Summary of "L7. All Kind of Patterns in Recursion | Print All | Print one | Count"
Summary of "L7. All Kind of Patterns in Recursion | Print All | Print One | Count"
In this video, the speaker discusses various patterns in Recursion, particularly focusing on Subsequences and their sums. The main goal is to print Subsequences whose sum equals a given value k. The speaker emphasizes the importance of understanding these techniques as they will be crucial in Dynamic Programming.
Main Ideas and Concepts:
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Recursion Basics:
- The speaker introduces the concept of Recursion and how it can be applied to problems involving Subsequences.
- The technique of "take and not take" is highlighted as a fundamental approach for solving these problems.
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Printing Subsequences:
- Given an array (e.g., [1, 2, 1]) and a target sum (e.g., 2), the speaker demonstrates how to identify and print all Subsequences that sum to this target.
- The recursive tree structure is explained, detailing how decisions at each index lead to different branches of the Recursion.
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Algorithm Steps:
- Start with an empty data structure and a sum initialized to zero.
- For each element, decide to either include it in the current subsequence (pick) or exclude it (not pick).
- When reaching the end of the array, check if the current sum matches the target; if it does, print the subsequence.
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Pseudocode Structure:
- The speaker provides a Pseudocode outline that includes parameters for the current index, the data structure holding the current subsequence, and the current sum.
- The Pseudocode includes conditions for printing the subsequence when the target sum is reached.
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Modifying the Problem:
- The speaker modifies the problem to print only one valid subsequence instead of all. This is done using a boolean flag to indicate when a valid subsequence has been found, allowing the Recursion to terminate early.
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Counting Subsequences:
- A method for counting the number of valid Subsequences is introduced. The base case returns 1 if a valid subsequence is found and 0 otherwise.
- The recursive calls are summed to provide the total count of valid Subsequences.
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Time Complexity:
- The Time Complexity of the recursive approach is discussed, noting that it can be O(2n) due to the binary choices at each index.
- An optimization is suggested for cases where the array contains only positive numbers.
Methodology and Instructions:
- To Print All Subsequences:
- Initialize an empty data structure and a sum variable.
- Recursively explore each index, deciding to include or exclude each element.
- Print the data structure when the target sum is reached.
- To Print One Subsequence:
- Use a boolean flag to track if a valid subsequence has been found.
- Return true when a valid subsequence is printed to avoid further recursive calls.
- To Count Subsequences:
- Return 1 if a valid subsequence is found and 0 if not.
- Sum the results of recursive calls to get the total count.
Speakers or Sources Featured:
The video is presented by a single speaker who provides detailed explanations and coding demonstrations throughout the session.
Category
Educational
