Searching Algorithms (linear search, binary search)

What is the optimal step size used in this jump search implementation?

function jumpSearch(arr, target) {
  const step = Math.floor(Math.sqrt(arr.length));
  let prev = 0;
  
  while(arr[Math.min(step, arr.length) - 1] < target) {
    prev = step;
    step += Math.floor(Math.sqrt(arr.length));
    if(prev >= arr.length) return -1;
  }
  
  while(arr[prev] < target) {
    prev++;
    if(prev === Math.min(step, arr.length)) return -1;
  }
  
  return arr[prev] === target ? prev : -1;
}

Array length
Square root of length
Jump search uses square root step size because: 1) Optimal balance between jump size and linear search, 2) Minimizes worst case time complexity, 3) Step size of √n is mathematically optimal, 4) Handles both small and large arrays efficiently, 5) Better than linear search for large sorted arrays, 6) Worse than binary search but simpler, 7) Good for searching on disk or external memory, 8) Balance between number of jumps and linear search distance.
Logarithm of length
Fixed step size

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