计算数论 [英] computational number theory

问题描述

此程序CubeSum.java可按排序顺序打印出a3 + b3形式的所有整数，其中a和b是按排序顺序在0到N之间的整数.

也就是说，与其计算N2和的数组并对其进行排序，不如建立一个面向最低优先级的队列，该队列最初包含(03，0，0)，(13，1，0)，(23，2，0)， ...，(N3，N，0).

然后，当优先级队列为非空时，删除最小的项(i3 + j3，i，j)，打印它，然后如果j< N，插入项目(i3 +(j + 1)3，i，j + 1).

This program CubeSum.java that prints out all integers of the form a3 + b3 where a and b are integers between 0 and N in sorted order, without using excessive space.

That is, instead of computing an array of the N2 sums and sorting them, build a minimum-oriented priority queue, initially containing (03, 0, 0), (13, 1, 0), (23, 2, 0), ..., (N3, N, 0).

Then, while the priority queue is nonempty, remove the smallest item (i3 + j3, i, j), print it, and then, if j < N, insert the item (i3 + (j+1)3, i, j+1).

public class CubeSum implements Comparable<CubeSum> {
    private final int sum;
    private final int sum2;
    private final int i;
    private final int j;
    private final int a;
    private final int b;

    public CubeSum(int i, int j,int a, int b) {
        this.sum = i*i*i + j*j*j;
        this.i = i;
        this.j = j;
        this.a = a;
        this.b = b;
        this.sum2 = a * a * a + b * b * b;

    }
public CubeSum(int w

    public int compareTo(CubeSum that) {
        if (this.sum < that.sum) return -1;
        if (this.sum < that.sum) return +1;
        return 0;
    }

    public String toString() {
        return sum + " = " + i + "^3" + " + " + j + "^3";
    }


    public static void main(String[] args) {

        int N = Integer.parseInt(args[0]);

        // initialize priority queue
        MinPQ<CubeSum> pq = new MinPQ<CubeSum>();
        pq.insert(new CubeSum(0,1);
         
        for (int i = 0,j = 1; i & j <= N; i+=2,j+=2) {
            pq.insert(new CubeSum(i, i,j,j,));
            if(i>0 && j>1)
{
            pq.insert(new CubeSum(0,i,0,j);
}
}
for(int i =0;i<N;i++)
{
for(int j=i+1;j<N;j++)
{
if(pq.sum[i] == pq.sum2[j])
System.out.println("the sum is" + sum[i] + "and the value of i is" + pq.i + " and j is" + pq.j + "and a is" + pq.a + "and b is " + pq.b
}
        }

        // find smallest sum, print it out, and update
        while (!pq.isEmpty()) {
            CubeSum s = pq.delMin();
            StdOut.println(s);
            
        }
    }

}

现在对如何使用该程序查找0和10 ^ 6之间的所有不同整数a，b，c和d感到困惑，例如a3 + b3 = c3 + d3，例如1729 = 9 ^ 3 + 10 ^ 3 = 1 ^ 3 + 12 ^ 3.

am now confused on how to use this program to find all distinct integers a, b, c, and d between 0 and 10^6 such that a3 + b3 = c3 + d3, e.g., 1729 = 9^3 + 10^3 = 1^3 + 12^3.

推荐答案

@理查德我不知道是谁张贴了以前的作品....这不是家庭作业....这只是我想做的一个项目.

@ richard i dont know who posted that previous work.... and this is not a homework assignment....it is just a project iam trying to do.

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