A triangle is a Heron’s triangle if it satisfies that the side lengths of it are consecutive integers t-1, t, t+ 1 and thatits area is an integer. Now, for given n you need to find a Heron’s triangle associated with the smallest t bigger than or equal to n. Input The input contains multiple test cases. The first line of a multiple input is an integer T (1 ≤ T ≤ 30000) followedby T lines. Each line contains an integer N (1 ≤ N ≤ 10^30). Output For each test case, output the smallest t in a line. If the Heron’s triangle required does not exist, output -1. Sample Input 4 1 2 3 4 Sample Output 4 4 4 4

• 題意:給你一個n,在t>=n的範圍內求一個數t.使得t-1,t,t+1所組成的三角形面接為整數.

• 解題思路:打一個表,發現遞增的很快,並且遞迴方程為s[n]=4*s[n-1]-s[n-2].由於資料太大,因此用java大數表示.

import java.math.BigInteger;
import java.math.*;
import java.util.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner input = new Scanner
 
(System.in);
        BigInteger []m=new BigInteger[60];
        m[0]=BigInteger.valueOf(2);
        m[1]=BigInteger.valueOf(4);
        for(int i=2;i<60;i++) {
        	m[i]=m[i-1].multiply(BigInteger.valueOf(4)).subtract(m[i-2]);
        }
        int t;t=input.nextInt();
        for(int j=0;j<t;
 
j++){
        	BigInteger h;
        	h=input.nextBigInteger();
        	for(int i=1;i<60;i++) {
        		if(m[i].compareTo(h)>=0) {System.out.println(m[i]);break;}
        	}
        }
    }
}