Binary Search Algorithm

Definition

Binary Search is a searching algorithm used in a sorted array by repeatedly dividing the search interval in half. The idea of binary search is to use the information that the array is sorted and reduce the time complexity to O(Log n).

---

Comparsion

Binary Search Big O Notation is O(log n), Compared to Linear Search which Has Time Complexity of O(n).

Binary Search is able to search sorted arrays much faster than Linear Search.

---

Real Life Example

I'm thinking of a number from 1 to 50, The answer is 1

Linear Search

Number = 50 ? No Number = 49 ? No ... Number = 2 ? No Number = 1 ? Yes!

It takes 50 Guesses at Worst Case!

Binary Search

Number = 25 ? No, Less Number = 12 ? No, Less Number = 6 ? No, Less Number = 3 ? No, Less Number = 2 ? No, Less Number = 1 ? Yes!

It takes 6 Guesses at Worst Case!

Conclusion

Assuming 1,000,000 Numbers! Linear Search would result in a 1,000,000 Guesses (Worst Case) Binary Search would result in a 20 Guesses (Worst Case)

---

Visualization

Binary Search

Linear Search

---

Coding

const binarySearch = (sortedArr, value) => {
  let left = 0;
  let right = sortedArr.length - 1;

  while (left <= right) {
    const mid = Math.floor((left + right) / 2);
    const midVal = sortedArr[mid];

    if (midVal === value) {
      return mid;
    } else if (midVal < value) {
      left = mid + 1;
    } else {
      right = mid - 1;
    }
  }

  return -1;
};

---