Question

Computer Science

Posted 5 months ago

`write test cases for a function that computes the left Riemann's sum`

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Answer from Sia

Posted 5 months ago

python

python

Explanation

The left_riemann_sum function calculates the left Riemann sum by summing the areas of rectangles under the curve of the function f, using the left endpoints of subintervals. The test_left_riemann_sum function defines test cases to verify the correctness of the left_riemann_sum function.

Step-by-step Instruction

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Implement the computation by dividing the interval into n subintervals, calculating the width of each subinterval, and summing the areas of the rectangles

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Define the test_left_riemann_sum function to test the left_riemann_sum function with specific use cases

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Use a simple linear function f(x) = x for testing because its integral can be easily calculated manually, providing clear expected results for comparison

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Write assertions to compare the computed left Riemann sum with the expected results for the given test cases

Time Complexity

The time complexity of the left_riemann_sum function is O(n) because it involves a loop that iterates n times to sum the areas of n rectangles.

Space Complexity

The space complexity of the left_riemann_sum function is O(1) because it uses a fixed amount of space; it does not allocate any additional space that grows with the input size n.

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