# heapq in Python to print all elements in sorted order from row and column wise sorted matrix

Given a row and column wise sorted matrix, we can use the `heapq`

module in Python to print all the elements in sorted order.

The `heapq`

module provides an implementation of the heap queue algorithm, also known as the priority queue algorithm. It allows us to maintain a heap data structure, which is a binary tree that satisfies the heap property. In a min-heap, the parent node is always smaller than its children, while in a max-heap, the parent node is always larger than its children.

To use `heapq`

to print all the elements in sorted order from a row and column wise sorted matrix, we can follow these steps:

- Import the
`heapq`

module. - Create an empty list to store the elements from the matrix.
- Iterate over each row in the matrix.
- For each row, iterate over each element in the row and add it to the list.
- Use the
`heapq.heapify()`

function to convert the list into a heap. - Use the
`heapq.heappop()`

function to remove the smallest element from the heap and print it. - Repeat step 6 until the heap is empty.

Here's an example implementation:

```
import heapq
def print_sorted(matrix):
# Step 2
elements = []
# Step 3
for row in matrix:
# Step 4
for element in row:
elements.append(element)
# Step 5
heapq.heapify(elements)
# Step 6 and 7
while elements:
print(heapq.heappop(elements), end=' ')
```

Let's test this function with a sample matrix:

```
matrix = [
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]
print_sorted(matrix)
```

Output:

```
1 2 3 4 5 6 7 8 9
```

Another method to solve this problem is to use the `sorted()`

function with a key function that returns the element at the current index in the matrix. Here's an example implementation:

```
def print_sorted(matrix):
# Step 2
elements = []
# Step 3
for row in matrix:
# Step 4
for element in row:
elements.append(element)
# Step 5
sorted_elements = sorted(elements, key=lambda x: (x // len(matrix[0]), x % len(matrix[0])))
# Step 6 and 7
for element in sorted_elements:
print(element, end=' ')
```

In this implementation, we first create a list of all the elements in the matrix, and then use the `sorted()`

function to sort the list based on the row and column indices of each element. The `key`

function returns a tuple of the row and column indices of each element, which is used to sort the list. Finally, we iterate over the sorted list and print each element.

Let's test this function with the same sample matrix:

```
matrix = [
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]
print_sorted(matrix)
```

Output:

```
1 2 3 4 5 6 7 8 9
```