【ural oj 1079】 Maximum(水)

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  a 0,  a 1, …,  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

Tags:  problem for beginners   ( hide tags for unsolved problems)

Difficulty: 112     Printable version     Submit solution     Discussion (82)
My submissions     All submissions (32638)     All accepted submissions (12992)    Solutions rating (10216)

直接打一个表，在计算第i个数的大小的时候更新出来0~i的最大值即可。

#include<iostream>
#include<algorithm>
using namespace std;
#define MAXN 100500
int dp[MAXN];
int a[MAXN];
void init()
{
	a[0]=0;
	a[1]=1;
	dp[0]=0;
	dp[1]=1;
	int maxx=0;
	for(int i=2;i<=100050;i++)
	{
		if(i&1)
		{
			a[i]=a[i/2]+a[i/2+1];
		}
		else
		{
			a[i]=a[i/2];
		}
		if(a[i]>maxx)
		{
			dp[i]=a[i];
			maxx=a[i];
		}
		else
		{
			dp[i]=maxx;
		}
	}
}
int main()
{
	init();
	int t,n;
	while(cin>>n&&n)
	{
		cout<<dp[n]<<endl;
	}
	return 0;
}