Poj 2853,2140 Sequence Sum Possibilities(因式分解)

一、Description

Most positive integers may be written as a sum of a sequence of at least two consecutive positive integers. For instance,

6 = 1 + 2 + 3
9 = 5 + 4 = 2 + 3 + 4

but 8 cannot be so written.

Write a program which will compute how many different ways an input number may be written as a sum of a sequence of at least two consecutive positive integers.

Input

The first line of input will contain the number of problem instances N on a line by itself, (1 ≤ N ≤ 1000) . This will be follo
wed by N lines, one for each problem instance. Each problem line will have the problem number, a single space and the number to be written as a sequence of consecutive positive integers. The second number will be less than 2³¹ (so will fit in a 32-bit integer).

Output

The output for each problem instance will be a single line containing the problem number, a single space and the number of ways the input number can be written as a sequence of consecutive positive integers.

二、题解

一种解法：

1. 这串连续的整数可以表示为:(x+1)+(x+2)+(x+3)+(x+4)+……+(x+i) , 其中x=0,1,2 ......

2. 假设已经找到:(x+1)+(x+2)+(x+3)+(x+4)+……+(x+i) =number;

3. A=number-(1+2+3+......+i)=number-(1+i)*i/2;

4. A=x*i;即A一定能被i整除,从而达到判定目的.

三、java代码

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int i,j,n,num,sum,temp;
		n=sc.nextInt();
		for(i=0;i<n;i++){
			num=sc.nextInt();
			sum=0;
			temp=sc.nextInt();
			for(j=2;(j+1)*j/2<=temp;j++){
				if((temp-(j+1)*j/2)%j==0)
					sum++;
			}
			System.out.println(num+" "+(sum));
		}
	}
}

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