Understanding Binary Search

Binary search is a powerful algorithm used to efficiently find the position of a target value within a sorted array or list. Its effectiveness lies in its ability to eliminate half of the remaining elements in each step, resulting in a logarithmic time complexity of O(log n), where n is the number of elements in the array.

Let’s break down how binary search works and provide a practical example in JavaScript.

How Binary Search Works

1 – Initial Setup:

  • Start with a sorted array.
  • Set two pointers, low and high, to the first and last indices of the array.

2 – Middle Element:

  • Find the middle element of the array: mid = Math.floor((low + high) / 2).

3 – Comparison:

  • Compare the middle element with the target value.

4 – Three Possible Cases:

  • If the middle element is equal to the target value, the search is successful.
  • If the middle element is greater than the target, update high to mid - 1 and search in the left half.
  • If the middle element is less than the target, update low to mid + 1 and search in the right half.

5 – Repeat:

    • Repeat steps 2-4 until the target value is found or low exceeds high.

    6 – Termination:

    • If low is greater than high, the target value is not in the array.

    Example in JavaScript

    Let’s implement a binary search algorithm in JavaScript:

    function binarySearch(arr, target) {
      let low = 0;
      let high = arr.length - 1;
      while (low <= high) {
        const mid = Math.floor((low + high) / 2);
        if (arr[mid] === target) {
          return mid; // Target found, return the index
        } else if (arr[mid] > target) {
          high = mid - 1; // Search in the left half
        } else {
          low = mid + 1; // Search in the right half
      return -1; // Target not found
    // Example usage:
    const sortedArray = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
    const targetValue = 7;
    const result = binarySearch(sortedArray, targetValue);
    if (result !== -1) {
      console.log(`Target ${targetValue} found at index ${result}.`);
    } else {
      console.log(`Target ${targetValue} not found in the array.`);

    In this example, we use a binarySearch function to find the index of a target value in a sorted array. The function returns the index if the target is found and -1 otherwise.

    Feel free to use this binary search algorithm in your projects when dealing with sorted data. Its efficiency makes it a valuable tool, especially for large datasets. Happy coding!

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