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What happens when a top-down approach of dynamic programming is applied to any problem?
- a)It increases both, the time complexity and the space complexity
- b)It increases the space complexity and decreases the time complexity.
- c)It increases the time complexity and decreases the space complexity
- d)It decreases both, the time complexity and the space complexity
Correct answer is option 'B'. Can you explain this answer?
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What happens when a top-down approach of dynamic programming is applie...
As the mentioned approach uses the memoization technique it always stores the previously calculated values. Due to this, the time complexity is decreased but the space complexity is increased.
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What happens when a top-down approach of dynamic programming is applie...
Explanation:
Dynamic programming is an algorithmic technique used to solve problems by breaking them down into smaller subproblems and solving each subproblem only once. There are two approaches to dynamic programming: top-down (memoization) and bottom-up (tabulation).
Top-down approach involves solving larger problems by recursively solving smaller subproblems. The results of solved subproblems are stored in a table for reuse in future calculations. This approach is also called memoization because it involves memoizing (i.e., storing) the results of solved subproblems.
When a top-down approach of dynamic programming is applied to any problem, the following happens:
1. Time complexity increases: The recursive nature of the top-down approach means that the algorithm has to repeatedly solve the same subproblems multiple times. This can lead to an increase in time complexity.
2. Space complexity increases: The memoization table used to store the results of solved subproblems can take up a significant amount of space. Therefore, the space complexity of the algorithm can increase.
3. Time complexity decreases: However, if the memoization table is used properly, it can help reduce the time complexity of the algorithm. This is because the algorithm can reuse the results of solved subproblems instead of solving them again.
4. Space complexity decreases: The top-down approach can also help reduce the space complexity of the algorithm if the memoization table is used properly. This is because the algorithm only needs to store the results of solved subproblems instead of storing all possible subproblems.
Therefore, the correct answer is option B: It increases the space complexity and decreases the time complexity.
Dynamic programming is an algorithmic technique used to solve problems by breaking them down into smaller subproblems and solving each subproblem only once. There are two approaches to dynamic programming: top-down (memoization) and bottom-up (tabulation).
Top-down approach involves solving larger problems by recursively solving smaller subproblems. The results of solved subproblems are stored in a table for reuse in future calculations. This approach is also called memoization because it involves memoizing (i.e., storing) the results of solved subproblems.
When a top-down approach of dynamic programming is applied to any problem, the following happens:
1. Time complexity increases: The recursive nature of the top-down approach means that the algorithm has to repeatedly solve the same subproblems multiple times. This can lead to an increase in time complexity.
2. Space complexity increases: The memoization table used to store the results of solved subproblems can take up a significant amount of space. Therefore, the space complexity of the algorithm can increase.
3. Time complexity decreases: However, if the memoization table is used properly, it can help reduce the time complexity of the algorithm. This is because the algorithm can reuse the results of solved subproblems instead of solving them again.
4. Space complexity decreases: The top-down approach can also help reduce the space complexity of the algorithm if the memoization table is used properly. This is because the algorithm only needs to store the results of solved subproblems instead of storing all possible subproblems.
Therefore, the correct answer is option B: It increases the space complexity and decreases the time complexity.
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What happens when a top-down approach of dynamic programming is applie...
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What happens when a top-down approach of dynamic programming is applied to any problem?a)It increases both, the time complexity and the space complexityb)It increases the space complexity and decreases the time complexity.c)It increases the time complexity and decreases the space complexityd)It decreases both, the time complexity and the space complexityCorrect answer is option 'B'. Can you explain this answer?
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