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博主主页:Yu·仙笙
专栏地址:洛谷千题详解
目录
题目描述
输入格式
输出格式
输入输出样例
解析:
C++源码:
Python源码:
Java源码:
Pascal源码:
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题目描述
用高精度计算出 S=1!+2!+3!+⋯+n!(n≤50)。
其中 !
表示阶乘,定义为n!=n×(n−1)×(n−2)×⋯×1。例如,5!=5×4×3×2×1=120。
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输入格式
一个正整数 n。
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输出格式
一个正整数 S,表示计算结果。
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输入输出样例
输入 #1
3
输出 #1
9
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解析:
思路就是高精乘+高精加,就是把高精乘的模板套上去接着套高精加的模板,b=c=i的阶乘。
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C++源码:
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
struct fantastic //嗯,开始重载了
{int len,s[9999];fantastic(){memset(s,0,sizeof(s));len=1;}fantastic operator=(const char*num){len=strlen(num);for(int i=0;i<len;++i)s[i]=num[len-i-1]-'0';return *this;}fantastic operator=(const int num){char a[9999];sprintf(a,"%d",num);*this=a;return *this;}fantastic (const int num){*this=num;}fantastic (const char * num){*this=num;}fantastic operator+(const fantastic &a) //这里在重载 “+” 的运算{fantastic c;c.len=max(len,a.len)+1; //这里就是我们熟悉的竖式模拟了for(int i=0,x=0;i<c.len;++i){c.s[i]=s[i]+a.s[i]+x;x=c.s[i]/10;c.s[i]=c.s[i]%10;}if(c.s[c.len-1]==0)--c.len;return c;}fantastic operator * (const fantastic &x) //然后再来波 “*” 的运算{fantastic c;c.len=len+x.len; //又是我们熟悉的竖式模拟for(int i=0;i<len;++i)for(int j=0;j<x.len;++j){c.s[i+j]+=s[i]*x.s[j];c.s[i+j+1]+=c.s[i+j]/10;c.s[i+j]%=10;}if(c.s[c.len-1]==0)--c.len;return c;}
};
ostream& operator<<(ostream &out,const fantastic& x) //重载一下输出
{for(int i=x.len-1;i>=0;--i)cout<<x.s[i];return out;
}
istream& operator>>(istream &in,fantastic &x) //重载一下输入
{char num[9999];in>>num;x=num;return in;
}
int main() //然后就可以愉快的开始主程序啦
{int n;fantastic ans=0,num=1;cin>>n;for(int i=1;i<=n;i++){num=num*i;ans=ans+num;}cout<<ans<<endl;
} //非常的简单明了
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Python源码:
print(reduce(lambda x,y:x+y,[reduce(lambda x,y:x*y,range(1,i+1)) for i in range(1, int(raw_input())+1)]))
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Java源码:
private static final BigInteger[] INTEGERS = new BigInteger[51];static {INTEGERS[0] = new BigInteger("1");}public static void main(String[] args) {BigInteger result = new BigInteger("0");Scanner scanner = new Scanner(System.in);int n = scanner.nextInt();for (int i = 1; i <= n; ++ i) {INTEGERS[i] = INTEGERS[i - 1].multiply(new BigInteger(String.valueOf(i)));result = result.add(INTEGERS[i]);}System.out.println(result);}
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Pascal源码:
var a,b:array[1..1000] of int64;i,j,la,lb,n:longint;
procedure cheng(t:longint);//高精度乘单精度
var i:longint;
beginfor i:=1 to la doa[i]:=a[i]*t;for i:=1 to la dobegina[i+1]:=a[i+1]+a[i] div 10;a[i]:=a[i] mod 10;end;while a[la+1]>0 do inc(la);
end;
procedure jia;//高精度加法
var i:longint;
beginfor i:=1 to la dobeginb[i]:=b[i]+a[i];b[i+1]:=b[i+1]+b[i] div 10;b[i]:=b[i] mod 10;end;while b[lb+1]>0 do inc(lb);
end;
beginread(n);a[1]:=1;for i:=1 to n dobegincheng(i);jia;end;for i:= lb downto 1 dowrite(b[i]);
end.
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