runtime complexity

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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I need help finding the runtime complexity Off the following code.

Here is the transcription of the image, suitable for display on an educational website:

---

/* In the worst-case scenario: what is the value of count for a sorted array A of size 'n'? */

```java
static int count = 0;
public static boolean binS(int[] A, int val) {
    return binS(A, val, 0, A.length-1);
}

public static boolean binS(int[] A, int val, int l, int h) {
    count++;
    if( l > h ) {
        return false;
    }
    int m = (l+h)/2;
    if( A[m] == val )
        return true;
    else if( A[m] < val )
        return binS(A, val, m+1, h);
    else
        return binS(A, val, l, m-1);
}
```

/* How would you describe the runtime of the above code?

In the best-case scenario, what is the value of count in the above code? */

---

**Explanation:**

The code above implements a recursive binary search algorithm for a sorted array `A`. Key points include:

- **Count Variable**: An integer `count` is initialized to zero and incremented with each recursive call to `binS`. This tracks the number of calls made in the search process.
  
- **Function binS**: 
  - **Parameters**: Takes an array `A`, a value `val`, and optionally, low `l` and high `h` indices for searching the subarray.
  - **Base Condition**: If `l > h`, it returns `false`, indicating the value is not found.
  - **Middle Calculation**: Computes the midpoint `m` as `(l + h) / 2`.
  - **Comparison**: Checks if the middle element `A[m]` equals the target value `val`.
    - If equal, returns `true`.
    - If `A[m]` is less than `val`, searches the right subarray.
    - Otherwise, searches the left subarray.

- **Runtime Considerations**: 
  - **Worst-Case Scenario**: The value of `count` will be O(log n), indicating the number of recursive calls made when the element is not found.
  - **Best-Case Scenario**: `count` will be 1 if the middle element is the
Transcribed Image Text:Here is the transcription of the image, suitable for display on an educational website: --- /* In the worst-case scenario: what is the value of count for a sorted array A of size 'n'? */ ```java static int count = 0; public static boolean binS(int[] A, int val) { return binS(A, val, 0, A.length-1); } public static boolean binS(int[] A, int val, int l, int h) { count++; if( l > h ) { return false; } int m = (l+h)/2; if( A[m] == val ) return true; else if( A[m] < val ) return binS(A, val, m+1, h); else return binS(A, val, l, m-1); } ``` /* How would you describe the runtime of the above code? In the best-case scenario, what is the value of count in the above code? */ --- **Explanation:** The code above implements a recursive binary search algorithm for a sorted array `A`. Key points include: - **Count Variable**: An integer `count` is initialized to zero and incremented with each recursive call to `binS`. This tracks the number of calls made in the search process. - **Function binS**: - **Parameters**: Takes an array `A`, a value `val`, and optionally, low `l` and high `h` indices for searching the subarray. - **Base Condition**: If `l > h`, it returns `false`, indicating the value is not found. - **Middle Calculation**: Computes the midpoint `m` as `(l + h) / 2`. - **Comparison**: Checks if the middle element `A[m]` equals the target value `val`. - If equal, returns `true`. - If `A[m]` is less than `val`, searches the right subarray. - Otherwise, searches the left subarray. - **Runtime Considerations**: - **Worst-Case Scenario**: The value of `count` will be O(log n), indicating the number of recursive calls made when the element is not found. - **Best-Case Scenario**: `count` will be 1 if the middle element is the
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