大数开根号（蓝桥杯-矩阵翻硬币）

来源：互联网发布：沈阳网络电玩城编辑：程序博客网时间：2024/05/16 00:52

在蓝桥上面交了个题目，测试了java和C++的速度发现差距还是蛮大的，java代码相对比较少但是时间和内存差不多就是十倍的差距了。
这里写图片描述

上C++版本代码：

#include <cstring>#include <iostream>using namespace std;struct Bigint{    int len;    int arg[1005];    Bigint()    {        len = 1;        memset(arg, 0, sizeof(arg));    }    void print()    {        for (int i = len - 1; i >= 0; i--){            cout<<arg[i];        }        cout<<endl;    }    void CharToBigint(char *str)    {        len = strlen(str);        for (int i = 0; i < len; i++){            arg[i] = str[len - i - 1] - 48;        }        while(arg[len-1] == 0){            len--;        }    }    friend bool operator==(Bigint r, Bigint w)    {        if (r.len != w.len) return false;        int i = r.len - 1;        while (i >= 0){            if (r.arg[i] != w.arg[i])                return false;            i--;        }        return true;    }    friend bool operator<=(Bigint r, Bigint w)    {        if (r.len < w.len) return true;        else if (w.len < r.len) return false;        int i = r.len - 1;        while (i >= 0){            if (r.arg[i]<w.arg[i])                return true;            else if (r.arg[i]>w.arg[i])                return false;            i--;        }        return true;    }    friend Bigint operator+(int r, Bigint w){        w.arg[0] += r;        int i = 0;        while (w.arg[i] >= 10){            w.arg[i + 1] += w.arg[i] / 10;            w.arg[i] = w.arg[i] % 10;            i++;        }        if(w.arg[i]) i++;        w.len = i > w.len ? i : w.len;        return w;    }    friend Bigint operator+(Bigint w, int r)    {        w.arg[0] += r;        int i = 0;        while (w.arg[i] >= 10){            w.arg[i + 1] += w.arg[i] / 10;            w.arg[i] = w.arg[i] % 10;            i++;        }        if(w.arg[i]) i++;        w.len = i > w.len ? i : w.len;        return w;    }    friend Bigint operator-(Bigint r, Bigint w)    {        for (int i = 0; i < r.len; i++){            if (r.arg[i] >= w.arg[i])                r.arg[i] = r.arg[i] - w.arg[i];            else{                r.arg[i] = r.arg[i] + 10;                r.arg[i + 1] = r.arg[i + 1] - 1;                r.arg[i] = r.arg[i] - w.arg[i];            }        }        while (r.arg[r.len - 1] == 0 && r.len > 1)            r.len--;        return r;    }    friend Bigint operator*(int x, Bigint w)    {        Bigint r;        if(x == 0 || (w.len == 1 && w.arg[0] == 0)){            return r;        }        for (int i = 0; i < w.len; i++){            r.arg[i] += w.arg[i] * x;            r.arg[i + 1] += r.arg[i] / 10;            r.arg[i] = r.arg[i] % 10;        }        int i = r.arg[w.len] == 0 ? w.len-1 : w.len;        while (r.arg[i] >= 10){            r.arg[i + 1] = r.arg[i] / 10;            r.arg[i] = r.arg[i] % 10;            i++;        }        r.len = (i >= 0) ? i + 1 : 1;        return r;    }    friend Bigint operator*(Bigint r, Bigint w)    {        Bigint v;        if((r.len == 1 && r.arg[0] == 0)|| (w.len == 1 && w.arg[0] == 0)){            return v;        }        for (int i = 0; i < r.len; i++){            for (int k = 0; k < w.len; k++){                v.arg[i + k] += w.arg[k] * r.arg[i];                v.arg[i + k + 1] += v.arg[i + k] / 10;                v.arg[i + k] = v.arg[i + k] % 10;            }        }        int i = w.len + r.len - 1;        i = v.arg[i] == 0 ? i-1 : i;        while (v.arg[i] >= 10){            v.arg[i + 1] = v.arg[i] / 10;            v.arg[i] = v.arg[i] % 10;            i++;        }        v.len = (i >= 0) ? i + 1 : 1;        return v;    }    Bigint sqrt()    {        Bigint w, r;        w.len = r.len = 0;        int lens = len - 1;        if(len == 1 && arg[0] == 1)            return *this;        r.arg[r.len++] = arg[lens--];        if (len % 2 == 0)            r = arg[lens--] + 10 * r;        while (lens >= -1){            int i = 0;            while ((i*(i + 20 * w)) <= r){                i++;            }            i--;            if (i == -1 || (r.len == 1 && r.arg[0] == 1))                i = 0;            r = r - (i*(i + 20 * w));            w = i + 10 * w;            if(lens >= 0){                r = arg[lens--] + 10 * r;                r = arg[lens--] + 10 * r;            }            else                lens -= 2;        }        return w;    }};int main(){    char stra[1005],strb[1005];    while(cin>>stra>>strb)    {        Bigint a, b;        a.CharToBigint(stra);        b.CharToBigint(strb);        a = a.sqrt()*b.sqrt();        a.print();    }    return 0;}

Java版本代码：

package HelloWord;import java.io.*;import java.util.*;import java.math.*;import java.math.BigInteger;import java.math.BigDecimal.*;import java.math.BigInteger.*;public class HelloWord {    public static int length(BigInteger a) {        int length = 0;        while (a != BigInteger.ZERO) {            a = a.divide(BigInteger.valueOf(10));            length++;        }        return length;    }    public static int GetNumber(BigInteger a, int pos) {        BigInteger flag = BigInteger.valueOf(10);        flag = flag.pow(pos - 1);        a = a.divide(flag);        a = a.mod(BigInteger.valueOf(10));        return a.intValue();    }    public static BigDecimal sqrt(BigInteger a, int cor) {        BigInteger w = BigInteger.ZERO;        BigInteger r = BigInteger.ZERO;        BigInteger num_10 = BigInteger.valueOf(10);        BigInteger num_20 = BigInteger.valueOf(20);        if (a == BigInteger.ONE) {            return BigDecimal.valueOf(1);        }        a = a.multiply(num_10.pow(2*cor));        int lens = length(a);        r = BigInteger.valueOf(GetNumber(a, lens--));        if (lens % 2 == 1)            r = r.multiply(num_10).add(BigInteger.valueOf(GetNumber(a, lens--)));        while (lens >= 0) {            int i = 0;            BigInteger num_i = BigInteger.valueOf(i);            while (r.compareTo(w.multiply(num_20).add(num_i).multiply(num_i)) >= 0) {                num_i = BigInteger.valueOf(++i);            }            num_i = BigInteger.valueOf(--i);            if (i == -1 || r == BigInteger.ONE)                i = 0;            r = r.subtract(w.multiply(num_20).add(num_i).multiply(num_i));            w = w.multiply(num_10).add(num_i);            if (lens >= 1) {                r = r.multiply(num_10).add(BigInteger.valueOf(GetNumber(a, lens--)));                r = r.multiply(num_10).add(BigInteger.valueOf(GetNumber(a, lens--)));            }            else                lens -= 2;        }        String str = w.toString();        StringBuilder strb = new StringBuilder(str);        strb.insert(strb.length() - cor, '.');        str = strb.toString();        return new BigDecimal(str);    }    public static void main(String[] args) {        Scanner cin = new Scanner(System.in);        while (cin.hasNext()) {            String str = cin.next();            BigInteger a = new BigInteger(str);            str = cin.next();            BigInteger b = new BigInteger(str);            System.out.println(sqrt(a, 0).multiply(sqrt(b, 0)));        }    }}

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