> For the complete documentation index, see [llms.txt](https://protegejj.gitbook.io/my-algorithm-summary/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://protegejj.gitbook.io/my-algorithm-summary/chapter1/binary-search.md).

# Binary Search

### Binary Search

## 1. Implementation

### **(1) Search the index of  target in the given set**

```java
public int binarySearch(int[] nums, int target) {
        int start = 0, end = nums.length - 1, mid;

        while (start <= end) {
            mid = start + (end - start) / 2; // avoid overflow

            if (nums[mid] == target) {
               return mid;
            }
            else if (nums[mid] < target) {
                start = mid + 1;
            }
            else {
                end = mid - 1;
            }
        }
        return -1;
    }
```

### (2) Search the index of first element which is equal to target /

### Search the index of  first element which is equal or greater than target

```java
public int binarySearch(int[] nums, int target) {
        int start = 0, end = nums.length - 1, mid;

        while (start < end) {
            mid = start + (end - start) / 2;

            if (nums[mid] < target) {
                start = mid + 1;
            }
            else {
                end = mid;
            }
        }
        return start;
    }
```

### (3) Search the index of last element which is equal to target

```java
public int binarySearch(int[] nums, int target) {
        int start = 0, end = nums.length - 1, mid;

        while (start < end) {
            mid = start + (end - start) / 2;

            if (nums[mid] > target) {
                end = mid - 1;
            }
            else {
                start = mid;
            }
        }
        return end;
    }
```