Write a 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). Use this program to find all distinct mintegers a, b, c, and d between 0 and 106 such that a3 + b3 = c3 + d3

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Merge sort

Merge Sort recursively sorts a given collection of numbers or elements by using the divide and conquer strategy in less time. It is one of the most used algorithms, with the worst-case time complexity of O (n log n). It was invented by John Von Neumann. The algorithm continuously divides an array into sub-arrays until each sub-array consists of a single element. It then merges those sub-arrays to produce a sorted array.