Aug 12, 2024
Dr. Richard Bellman looks at a printout
(Alfred Eisenstaedt. 1962)
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Dr. Richard Bellman looks at a printout
(Alfred Eisenstaedt. 1962)
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để nhớ em tối ưu,
anh dùng quy hoạch động.
all-pairs shortest paths
In this article, we will cover a famous dynamic programming question, Climbing Stairs. Each time you can either climb 1 or 2 steps. In how m
Of some fields it is difficult to tell whether they are sound or phony. Perhaps they are both. Catastrophe theory started out with impeccable credentials, then turned out to resemble a three-dollar bill. Dynamic programming overcame a questionable background to be seen as substantial.
Gian-Carlo Rota, Discrete Thoughts
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Divide and Conquer
Divide and Conquer basically works in three steps.
1. Divide - It first divides the problem into small chunks or sub-problems. 2. Conquer - It then solve those sub-problems recursively so as to obtain a separate result for each sub-problem. 3. Combine - It then combine the results of those sub-problems to arrive at a final result of the main problem.
Some Divide and Conquer algorithms are Merge Sort, Binary Sort, etc.
Dynamic Programming
Dynamic Programming is similar to Divide and Conquer when it comes to dividing a large problem into sub-problems. But here, each sub-problem is solved only once. There is no recursion. The key in dynamic programming is remembering. That is why we store the result of sub-problems in a table so that we don't have to compute the result of a same sub-problem again and again.
Some algorithms that are solved using Dynamic Programming are Matrix Chain Multiplication, Tower of Hanoi puzzle, etc..
Solving a term of the Fibonacci sequence
Edsger Dijkstra: Computer science
English: Portrait of Edsger W. Dijkstra, one of the greatest mathematicans in history of modern mathematics. Tiếng Việt: Chân dung của Edsger W. Dijkstra, một trong những nhà toán học vĩ đại nhất trong lịch sử toán học hiện đại. Español: Retrato de Edsger W. Dijkstra, uno de los grandes matemáticos en la historia de la matemática moderna. Français : Portrait de Edsger W. Dijkstra, l’un des plus…
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[Leetcode] - Maximum Product Subarray Solution
In this blog post, we'll explore the "Maximum Product Subarray" problem, where our task is to find the contiguous subarray within an array that yields the maximum product. We'll discuss the problem statement in detail and explore two approaches: the brute
In the given problem statement, we have an array of integers and we need to find the maximum product possible for a contiguous subarray. The most important part of this problem is that the elements have to be contiguous. So special attention needs to be given for negative numbers and zeroes. Input: nums = [ 2 , 3 , -2 , 4 ] Output: 6 Explanation: [ 2 , 3 ] has the largest product 6. Fig:…
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