function binarySearch(numbers, element) {
//time complexity is log(n) it excecutes very fast than linear search  n=arraylength;
  
return search(numbers,element,0,numbers.length-1)}

function search(numbers,element,left,right){
  if(left>right) return -1;
  
  let pivot =Math.floor((left+right)/2)
  
  if(numbers[pivot]===element) return pivot
  
   if(numbers[pivot]>element) return search(numbers,element,left,pivot-1)
  
    return search(numbers,element,pivot+1,right)
  
    
}

function binarySearch(numbers, element) {
//time complexity is log(n) it excecutes very fast than linear search  n=arraylength;
  let left = 0;
  let right = numbers.length - 1;
  
  while(left <= right) {
    let pivot = Math.floor((left + right) / 2);
    
    if(numbers[pivot]==element){
      return pivot;
    }
    else if(numbers[pivot]>element){
      right=pivot-1;
    }
    else{
      left=pivot+1;
    }
   }
  return -1;
}

function binarySearch(numbers, element) {

  let left = 0;
  let right = numbers.length - 1;
  
  while(left <= right) {
    let pivot = Math.floor((left + right) / 2);
    
    if(numbers[pivot]==element){
      return pivot;
    }
    else if(numbers[pivot]>element){
      right=pivot-1;
    }
    else{
      left=pivot+1;
    }
   }
  return -1;
}