19 lines
761 B
Plaintext
19 lines
761 B
Plaintext
Coin Change: greedy, the overflow bug, call counts, loop order
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1) Greedy fails: coins {1,3,4}, amount 6
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greedy -> 3 coins (4+1+1)
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DP (table) -> 2 coins (3+3)
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2) 'Impossible' = Integer.MAX_VALUE, then dp[a-c] + 1: coins {2}, amount 3 (really impossible)
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correct (impossible = amount + 1) -> -1
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Integer.MAX_VALUE version -> -2147483648
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3) Calls made: coins {1,2,5}, amount 27, answer 6
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naive recursion -> 2688332 calls
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memoized -> 77 calls
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4) Loop order changes the question: coins {1,2,5}, amount 5
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coins in the OUTER loop -> 4 (combinations: 5 / 2+2+1 / 2+1+1+1 / 1x5)
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amount in the OUTER loop -> 9 (permutations: 1+2 and 2+1 now count separately)
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