Scientific Problem(数学，简单)

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最新推荐文章于 2025-08-06 16:57:52 发布

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原文链接：http://www.cnblogs.com/cszlg/archive/2012/08/29/2910473.html

本文探讨了在列车上利用给定数值x，通过算法找到一个整数n，使得n乘以x小于所有小于n的正整数之和的问题。通过提供输入样例和输出样例，展示了算法的具体应用，并通过代码实现验证了解决方案的有效性。

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Scientific Problem

Time Limit:500MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u

Submit Status Practice SGU 403

Description

Once upon a time Professor Idioticideasinventor was travelling by train. Watching cheerless landscape outside the window, he decided to invent the theme of his new scientific work. All of a sudden a brilliant idea struck him: to develop an effective algorithm finding an integer number, which is x times less than the sum of all its integer positive predecessors, where number x is given. As far as he has no computer in the train, you have to solve this difficult problem.

Input

The first line of the input file contains an integer number x (1 ≤ x ≤ 10 ⁹).

Output

Output an integer number — the answer to the problem.

Sample Input

sample input	sample output
1	3

sample input	sample output
2	5

设答案为n，则nx < 1 +2 +3 + ... + n - 1 ,得到 n > 2x,所以n = 2x +1
AC CODE

//Memory: 935 KB         Time: 31 MS
//Language: GNU CPP (MinGW, GCC 4)         Result: Accepted

#include <iostream>
#include <string>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#define LL long long
#define MAXI 2147483647
#define MAXL 9223372036854775807
#define eps (1e-8)
#define dg(i) cout << "*" << i << endl;
using namespace std;

int main()
{
    LL x;
    while(scanf("%I64d", &x) != EOF)
    {
        printf("%I64d\n", 2 * x + 1);
    }
    return 0;
}