YTU OJ-1018: Give me the answer

1018: Give me the answer

Time Limit: 1 Sec   Memory Limit: 32 MB
Submit: 43   Solved: 10
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Description

Farmer John commanded his cows to search for different sets of numbers that sum to a given number.

The cows use only numbers that are an integer power of 2. Here are the possible sets of numbers that

sum to 7:

1) 1+1+1+1+1+1+1

2) 1+1+1+1+1+2

3) 1+1+1+2+2

4) 1+1+1+4

5) 1+2+2+2

6) 1+2+4

Help FJ count all possible representations for a given integer N (1 <= N <= 1 ,000,000)

Input

The first line of the input contains the number of test cases in the file. And t he first line of each case

contains one integer numbers n

Output

For each test case, output a line with the ans % 1000000000.

Sample Input

1
7

Sample Output

6

题解：这个题当数据量不大的时候，完全可以用搜索得出结果，但数据量大时，会超时。所以，可以先用dfs搜索得出前面若干项的结果，看一下有什么规律。

这个题从1开始，结果一次为 1   2   2   4   4   6   6   10   10   14   14   20   20   26   26   36   36   46   46   60   60   74。

递推公式：p[ i ]=(p[ i-1 ]+p[ i/2 ]) % mod ; （mod=1e9）

import java.util.*;

public class Give_me_the_answer {
static long [] a=new long[1020000];
static int n;
public static void f() {
a[1]=1;a[2]=2;
for(int i=2;i<1000010;i+=2) {
a[i]=(a[i-1]+a[i/2])%1000000000;
a[i+1]=a[i];
}
}
public static void main(String[] args) {
Scanner in=new Scanner(System.in);
int t;
t=in.nextInt();
while(t!=0) {
f();
n=in.nextInt();
System.out.println(a[n]);
t--;
}
}
}