How Pascal trigle is considered to be a divide and conquer algorithm ?
What are the divide, conquer, merge steps ?
Although I have the same confusion, I think we could try to think the divide and conquer as:
(1)divide: split the question to smaller size (recursively)
(2)conquer: solve the smallest version of problem( first row of the triagle)
(3)merge: use the smaller version result to build bigger result( calc next row based on current row)
However, I think the Time complexity is not O(n), because eventually we calculated all the numbers in the triangle. which is 0.5n^2 numbers. the time complexity should be O(n^2).
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I disagree. This is no division and conquering and no merging. We narrowed down the problem to the minimum scope and construct the solution after reaching the base case. If this is a Divide and conquer technique, the pascaltrianglefunction(5) should be split into pascaltrianglefunction(2) and pascaltrianglefunction(3) where each function provides partial results and these can be combined to final answer.
However, the code is not implemented this way. That was purely a normal recursive approach. And the time complexity is O(n^2)
Hi @mohamed2
The Pascal triangle can indeed be considered a divide and conquer algorithm, albeit in a slightly different sense compared to traditional divide and conquer algorithms. Let’s break down the steps:
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Divide: Each row in the Pascal triangle can be considered a smaller version of the overall problem. By iteratively generating rows, we’re essentially dividing the problem into smaller subproblems.
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Conquer: When we reach the base case (the first row of the triangle), we have solved the smallest version of the problem.
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Merge: While there isn’t a traditional merging step, we’re using the results of the smaller versions (previous rows) to build the next row. So in a sense, we’re merging the results of smaller subproblems to construct the solution for larger subproblems.
Regarding the time complexity, you’re correct that eventually, we calculate all the numbers in the triangle, resulting in O(n^2) complexity.
In summary, while the Pascal triangle problem shares some similarities with divide and conquer algorithms, it’s not a perfect fit for the model. It’s more of a recursive construction of the solution iteratively rather than dividing into strictly smaller subproblems.
I hope it helps. Happy Learning 
Hi @Jo_Wang !!
Your breakdown of divide, conquer, and merge steps is quite insightful. Indeed, the Pascal triangle problem doesn’t follow the traditional divide and conquer pattern in the sense of dividing into strictly smaller subproblems. Instead, it’s more like iteratively solving smaller instances to construct the larger solution. The time complexity being O(n^2) is also accurate because we’re computing all the numbers in the triangle.
In summary, while the Pascal triangle problem shares some similarities with divide and conquer algorithms, it’s not a perfect fit for the model. It’s more of a recursive construction of the solution iteratively rather than dividing into strictly smaller subproblems.
I hope it helps. Happy Learning
Hi @Haritha_Nagubady!!
You raise a valid point that the Pascal triangle function doesn’t strictly adhere to the traditional divide and conquer paradigm, especially in terms of how it’s implemented. It’s more of a recursive approach where we construct the solution iteratively rather than splitting the problem into strictly smaller subproblems.
The time complexity being O(n^2) is indeed correct, as we’re calculating all the numbers in the triangle, resulting in quadratic complexity.
In summary, while the Pascal triangle problem shares some similarities with divide and conquer algorithms, it’s not a perfect fit for the model. It’s more of a recursive construction of the solution iteratively rather than dividing into strictly smaller subproblems.
I hope it helps. Happy Learning