# Spiral Matrix II

## Problem

Given a positive integer *n*, generate a square matrix filled with elements from 1 to  $$n^2$$ in spiral order.  

{% hint style="info" %}
For example:

```
Input: 3
Output:
[
 [ 1, 2, 3 ],
 [ 8, 9, 4 ],
 [ 7, 6, 5 ]
]
```

{% endhint %}

###

### Thought Process

* *How would we go about changing the directions when filling the 2D matrix?*

  * Have a variable *d* for the direction and updating this variable whenever we "shave" off a row or column.

* *How would we generate the numbers to fill the 2D matrix from 1 to* $$n^2$$.
  * Have a varaible called *num* initially set 1, incrementing this variable at each cell, and filling each cell with the variable.

## Solution 

```
class Solution:
    def generateMatrix(self, n: int) -> List[List[int]]:
        
        matrix = [[0 for j in range(n)] for i in range(n)]
        d = 0
        num = 1
        top, bottom = 0, len(matrix)-1
        left,right = 0, len(matrix[0])-1
        
        while top<=bottom and left<=right:
            if d == 0:
                for j in range(left,right+1):
                    matrix[top][j] = num
                    num+=1
                top+=1
                d+=1
            elif d == 1:
                for i in range(top, bottom+1):
                    matrix[i][right] = num
                    num+=1
                right-=1
                d+=1
            elif d == 2:
                for j in range(right, left-1,-1):
                    matrix[bottom][j] = num
                    num+=1
                bottom-=1
                d+=1
            elif d == 3:
                for i in range(bottom, top-1,-1):
                    matrix[i][left] = num
                    num+=1
                left+=1
                d = 0
        return matrix
        
```

## Key Facts

* The direction and boundary variables are most important
* For updating the number, just have a *num* variable and increment by 1 in the for-loops
* With each direction, there is either a constant row or column (i.e. when doing in the down direction, the constant is the right column.)

## Time Complexity&#x20;

**Time:** O($$n^2$$) because we have to fill every row and column

**Space:** O($$n^2$$) because we are initilizing a matrix and storing the numbers here.


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