Ural 1079 - Maximum

Consider the sequence of numbers   a_i,   i  = 0, 1, 2, …, which satisfies the following requirements:

• a₀ = 0
• a₁ = 1
• a_2i = a_i
• a_2i+1 = a_i + a_i+1

for every   i  = 1, 2, 3, … .

Write a program which for a given value of   n  finds the largest number among the numbers   a ₀,   a ₁, …, a_n.

Input

You are given several test cases (not more than 10). Each test case is a line containing an integer n  (1 ≤  n ≤ 99 999). The last line of input contains 0.

Output

For every   n  in the input write the corresponding maximum value found.

Sample

input	output
5 10 0	3 4

Problem Author: Emil Kelevedzhiev
Problem Source: Winter Mathematical Festival Varna '2001 Informatics Tournament

// Ural Problem 1079. Maximum

// Verdict: Accepted  

// Submission Date: 14:33:08 15 Jan 2014

// Run Time: 0.031s

//  

// 版权所有（C）acutus   (mail: [email protected]) 

// 博客地址：http://www.cnblogs.com/acutus/

// [解题方法]  

// 简单题模拟题

// 注意：最大项有可能是奇数项



#include<stdio.h>



long long a[100000], b[100000];



void solve()

{

    int i, j, max, n;

    a[0] = b[0] = 0;

    a[1] = b[1] = 1;

    max = 1;

    for(i = 2; i < 100000; i++) {

        if(i % 2) {

            j = (i - 1) >> 1;

            a[i] = a[j] + a[j + 1];

        } else {

            a[i] = a[i >> 1];

        }

        if(a[i] > max)

            max = a[i];

        b[i] = max;

    }

    while(scanf("%d", &n) && n) {

        printf("%lld\n", b[n]);

    }

}



int main()

{

    solve();

    return 0;

}