Ural 1248 Sequence Sum 题解

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Ural 1248 Sequence Sum 题解

题意

给定$n$个用科学计数法表示的实数$(10^{-100}\sim10^{100})$，输出它们的和。

Tip: 一个实数可以用科学计数法表示为$x\times10^y$，其中$1\le x<10$ $x$为实数，$y$是整数。输入时表示为$xey$。保证输入的实数有$19$位有效数字。输出时用科学计数法，必须包括$19$位正确数字。

题解

  1. 读入字符串，把它们换成正常形态放入数组。
  2. 小数点对齐。
  3. 计算。
  4. 换成科学计数法输出。

Tip: 口胡得很简单，写起来可能有点麻烦，要仔细。

程序

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// #pragma GCC optimize(2)
// #pragma G++ optimize(2)
// #pragma comment(linker,"/STACK:102400000,102400000")

// #include <bits/stdc++.h>
#include <map>
#include <set>
#include <list>
#include <array>
#include <cfenv>
#include <cmath>
#include <ctime>
#include <deque>
#include <mutex>
#include <queue>
#include <ratio>
#include <regex>
#include <stack>
#include <tuple>
#include <atomic>
#include <bitset>
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <chrono>
#include <cstdio>
#include <cwchar>
#include <future>
#include <limits>
#include <locale>
#include <memory>
#include <random>
#include <string>
#include <thread>
#include <vector>
#include <cassert>
#include <climits>
#include <clocale>
#include <complex>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <ctgmath>
#include <cwctype>
#include <fstream>
#include <iomanip>
#include <numeric>
#include <sstream>
#include <ccomplex>
#include <cstdbool>
#include <iostream>
#include <typeinfo>
#include <valarray>
#include <algorithm>
#include <cinttypes>
#include <cstdalign>
#include <stdexcept>
#include <typeindex>
#include <functional>
#include <forward_list>
#include <system_error>
#include <unordered_map>
#include <unordered_set>
#include <scoped_allocator>
#include <condition_variable>
// #include <conio.h>
// #include <windows.h>
using namespace std;

typedef long long LL;
typedef unsigned int ui;
typedef unsigned long long ull;
typedef float fl;
typedef double ld;
typedef long double LD;
typedef pair<int,int> pii;
#if (WIN32) || (WIN64) || (__WIN32) || (__WIN64) || (_WIN32) || (_WIN64) || (WINDOWS)
#define lld "%I64d"
#define llu "%I64u"
#else
#define lld "%lld"
#define llu "%llu"
#endif
#define ui(n) ((unsigned int)(n))
#define LL(n) ((long long)(n))
#define ull(n) ((unsigned long long)(n))
#define fl(n) ((float)(n))
#define ld(n) ((double)(n))
#define LD(n) ((long double)(n))
#define char(n) ((char)(n))
#define Bool(n) ((bool)(n))
#define fixpoint(n) fixed<<setprecision(n)

const int INF=1061109567;
const int NINF=-1044266559;
const LL LINF=4557430888798830399;
const ld eps=1e-15;
#define MOD (1000000007)
#define PI (3.1415926535897932384626433832795028841971)

/*
#define MB_LEN_MAX 5
#define SHRT_MIN (-32768)
#define SHRT_MAX 32767
#define USHRT_MAX 0xffffU
#define INT_MIN (-2147483647 - 1)
#define INT_MAX 2147483647
#define UINT_MAX 0xffffffffU
#define LONG_MIN (-2147483647L - 1)
#define LONG_MAX 2147483647L
#define ULONG_MAX 0xffffffffUL
#define LLONG_MAX 9223372036854775807ll
#define LLONG_MIN (-9223372036854775807ll - 1)
#define ULLONG_MAX 0xffffffffffffffffull
*/

#define MP make_pair
#define MT make_tuple
#define All(a) (a).begin(),(a).end()
#define pall(a) (a).rbegin(),(a).rend()
#define log2(x) log(x)/log(2)
#define Log(x,y) log(x)/log(y)
#define SZ(a) ((int)(a).size())
#define rep(i,n) for(int i=0;i<((int)(n));i++)
#define rep1(i,n) for(int i=1;i<=((int)(n));i++)
#define repa(i,a,n) for(int i=((int)(a));i<((int)(n));i++)
#define repa1(i,a,n) for(int i=((int)(a));i<=((int)(n));i++)
#define repd(i,n) for(int i=((int)(n))-1;i>=0;i--)
#define repd1(i,n) for(int i=((int)(n));i>=1;i--)
#define repda(i,n,a) for(int i=((int)(n));i>((int)(a));i--)
#define repda1(i,n,a) for(int i=((int)(n));i>=((int)(a));i--)
#define FOR(i,a,n,step) for(int i=((int)(a));i<((int)(n));i+=((int)(step)))
#define repv(itr,v) for(__typeof((v).begin()) itr=(v).begin();itr!=(v).end();itr++)
#define repV(i,v) for(auto i:v)
#define repE(i,v) for(auto &i:v)
#define MS(x,y) memset(x,y,sizeof(x))
#define MC(x) MS(x,0)
#define MINF(x) MS(x,63)
#define MCP(x,y) memcpy(x,y,sizeof(y))
#define sqr(x) ((x)*(x))
#define UN(v) sort(All(v)),v.erase(unique(All(v)),v.end())
#define filein(x) freopen(x,"r",stdin)
#define fileout(x) freopen(x,"w",stdout)
#define fileio(x)\
	freopen(x".in","r",stdin);\
	freopen(x".out","w",stdout)
#define filein2(filename,name) ifstream name(filename,ios::in)
#define fileout2(filename,name) ofstream name(filename,ios::out)
#define file(filename,name) fstream name(filename,ios::in|ios::out)
#define Pause system("pause")
#define Cls system("cls")
#define fs first
#define sc second
#define PC(x) putchar(x)
#define GC(x) x=getchar()
#define Endl PC('\n')
#define SF scanf
#define PF printf

inline int Read()
{
    int X=0,w=0;char ch=0;while(!isdigit(ch)){w|=ch=='-';ch=getchar();}while(isdigit(ch))X=(X<<3)+(X<<1)+(ch^48),ch=getchar();
	return w?-X:X;
}
inline void Write(int x){if(x<0)putchar('-'),x=-x;if(x>9)Write(x/10);putchar(x%10+'0');}

inline LL powmod(LL a,LL b){LL RES=1;a%=MOD;assert(b>=0);for(;b;b>>=1){if(b&1)RES=RES*a%MOD;a=a*a%MOD;}return RES%MOD;}
inline LL gcdll(LL a,LL b){return b?gcdll(b,a%b):a;}
const int dx[]={0,1,0,-1,1,-1,-1,1};
const int dy[]={1,0,-1,0,-1,-1,1,1};
/************************************************************Begin************************************************************/
const int maxn=1010;
const int Dot=500;

int n,dig[maxn][maxn];

inline int Atoi(string x)
{
	int res=0;
	repV(i,x) if(isdigit(i)) res=(res+i-'0')*10;res/=10;
	return (x[0]=='-'?-res:res);
}

inline void func(int k,string x)
{
	int e=x.find("e");

	string a=x.substr(0,e),b=x.substr(e+1);
	if(a.find(".")==string::npos) a+='.';

	rep(i,101) a='0'+a;
	rep(i,101) a+='0';

	int dot=a.find(".")+Atoi(b)-(b[0]=='-'?1:0);

	int hav=0;
	repd(i,dot+1)
	{
		if(a[i]=='.')
		{
			hav=1;
			continue;
		}

		dig[k][Dot-(dot-i+1)+hav]=a[i]-'0';
	}

	hav=0;
	repa(i,dot+1,a.size())
	{
		if(a[i]=='.')
		{
			hav=1;
			continue;
		}

		dig[k][Dot+(i-dot)-hav]=a[i]-'0';
	}
}

int main()
{
	cin>>n;
	rep(i,n)
	{
		string x;cin>>x;
		func(i,x);
	}

	rep(i,n) rep(j,1000) dig[n][j]+=dig[i][j];

	repd(j,1000)
	{
		while(dig[n][j]>=10)
		{
			int hav=0;
			if(j-1==Dot) hav=1;

			dig[n][j-1-hav]+=dig[n][j]/10;
			dig[n][j]%=10;
		}
	}

	int w=INF,e=0;
	rep(i,Dot) if(dig[n][i])
	{
		w=i;
		e=Dot-w-1;
		break;
	}

	if(w==INF)
	{
		repa(i,Dot+1,1000) if(dig[n][i])
		{
			w=i;
			e=i-Dot;
			break;
		}
		e=-e;
	}

	cout<<dig[n][w]<<'.';
	repa(i,w+1,w+20) if(i!=Dot) cout<<dig[n][i];
	cout<<'e'<<e;

	return 0;
}
/*************************************************************End**************************************************************/
__EOF__