1079. Maximum

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1079. Maximum
Time limit: 2.0 second
Memory limit: 64 MB
Consider the sequence of numbers ai, i = 0, 1, 2, …, which satisfies the following requirements:
a0 = 0
a1 = 1
a2i = ai
a2i+1 = ai + ai+1
for every i = 1, 2, 3, … .
Write a program which for a given value of n finds the largest number among the numbers a0, a1, …, an.
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

#include <iostream>

#include <vector>

using namespace std;

void Maximum(int n){

    vector<int> nums;

    nums.insert(nums.end(), 0);

    nums.insert(nums.end(), 1);

    if(n<=1){

        cout<<nums[n]<<endl;

        return;

    }

    int max = nums[1];

    for(int i = 2 ; i <= n ; i++){

        if(i%2==0){

            nums.insert(nums.end(), nums[i/2]);

        }

        else{

            nums.insert(nums.end(), (nums[(i-1)/2]+nums[((i-1)/2) + 1]));

        }

        if(nums[i]>max){

            max = nums[i];

        }

    }

    cout<<max<<endl;

    

}

int main(){

    vector<int> inputnum;

    int n;

    cin>>n;

    while (n!=0) {

        inputnum.insert(inputnum.end(), n);

        cin>>n;

    }

    for(int i = 0 ; i < inputnum.size() ; i++){

        Maximum(inputnum[i]);

    }

    return 0;

}

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