Lab 5?–?CPS?106

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This lab helps you practice recursion, string manipulation and numerical approximation.

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1. ??Find ?a??given??element??in??a??list??using??a??recursive??function.??The??function??is??defined??as?find(elm_list, x), where elm_list is the input list and x is the element to be?found. The?function?return the index of?x if?x is in the list, otherwise it returns -1.

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Test you function with following:

[1.2,?3,?555,?66,?6,?35,?345,?345,?78,?12341],

x?=?78,

x?=?11

2. ??Write?a?function?that?computes?the?inner product?of two lists. The?inner product?of two?lists?L1 and L2 of?length n is defined?as?L1[0]?*?L2[0]?+?L1[1]?*?L2[1]?+?...?+?L1[n?–?1]?*?L2[n?–?1].?If?the lists are not of?the same length, the function should return None.

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Test your function with the following:

L1?=?[8.17, 4.99,?16.56,?7.31,?0.21,?16.18,?13.75,?11.28, 4.3,?17.79]

L2?=?[17.68,?1.19,?2.64,?13.01,?8.5,?15.04,?0.3,?18.72, 4.58,?9.66]

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3. ??Write?a?function?that?extract?a?number?from?a?string.?The?string?can?contain?any?character.?The?number?you?return?is?the?concatenation?of?all?the?digits?you?find?in?the?string.?For?example, the extracted number from the string “sk8dfjn*HG23Yh$%7-5~5”?is?823755.

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Test your function with the following:

“1ksdj4sdf>R?387BDYGrrf%44@2”

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4. ??Write a function that computes the?sum

1?+?1 /?2**2?+?1 / 3**2?+?...?+?1?/?n**2

for??a??given??integer??n.??For??large??n,??this??sum??converges??to??pi**2??/??6??where??pi??=?3.141592653589793. How large should n be for the sum to be?within?distance?0.001?of?pi**2?/?6?

代碼

5-1

5-2

5-3

5-4

5-4-2