Add dynamic-programming module: ten classic DP problems, memoization vs tabulation vs space-optimised, call-count and pitfall transcripts (11 tests)

2026-11-09 08:41:01 +00:00
parent 911aef5515
commit cb1b28682f
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+Coin Change: greedy, the overflow bug, call counts, loop order
+==============================================================
+
+1) Greedy fails: coins {1,3,4}, amount 6
+   greedy      -> 3 coins (4+1+1)
+   DP (table)  -> 2 coins (3+3)
+
+2) 'Impossible' = Integer.MAX_VALUE, then dp[a-c] + 1: coins {2}, amount 3 (really impossible)
+   correct (impossible = amount + 1) -> -1
+   Integer.MAX_VALUE version         -> -2147483648
+
+3) Calls made: coins {1,2,5}, amount 27, answer 6
+   naive recursion -> 2688332 calls
+   memoized        -> 77 calls
+
+4) Loop order changes the question: coins {1,2,5}, amount 5
+   coins in the OUTER loop  -> 4 (combinations: 5 / 2+2+1 / 2+1+1+1 / 1x5)
+   amount in the OUTER loop -> 9 (permutations: 1+2 and 2+1 now count separately)