Linear Search

A simple approach is to do linear search, i.e

Start from the leftmost element of arr[] and one by one compare x with each element of arr[].

If x matches with an element, return the index.

If x doesn't match with any of elements, return -1.

                    
// Linearly search x in arr[].  If x is present then return its 
// location,  otherwise return -1
int search(int arr[], int n, int x){
    int i;
    for (i=0; i<n; i++){
        if (arr[i] == x)
            return i;
    }
    return -1;
}

Binary Search

Search a sorted array by repeatedly dividing the search interval in half. Begin with an interval covering the whole array. If the value of the search key is less than the item in the middle of the interval, narrow the interval to the lower half. Otherwise narrow it to the upper half. Repeatedly check until the value is found or the interval is empty.
We basically ignore half of the elements just after one comparison.

Compare x with the middle element.

If x matches with middle element, we return the mid index.

Else If x is greater than the mid element, then x can only lie in right half subarray after the mid element. So we recur for right half.

Else (x is smaller) recur for the left half.

                    
// A recursive binary search function. It returns location of x in
// given array arr[l..r] is present, otherwise -1
int binarySearch(int arr[], int l, int r, int x){
   if (r >= l){
        int mid = l + (r - l)/2;
 
        // If the element is present at the middle itself
        if (arr[mid] == x)  return mid;
 
        // If element is smaller than mid, then it can only be present
        // in left subarray
        if (arr[mid] > x) return binarySearch(arr, l, mid-1, x);
 
        // Else the element can only be present in right subarray
        return binarySearch(arr, mid+1, r, x);
   }
 
   // We reach here when element is not present in array
   return -1;
}