = b;

        res.Size = max(res.Size, Size);

        for(int i=0; i<res.Size; i++)
            res.num[i] += num[i];
        res.CarryBit();

        return res;
    }
    BigNum operator - (const BigNum &b)const
    {///b值小，先比较在进行相减
        BigNum res;

        res.Size = Size;
        for(int i=0; i<Size; i++)
        {
            if(i < b.Size)
                res.num[i] = num[i] - b.num[i];
            else
                res.num[i] = num[i];
        }
        res.CarryBit();

        return res;
    }
    void CarryBit()
    {///进位,注意减法的时候进位结果需要是非负数
        for(int i=0; i<Size; i++)
        {
            if(num[i] >= 10)
            {
                if(i+1==Size)
                {
                    num[i+1] = 0;
                    Size += 1;
                }

                num[i+1] += num[i]/10;
                num[i] %= 10;
            }
            else if(num[i] < 0)
            {
                num[i+1] -= 1;
                num[i] += 10;
            }
        }
        while(Size > 1 && !num[Size-1])
            Size -= 1;
    }
    void Out()
    {
        for(int i=Size-1; i>=0; i--)
            printf("%d", num[i]);
        printf("
");
    }
};
int Find(const BigNum &a, BigNum &Mod)
{
    int i;
    BigNum t;

    for(i=1; i<=9; i++)
    {
        t = (((a*2)<<1)+i) * i;

        if(t <= Mod)
            continue;
        break;
    }

    i--;
    t = (((a*2)<<1)+i) * i;

    Mod = Mod - t;

    return i;
}
BigNum Sqrt(const BigNum &a)
{
    BigNum ans, Mod;
    int len=a.Size-1;

    if(a.Size % 2 == 0)
    {
        Mod = Mod + (a.num[len]*10+a.num[len-1]);
        len -= 2;
    }
    else
    {
        Mod = Mod + a.num[len];
        len -= 1;
    }

    ans = Find(ans, Mod);

    while(len > 0)
    {
        Mod = (Mod<<2) + (a.num[len]*10+a.num[len-1]);
        ans = (ans<<1) + Find(ans, Mod);

        len -= 2;
    }

    return ans;
}

int main()
{
    BigNum a;

    a.Cin();
    a = Sqrt(a);

    a.Out();

    return 0;
}