The following algorithm determines if all the numbers in the vector are different from each other, i.e., they are all distinct values. Explain when the best-case running time happens. Determine the Ω function for this algorithm.```cppbool allDistinct(const vector& a) { for (int i = 0; i < a.size() - 1; i++) { for (int j = i+1; j < a.size(); j++) { if (a[i] == a[j]) return false; } } return true;}```| | # of primitive operations ||------------------|---------------------------|| (Content missing) | |**Explanation:**- **Outer Loop:** Iterates from 0 to `a.size() - 1`.- **Inner Loop:** Starts from `i+1` up to `a.size()`.- **Comparison:** Checks if any two elements are equal (`a[i] == a[j]`).- **Return:** If a duplicate is found, the function returns `false`. If the loop completes, it returns `true`.**Best-Case Scenario:**The best-case running time occurs when the first pair `(a[i], a[j])` has an equal value, causing the algorithm to return `false` immediately. This scenario gives a best-case complexity of Ω(1) because the loop exits after the first comparison.

Best Case Running Time : The best case runtime is a process that users are refreshing the…

The following algorithm determines if all the numbers in the vector are different from each other, i.e. they are all distinct values. Explain when the best-case running time happens. Determine the function for this algorithm. bool all Distinct(const vector& a) { for (int i = 0; i < a.size()-1; i++) { for (int j =i+1; j < a.size(); j++){ if (a[i] == a[j]) } return false; # of primitive operations

The following algorithm determines if all the numbers in the vector are different from each other, i.e. they are all distinct values. Explain when the best-case running time happens. Determine the function for this algorithm. bool all Distinct(const vector& a) { for (int i = 0; i < a.size()-1; i++) { for (int j =i+1; j < a.size(); j++){ if (a[i] == a[j]) } return false; # of primitive operations

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

Problem 1PE

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Concept explainers

Topological Sort

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.

Question

The following algorithm determines if all the numbers in the vector are different from each other, i.e., they are all distinct values. Explain when the best-case running time happens. Determine the Ω function for this algorithm.

```cpp
bool allDistinct(const vector<int>& a) {

for (int i = 0; i < a.size() - 1; i++) {

for (int j = i+1; j < a.size(); j++) {

if (a[i] == a[j])

return false;

}

}

return true;
}
```

| | # of primitive operations |
|------------------|---------------------------|
| (Content missing) | |

**Explanation:**

- **Outer Loop:** Iterates from 0 to `a.size() - 1`.
- **Inner Loop:** Starts from `i+1` up to `a.size()`.
- **Comparison:** Checks if any two elements are equal (`a[i] == a[j]`).
- **Return:** If a duplicate is found, the function returns `false`. If the loop completes, it returns `true`.

**Best-Case Scenario:**
The best-case running time occurs when the first pair `(a[i], a[j])` has an equal value, causing the algorithm to return `false` immediately. This scenario gives a best-case complexity of Ω(1) because the loop exits after the first comparison.

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