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Add boundary checking to optimal bst #11771

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Add boundary checking to optimal bst #11771

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11 changes: 8 additions & 3 deletions dynamic_programming/optimal_binary_search_tree.py
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Original file line number Diff line number Diff line change
Expand Up @@ -115,9 +115,14 @@ def find_optimal_binary_search_tree(nodes):
dp[i][j] = sys.maxsize # set the value to "infinity"
total[i][j] = total[i][j - 1] + freqs[j]

# Apply Knuth's optimization
# Loop without optimization: for r in range(i, j + 1):
for r in range(root[i][j - 1], root[i + 1][j] + 1): # r is a temporal root
# Apply Knuth's optimization with boundary checking
r_start = max(i, root[i][j - 1] if j > i else i)
r_end = min(j, root[i + 1][j] if i < j else j)

if r_start > r_end:
r_start, r_end = i, j # fall back to the full range

for r in range(r_start, r_end + 1):
left = dp[i][r - 1] if r != i else 0 # optimal cost for left subtree
right = dp[r + 1][j] if r != j else 0 # optimal cost for right subtree
cost = left + total[i][j] + right
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