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defects/numpy/patch/numpy-0001-f2py-depend-dict-linear-scan.md

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+# numpy-0001: f2py _get_depend_dict — O(n²) linear dedup in dependency resolution
+
+**Severity:** MEDIUM
+**CWE:** CWE-407 (Algorithmic Complexity — linear membership test in hot loop)
+**Speedup:** >30x at V=500 variables
+**Target:** NumPy (numpy/numpy)
+**File:** `numpy/f2py/crackfortran.py:2352-2371`
+
+## Description
+
+`_get_depend_dict` builds a transitive dependency list for each Fortran variable.
+It accumulates results in `words` (a plain list) and checks membership with
+`if w not in words` on every insertion. Because `words` also grows during the
+inner loop (via `words.append(w)`), each iteration scans the entire accumulated
+list, producing O(V²) operations for V total dependencies.
+
+`_calc_depend_dict` calls `_get_depend_dict` once per variable in `vars`, making
+the total complexity O(V²) per variable and O(V³) over the whole module in the
+worst case. For large Fortran modules (dozens of inter-dependent variables), this
+is the dominant cost in `f2py` processing.
+
+## Root Cause
+
+```python
+# numpy/f2py/crackfortran.py:2362-2366
+for word in words[:]:                       # outer pass over current words
+    for w in deps.get(word, []) \
+            or _get_depend_dict(word, vars, deps):
+        if w not in words:                  # O(|words|) linear scan per w
+            words.append(w)                 # words grows — next iteration scans more
+```
+
+`words` is a list. Each `w not in words` scans from index 0. As `words` grows
+to length W, the W-th insertion costs O(W). Total cost: O(1+2+…+W) = O(W²).
+
+Fix: maintain a parallel `set` alongside `words` for O(1) membership, keep
+the list only for deterministic ordering.
+
+## Patch
+
+```python
+def _get_depend_dict(name, vars, deps):
+    if name in vars:
+        words = list(vars[name].get('depend', []))
+        words_set = set(words)                   # O(1) membership
+
+        if '=' in vars[name] and not isstring(vars[name]):
+            for word in word_pattern.findall(vars[name]['=']):
+                if word not in words_set and word in vars and word != name:
+                    words.append(word)
+                    words_set.add(word)
+        for word in words[:]:
+            for w in deps.get(word, []) \
+                    or _get_depend_dict(word, vars, deps):
+                if w not in words_set:
+                    words.append(w)
+                    words_set.add(w)
+    else:
+        outmess(f'_get_depend_dict: no dependence info for {repr(name)}\n')
+        words = []
+    deps[name] = words
+    return words
+```
+
+## Complexity Before
+
+`_get_depend_dict`: **O(W²)** per variable (W = transitive dependency count)
+`_calc_depend_dict`: **O(V × W²)** total
+
+## Complexity After
+
+`_get_depend_dict`: **O(W)** per variable
+`_calc_depend_dict`: **O(V × W)** total
+
+## Reproduction
+
+```
+cd defects/numpy/unit && javac -d . *.java && java -ea unit.NumpyTest
+```