<p>Given a 2D integer array <code>nums</code>, return <em>all elements of </em><code>nums</code><em> in diagonal order as shown in the below images</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/08/sample_1_1784.png" style="width: 158px; height: 143px;" />
<pre>
<strong>Input:</strong> nums = [[1,2,3],[4,5,6],[7,8,9]]
<strong>Output:</strong> [1,4,2,7,5,3,8,6,9]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/08/sample_2_1784.png" style="width: 230px; height: 177px;" />
<pre>
<strong>Input:</strong> nums = [[1,2,3,4,5],[6,7],[8],[9,10,11],[12,13,14,15,16]]
<strong>Output:</strong> [1,6,2,8,7,3,9,4,12,10,5,13,11,14,15,16]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i].length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= sum(nums[i].length) &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i][j] &lt;= 10<sup>5</sup></code></li>
</ul>

from typing import List, Optional


class Solution:
    
    def findDiagonalOrder(self, nums: List[List[int]]) -> List[int]:

        result: List[int] = []

        seen = set()
        
        fringe = [(0, 0)]
        while len(fringe) > 0:
            (i, j) = fringe.pop()
            result.append(nums[i][j])

            # First, add element below (if any) to fringe:
            if (i + 1, j) not in seen and self.has_element_at(nums, i + 1, j):
                seen.add((i + 1, j))
                fringe.insert(0, (i + 1, j))

            # Then, add element to the right (if any) to fringe:
            if (i, j + 1) not in seen and self.has_element_at(nums, i, j + 1):
                seen.add((i, j + 1))
                fringe.insert(0, (i, j + 1))
        
        return result

    def has_element_at(self, nums: List[List[int]], i: int, j: int) -> bool:
        if 0 <= i < len(nums):
            row = nums[i]
            if 0 <= j < len(row):
                return True
            else:
                return False
        else:
            return False

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