01 - methodical problem solving - in-class problems #3
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janiceshiu
commented
Jun 2, 2020
janiceshiu
commented
- roman numerals
janiceshiu
changed the title
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| Analysis | ||
| Time - o(n) where n is the length of the string | ||
| * no matter what, we have to iterate through each character in the |
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Technically twice, but yes, I agree still O(n)!
| idx = 0 | ||
| str_length = len(string) | ||
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| while idx < str_length: |
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Great! I think this handles the edge cases nicely.
One way you might split things up even more is to introduce a separate function like "should_subtract" or "is_subtractive_pair".
| * not very sure. lookup length is constant but we have to go through the whole string as well | ||
| * so maybe o(n) where n is length of the string? | ||
| * each iteration uses o(k) time to slice the string in `string[len(elem[0]):]` | ||
| * also not sure how long `string.startswith` takes |
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One way I estimate time complexity for library functions is just to imagine how I'd implement something. The library function should be at least that efficient!
For example, one easy way to implement startswith is to check each character one by one. So if the string has length n and the thing you're checking has length m, the time complexity is likely O(min(n, m)).
| time - o(nk)? | ||
| * not very sure. lookup length is constant but we have to go through the whole string as well | ||
| * so maybe o(n) where n is length of the string? | ||
| * each iteration uses o(k) time to slice the string in `string[len(elem[0]):]` |
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One suggestion is to write down what n and k are, so it's really cleaer.
| for elem in lookup: | ||
| while string.startswith(elem[0]): | ||
| acc += elem[1] | ||
| string = string[len(elem[0]):] |
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Can you think of a way to improve this (to avoid an expensive slice operation)?
| Analysis | ||
| time - o(n) where n is length of acc? | ||
| * time to iterate through lookup is constant | ||
| * however, `''.join(acc)`... does this take o(n) time to iterate through the length of acc? |
| eg: IIIII returns V | ||
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| Analysis | ||
| time & space - combination of roman_to_number_3 and number_to_roman |
