Find all the quadruples [a, b, c, d] where a^3 + b^3 = c^3 + d^3 when 1 <= a, b, c or d <= 10000 [closed]

Answer 1

Starting with the brute force approach, its pretty obvious it will O(n^4) time to execute. If space is not a constraint, we can go for combination of list and maps. The code is self-explanatory, we are using a nested list to keep track of all entries for a particular sum (key in map). The time complexity is thus reduced from O(n^4) to O(n^2)

public void printAllCubes() {
  int n = 50;
  Map> resMap = new HashMap>();
  ArrayList pairs = new ArrayList();
  ArrayList allPairsList = new ArrayList();
  for (int c = 1; c < n; c++) {
    for (int d = 1; d < n; d++) {
      int res = (int) (Math.pow(c, 3) + Math.pow(d, 3));
      pairs.add(c);
      pairs.add(d);
      if (resMap.get(res) == null) {
        allPairsList = new ArrayList();
      } else {
        allPairsList = resMap.get(res);
      }
      allPairsList.add(pairs);
      resMap.put(res, allPairsList);
      pairs = new ArrayList();
    }
  }

  for (int a = 1; a < n; a++) {
    for (int b = 1; b < n; b++) {
      int result = (int) (Math.pow(a, 3) + Math.pow(b, 3));
      ArrayList pairList = resMap.get(result);
      for (List p : pairList) {
        System.out.print(a + " " + b + " ");
        for (Object num : p)
          System.out.print(num + " ");
        System.out.println();
      }
    }
  }
}