Huawei Machine Question "9"-integer divided into 2 power times

Title Description:

An integer can be split into the sum of 2 powers, for example:

7 = 1+ 2 +
4

7 = 1 + 2
+ 2 + 2

7 = 1 + 1
+ 1 + 4

7 = 1 + 1
+ 1 + 2 + 2

7 = 1 + 1
+ 1 + 1 + 1 + 2

7 = 1 + 1
+ 1 + 1 + 1 + 1 + 1

There are six different ways to split

Another example: 4 can be split into:
4 = 4, 4 = 1+1+1+1, 4 = 1+1+2, 4 =.

Use f (n) to denote the number of different splits of N, e.g. F (7)
= 6.

Requirements:

Required to read n (not more than 1000000), output f (n)
% 1000000000.

Thinking Analysis:

• This topic has no direct formula to use, consider recursion
• Using the idea of dynamic programming
• When that 2k +1,f (2k+1) certainly contains a 1,f (2k+1) =f (2k)
• n is even when the split is divided into 1 and does not contain 12 cases, f (2k) = f (2k-2) +f (k), containing 1 of the case, must contain at least two 1, not including 1 is divided by 2, is f (k)
• Also note the output to% 1000000000, note the remainder of the nature: (a+b)%m = (a%m+b%m)%m, so as long as each intermediate result also take the remainder, there will be no overflow problem, and will not change the final output results
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Code:

Import Java.util.Scanner; Public classMain {Static int[] num = {1,2,5,Ten, -, -, -}; Public Static void Main(string[] args) {Scanner scan =NewScanner (System.inch); while(Scan.hasnext ()) {intinput = Scan.nextint ();if(Input <1){return; } System. out. println (GetNumber (input)); }       } Public Static int GetNumber(intN) {if(n = =1){return 1; }if(n = =2){return 2; }if(n%2!=0){returnGetNumber (n1)%1000000000; }Else{returnGetNumber (n2)%1000000000+getnumber (n/2)%1000000000; }    }}

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Huawei Machine Question "9"-integer divided into 2 power times