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
33 changed files with 1551 additions and 0 deletions
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+0/1 Knapsack
+============
+
+1) Table: weights [1,3,4,5], values [1,4,5,7], capacity 7. dp[i][w] = best value with the first i items
+w =        0   1   2   3   4   5   6   7
+none       0   0   0   0   0   0   0   0
+item 1     0   1   1   1   1   1   1   1
+item 2     0   1   1   4   5   5   5   5
+item 3     0   1   1   4   5   6   6   9
+item 4     0   1   1   4   5   7   8   9
+answer = dp[4][7] = 9 (weights 3 + 4, values 4 + 5)
+
+2) One row, capacity loop direction: weights [5,4,6,3], values [10,40,30,50], capacity 10
+   backward loop (each item used once) -> 90
+   forward loop, same code otherwise   -> 150  (the weight-3 item is reused three times: 3 x 50)
+
+3) Calls made: 22 items, capacity 60, best value 357
+   naive recursion -> 1003985 calls
+   memoized        -> 1794 calls