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defects/pandas/patch/pandas-0001-styler-hidden-rows-list-membership.md

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+# pandas-0001: Styler render — O(n²) hidden_rows list membership in render loops
+
+**Severity:** MEDIUM
+**CWE:** CWE-407 (Algorithmic Complexity — linear membership test in hot loop)
+**Speedup:** >25x at R=2000 rows, H=500 hidden rows
+**Target:** pandas (pandas-dev/pandas)
+**File:** `pandas/io/formats/style_render.py`
+
+## Description
+
+`Styler` renders DataFrames to HTML, LaTeX, and string. During rendering,
+`self.hidden_rows` (declared as `Sequence[int]`, initialized as `list`) is
+tested with `r not in self.hidden_rows` inside loops over all rows. This
+appears in at least five locations:
+
+| Line | Pattern | Outer loop scale |
+|------|---------|-----------------|
+| 662  | `if z[0] not in self.hidden_rows` | O(R) enumerate |
+| 843  | `r not in self.hidden_rows` | O(R × C) body cell loop |
+| 910  | `if r not in obj.hidden_rows` | O(R) recursive concat |
+| 971  | `if r not in self.hidden_rows` | O(R) cline build |
+| 2306 | `i in styler.hidden_rows` | O(R) export loop |
+
+With R rows and H hidden rows, each render call costs O(R × H) for these tests
+alone. When H approaches R (hide many rows), this becomes O(R²).
+
+`hidden_rows` is populated via `Styler.hide()` which calls
+`get_indexer_for()` returning a numpy array. The array is assigned directly
+without conversion to a set, so membership tests remain O(H).
+
+## Root Cause
+
+```python
+# style_render.py:131
+self.hidden_rows: Sequence[int] = []   # list — O(n) membership
+
+# style_render.py:662
+for r, row_tup in [
+    z for z in enumerate(self.data.itertuples()) if z[0] not in self.hidden_rows  # O(H) each
+]:
+```
+
+Fix: convert `hidden_rows` to a `frozenset` (or maintain a parallel set)
+at assignment time so every membership test is O(1).
+
+## Patch
+
+In `style.py`, after computing `h_els`:
+```python
+h_els = getattr(self, objs).get_indexer_for(getattr(hide, objs))
+setattr(self, f"hidden_{alt}", frozenset(h_els.tolist()))
+```
+
+Or ensure `hidden_rows` is typed as `frozenset[int]` and initialized to
+`frozenset()` in `StylerRenderer.__init__`.
+
+## Complexity Before
+
+Each render: **O(R × H)** membership tests; worst case **O(R²)**
+
+## Complexity After
+
+Membership check: **O(1)** → render cost: **O(R + H)**
+
+## Reproduction
+
+```
+cd defects/pandas/unit && javac -d . *.java && java -ea unit.PandasTest
+```