The sum problem

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Problem Description
Given a sequence 1,2,3,......N, your job is to calculate all the possible sub-sequences that the sum of the sub-sequence is M.
 

 

Input
Input contains multiple test cases. each case contains two integers N, M( 1 <= N, M <= 1000000000).input ends with N = M = 0.
 

 

Output
For each test case, print all the possible sub-sequence that its sum is M.The format is show in the sample below.print a blank line after each test case.
 

 

Sample Input
20 10 50 30 0 0
 

 

Sample Output
[1,4] [10,10] [4,8] [6,9] [9,11] [30,30]

 思路:

1.由高斯求和公式文字表述:和=(首项 + 末项)x项数 /2可知:

技术分享图片

区间[a,b]的各项和且b=a+i-1

 

2.转化该式子求出a,由a即可推导出b

     (a+b)*i/2 = m
     (a+b)*i = 2*m
     (a+ a+i-1)*i = 2*m
      2*a = 2*m/i + 1 – i

               a = m/i –(i-1)/2

 

3.限定循环次数,条件需满足a>=1,即m/i –(i-1)/2>=1,化简可得i <= (int)Math.sqrt(2 * m)

 

AC代码:

import java.util.Scanner;

public class Main {
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        while (sc.hasNext()) {
            int n = sc.nextInt();
            int m = sc.nextInt();
            //暴力法,但会LTE
//            if (m == 0 && n == 0) {
//                break;
//            }
//            for (int i = 1; i <= m; i++) {
//                int sum = 0;
//                for (int j = i; j <= m; j++) {
//                    sum += j;
//                    if (sum == m) {
//                        System.out.println("[" + i + "," + j + "]");
//                    }
//                }
//            }
//            System.out.println();
            //高斯公式法
            if(n == 0 && m == 0){
                break;
            }
            int a,b;
            for(int i = (int)Math.sqrt(2 * m); i > 0; i--){
                a = m / i - (i - 1) / 2;
                b = a + i - 1;
                if((a + b) * i == 2 * m){
                    System.out.println("[" + a + "," + b +"]");
                }
            }
            System.out.println();
        }
    }
}

  

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