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:
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*m2*a = 2*m/i + 1 – ia = 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(); } } }