Two Crystal Ball Problem Using JavaScript

Last updated on 18 Jan, 2023

Here is the Two Crystal Ball problem:

Given two crystal balls that will break if dropped from high enough distance, determine the exact spot in which it will break in the most optimized way.


To understand the problem, let us assume the crystal ball will break if dropped from a height of 8 meters. So, if we drop from 1 meter, the ball will not break(0). If dropped from height of 2 meter, again the ball will not break(0). We keep on doing it. When dropped from 8 meters, the ball will break(1). If we list all 0s and 1s in an array, it will look like below:

[0, 0, 0, 0, 0, 0, 0, 1, 1, 1...]

Basically, we want to find the first position of 1.

Another point here, is the array is sorted.

Since there are two balls, we can use first ball to find an approximate breaking point by jumping by a certain amount in each loop(sqrt(n) in our case). We will do linear search in that interval to find the correct breaking position.

Here is the code:

function twoCrystalBall(arr) {
  // Calculate jump length with sqrt of array length
  const jumpLength = Math.floor(Math.sqrt(arr.length));
  let i = 0;

  // Leaping through array with distance of jumplength in each leap
  for (; i < arr.length; i = i + jumpLength) {
    if (arr[i] == 1) {

  // Going back by one leap to start walking using linear search
  i = i - jumpLength;

  // Walk one by one using linear search
  for (let j = i; j < i + jumpLength; j++) {
    if (arr[j] == 1) {
      return j;

  // If reached here means, the ball is not breaking within this height
  return -1;

The Big O of this algorithm is O(sqrt(n)).

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Joby Joseph
Web Architect