Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Question
Rearrange to the code to insert each element into 'left' if it is smaller than the largest element of left.
You can find the median element of a sequence by using two priority queues, left and right, where right is a min-heap. Insert each element into left if it is smaller than the largest element of left, or into right otherwise. Then rebalance the priority queues so that their sizes differ by at most 1.
Rearrange the following lines of code to implement this
![Certainly! Below is the transcription and explanation of the code snippet from the image, suitable for an educational website:
### Code Snippet
```cpp
Unused
if (left.size() < right.size())
{
if (a[i] <= left.top())
{
right.push(-a[i]);
}
}
else if (left.size() > right.size() + 1)
{
left.push(a[0]);
for (int i = 1; i < n; i++)
{
left.push(a[i]);
}
else
{
right.push(-left.top()); left.pop();
}
}
return median;
left.push(-right.top()); right.pop();
int median = left.top();
```
### Explanation
This code appears to implement part of an algorithm to find the median of an array using two heaps (`left` and `right`). These heaps typically represent the two halves of the data, helping efficiently find the median as elements are added.
- **Heaps Structure:**
- `left`: Typically a max heap.
- `right`: Typically a min heap.
- **Process:**
- The algorithm balances two heaps to make sure their sizes do not differ by more than one.
- If the left heap has fewer elements than the right, the element `a[i]` is evaluated. If `a[i]` is less than or equal to the top of the `left`, it is pushed onto the `right` heap (negated to simulate max heap behavior using a min heap).
- If the left heap has more elements than the right by more than one, elements are added to the `left` heap (starting with `a[0]` and iterating to include others), and balancing is achieved by moving elements from the top of `left` to `right`.
- **Return Median:**
- After balancing, the median is identified usually as either the top of the `left` heap or an average of the tops of both heaps, depending on the total number of elements.
### Note
This code snippet appears incomplete or extracted from a larger context, given that some structures (`left`, `right`, `a`, `n`) are not fully defined within this fragment.](https://content.bartleby.com/qna-images/question/6a04cd63-2ba9-4f83-bc88-6194bfc3fa72/7616ece8-b446-49ca-a994-1418e72de39e/nq4fja_processed.jpeg)
Transcribed Image Text:Certainly! Below is the transcription and explanation of the code snippet from the image, suitable for an educational website:
### Code Snippet
```cpp
Unused
if (left.size() < right.size())
{
if (a[i] <= left.top())
{
right.push(-a[i]);
}
}
else if (left.size() > right.size() + 1)
{
left.push(a[0]);
for (int i = 1; i < n; i++)
{
left.push(a[i]);
}
else
{
right.push(-left.top()); left.pop();
}
}
return median;
left.push(-right.top()); right.pop();
int median = left.top();
```
### Explanation
This code appears to implement part of an algorithm to find the median of an array using two heaps (`left` and `right`). These heaps typically represent the two halves of the data, helping efficiently find the median as elements are added.
- **Heaps Structure:**
- `left`: Typically a max heap.
- `right`: Typically a min heap.
- **Process:**
- The algorithm balances two heaps to make sure their sizes do not differ by more than one.
- If the left heap has fewer elements than the right, the element `a[i]` is evaluated. If `a[i]` is less than or equal to the top of the `left`, it is pushed onto the `right` heap (negated to simulate max heap behavior using a min heap).
- If the left heap has more elements than the right by more than one, elements are added to the `left` heap (starting with `a[0]` and iterating to include others), and balancing is achieved by moving elements from the top of `left` to `right`.
- **Return Median:**
- After balancing, the median is identified usually as either the top of the `left` heap or an average of the tops of both heaps, depending on the total number of elements.
### Note
This code snippet appears incomplete or extracted from a larger context, given that some structures (`left`, `right`, `a`, `n`) are not fully defined within this fragment.
![```cpp
#include <iostream>
#include <vector>
#include <queue>
#include <bits/stdc++.h>
using namespace std;
int get_median(vector<int> a, int n)
{
priority_queue<int> left;
priority_queue<int> right;
}
int main()
{
vector<int> a;
int i;
cin >> i;
while (i)
{
a.push_back(i);
cin >> i;
}
int median = get_median(a, a.size());
sort(a.begin(), a.end());
cout << "Sorted: (";
for (int x = 0; x < a.size(); x++)
{
cout << a[x];
if (x != a.size() - 1) cout << ", ";
}
cout << ")" << endl;
cout << "Median: " << median << endl;
return 0;
}
```
### Explanation:
This C++ program is designed to read a sequence of integers from the input, sort them, and then determine the median of these integers. The program structure includes:
1. **Libraries Included**:
- `<iostream>`: For input and output operations.
- `<vector>`: To use the vector container.
- `<queue>`: Possibly used for handling queues, although not fully implemented.
- `<bits/stdc++.h>`: A header to include almost all standard library headers.
2. **Namespaces**:
- `using namespace std;`: To avoid needing to prefix standard library names with `std::`.
3. **Functions**:
- `get_median(vector<int> a, int n)`: Placeholder function intended to calculate the median, but its implementation is incomplete.
4. **Main Function**:
- Reads integers into a vector `a` until a zero is entered.
- Sorts the vector `a`.
- Prints the sorted vector.
- Attempts to compute and print the median using the `get_median` function, although this function does not have implementation details.
5. **Control Flow**:
- A `while` loop to collect integers until zero is entered.
- A `for` loop to iterate through the sorted vector and format the output.
### Graphs or Diagrams:
There are no graphs or diagrams in this code.](https://content.bartleby.com/qna-images/question/6a04cd63-2ba9-4f83-bc88-6194bfc3fa72/7616ece8-b446-49ca-a994-1418e72de39e/eq5m3ow_processed.jpeg)
Transcribed Image Text:```cpp
#include <iostream>
#include <vector>
#include <queue>
#include <bits/stdc++.h>
using namespace std;
int get_median(vector<int> a, int n)
{
priority_queue<int> left;
priority_queue<int> right;
}
int main()
{
vector<int> a;
int i;
cin >> i;
while (i)
{
a.push_back(i);
cin >> i;
}
int median = get_median(a, a.size());
sort(a.begin(), a.end());
cout << "Sorted: (";
for (int x = 0; x < a.size(); x++)
{
cout << a[x];
if (x != a.size() - 1) cout << ", ";
}
cout << ")" << endl;
cout << "Median: " << median << endl;
return 0;
}
```
### Explanation:
This C++ program is designed to read a sequence of integers from the input, sort them, and then determine the median of these integers. The program structure includes:
1. **Libraries Included**:
- `<iostream>`: For input and output operations.
- `<vector>`: To use the vector container.
- `<queue>`: Possibly used for handling queues, although not fully implemented.
- `<bits/stdc++.h>`: A header to include almost all standard library headers.
2. **Namespaces**:
- `using namespace std;`: To avoid needing to prefix standard library names with `std::`.
3. **Functions**:
- `get_median(vector<int> a, int n)`: Placeholder function intended to calculate the median, but its implementation is incomplete.
4. **Main Function**:
- Reads integers into a vector `a` until a zero is entered.
- Sorts the vector `a`.
- Prints the sorted vector.
- Attempts to compute and print the median using the `get_median` function, although this function does not have implementation details.
5. **Control Flow**:
- A `while` loop to collect integers until zero is entered.
- A `for` loop to iterate through the sorted vector and format the output.
### Graphs or Diagrams:
There are no graphs or diagrams in this code.
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