simplex-chat-0004: introduceToRemaining notElem O(N×M) member dedup; fix: Set.notMember O(log N)
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# UNDF: (pending)
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# scipy-0001: SHGO minimizers() — xl_maps list scan ignores xl_maps_set O(V×L)
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## CWE-407 — Algorithmic Complexity: O(V×L) list scan despite O(1) set already present
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| Field | Value |
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|-------|-------|
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| ID | scipy-0001 |
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| Severity | MEDIUM |
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| Ecosystem | scipy |
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| Package | `scipy.optimize` |
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| File | `scipy/optimize/_shgo.py` |
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| Lines | 1155–1174 |
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| Complexity | O(V×L) — vertices × local minima, inside per-iteration minimizers() call |
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| Hot path | `SHGO.minimizers()` — called every iteration of the SHGO optimizer |
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## Background
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SHGO (Simplicial Homology Global Optimization) is scipy's global optimizer for
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non-convex problems. Each iteration calls `minimizers()` to find all current
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local minima of the simplicial complex. It iterates all vertices in `HC.V.cache`
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(V vertices) and for each checks whether it has already been mapped as a local
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minimum via the `LMC` (Local Minima Cache).
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## Defect
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```python
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# scipy/optimize/_shgo.py lines 1155–1174
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def minimizers(self):
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self.minimizer_pool = []
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for x in self.HC.V.cache: # V vertices
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in_LMC = False
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if len(self.LMC.xl_maps) > 0:
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for xlmi in self.LMC.xl_maps: # DEFECT: O(L) list scan
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if np.all(np.array(x) == np.array(xlmi)):
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in_LMC = True
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if in_LMC:
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continue
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if self.HC.V[x].minimiser():
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if self.HC.V[x] not in self.minimizer_pool: # DEFECT: O(M) list scan
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self.minimizer_pool.append(self.HC.V[x])
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```
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`LMapCache` already maintains `xl_maps_set` — a set of tuples for O(1) lookup:
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```python
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# scipy/optimize/_shgo.py lines 1560–1595
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class LMapCache:
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def __init__(self):
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self.xl_maps = []
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self.xl_maps_set = set() # ← already exists, not used here
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...
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def add_res(self, v, lres, bounds=None):
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...
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self.xl_maps.append(lres.x)
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self.xl_maps_set.add(tuple(lres.x)) # maintained on every insert
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```
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The set is populated on every `add_res()` call but never consulted in
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`minimizers()` — the code uses the slower list instead.
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### Total cost per optimization run
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`minimizers()` is called once per SHGO iteration (line 885). For a problem with
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N function evaluations, the simplicial complex has V ~ O(N) vertices, and
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L ~ O(N) local minima in the worst case. The loop is O(V×L) = O(N²) per
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iteration × I iterations = O(I×N²).
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For a typical optimization with N=500 sample points and 10 iterations:
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- List path: 500 × 250 × 10 = 1,250,000 element comparisons (each involving
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`np.all(np.array(x) == np.array(xlmi))` — not just a Python int comparison)
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- Set path: 500 × 10 = 5,000 set probes
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## Complexity table
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| Vertices (V) | Local minima (L) | Iterations (I) | list np.all ops | set ops | Speedup |
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|-------------|-----------------|---------------|----------------|---------|---------|
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| 100 | 20 | 5 | 10,000 | 500 | 20× |
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| 500 | 100 | 10 | 500,000 | 5,000 | 100× |
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| 1,000 | 300 | 20 | 6,000,000 | 20,000 | 300× |
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| 2,000 | 500 | 30 | 30,000,000 | 60,000 | 500× |
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## Fix
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Use `xl_maps_set` for the LMC membership check, and drop the redundant
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`minimizer_pool` dedup (safe because the cache iteration visits each key once):
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```python
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def minimizers(self):
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self.minimizer_pool = []
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for x in self.HC.V.cache:
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# FIX: O(1) set lookup instead of O(L) list scan
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if tuple(x) in self.LMC.xl_maps_set:
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continue
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if self.HC.V[x].minimiser():
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# No need for not-in check: each x is a unique cache key
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self.minimizer_pool.append(self.HC.V[x])
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```
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`tuple(x)` is already the native key type (cache keys are tuples of coordinates),
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matching the `tuple(lres.x)` stored by `add_res()`. `set.__contains__` is O(1)
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amortised.
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Note: `xl_maps_set` is invalidated by `sort_cache_result()` which converts
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`xl_maps` to numpy array; ensure `xl_maps_set` is rebuilt or frozen at that point.
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127
defects/scipy/unit/ScipyTest.java
Normal file
127
defects/scipy/unit/ScipyTest.java
Normal file
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package unit;
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import java.util.*;
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/**
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* ScipyTest — CWE-407 benchmark for scipy-0001
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*
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* scipy-0001: SHGO.minimizers() — xl_maps list scan ignores xl_maps_set O(V×L)
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* Real code (scipy/optimize/_shgo.py:1155-1174):
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* for x in self.HC.V.cache: # V vertices
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* for xlmi in self.LMC.xl_maps: # O(L) list scan
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* if np.all(np.array(x) == np.array(xlmi)):
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* in_LMC = True
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*
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* xl_maps_set = set() is maintained by LMapCache.add_res() but never used here.
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*
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* Fix: replace list scan with xl_maps_set.contains(tuple(x)) — O(1).
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*/
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public class ScipyTest {
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/**
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* Simulates SHGO.minimizers() with xl_maps list scan.
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* @param V vertices in HC.V.cache
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* @param L local minima already in LMC (xl_maps length)
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* @param I optimizer iterations
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* @return total comparisons
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*/
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static long slowShgoMinimizers(int V, int L, int I) {
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// Build xl_maps as list of "tuples" (represented as Strings here)
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List<String> xlMaps = new ArrayList<>();
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for (int i = 0; i < L; i++) xlMaps.add("min_" + i);
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long ops = 0;
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for (int iter = 0; iter < I; iter++) {
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List<Object> minimizerPool = new ArrayList<>();
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for (int v = 0; v < V; v++) {
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String x = "vertex_" + v;
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boolean inLMC = false;
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// DEFECT: O(L) scan
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for (int k = 0; k < xlMaps.size(); k++) {
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ops++;
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if (xlMaps.get(k).startsWith("min_" + (v % L))) {
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inLMC = true;
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break;
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}
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}
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if (inLMC) continue;
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// if minimiser(): check not in pool (also a list)
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boolean isMin = (v % 7 == 0); // ~14% of vertices are local minima
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if (isMin) {
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boolean inPool = false;
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for (int k = 0; k < minimizerPool.size(); k++) {
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ops++;
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if (minimizerPool.get(k).equals(x)) { inPool = true; break; }
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}
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if (!inPool) minimizerPool.add(x);
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}
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}
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}
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return ops;
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}
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/**
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* Simulates fixed SHGO.minimizers() using xl_maps_set.
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* @return total ops
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*/
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static long fastShgoMinimizers(int V, int L, int I) {
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Set<String> xlMapsSet = new HashSet<>();
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for (int i = 0; i < L; i++) xlMapsSet.add("min_" + i);
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long ops = 0;
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for (int iter = 0; iter < I; iter++) {
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List<Object> minimizerPool = new ArrayList<>();
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for (int v = 0; v < V; v++) {
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String x = "vertex_" + v;
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ops++; // O(1) set probe
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if (xlMapsSet.contains("min_" + (v % L))) continue;
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boolean isMin = (v % 7 == 0);
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if (isMin) minimizerPool.add(x); // no dedup needed (unique keys)
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}
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}
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return ops;
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}
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static void bench(String label, Runnable slow, Runnable fast, long sOps, long fOps) {
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slow.run(); fast.run();
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long t0 = System.nanoTime(); slow.run(); long sMs = (System.nanoTime() - t0) / 1_000_000;
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long t1 = System.nanoTime(); fast.run(); long fMs = (System.nanoTime() - t1) / 1_000_000;
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double speedup = fMs > 0 ? (double) sMs / fMs : (double) sOps / fOps;
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System.out.printf(" %-60s slow:%4dms (%,d ops) fast:%4dms (%,d ops) speedup:%.0fx%n",
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label, sMs, sOps, fMs, fOps, speedup);
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}
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public static void main(String[] args) {
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System.out.println("ScipyTest — scipy-0001: SHGO.minimizers() xl_maps list scan vs xl_maps_set");
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System.out.println();
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System.out.println(" [scipy-0001: SHGO minimizers() LMC lookup]");
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int[][] cases = {{500, 100, 10}, {1000, 300, 20}, {2000, 500, 30}};
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for (int[] c : cases) {
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int V = c[0], L = c[1], I = c[2];
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long sOps = slowShgoMinimizers(V, L, I);
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long fOps = fastShgoMinimizers(V, L, I);
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bench(
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String.format("V=%d vertices, L=%d local-minima, I=%d iters", V, L, I),
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() -> slowShgoMinimizers(V, L, I),
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() -> fastShgoMinimizers(V, L, I),
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sOps, fOps
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);
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}
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System.out.println();
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int pass = 0;
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long s = slowShgoMinimizers(1000, 300, 20);
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long f = fastShgoMinimizers(1000, 300, 20);
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assert s > f * 50 : "scipy-0001 expected >50x ratio; slow=" + s + " fast=" + f;
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pass++;
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System.out.printf("%d/1 PASS%n", pass);
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System.out.printf("scipy-0001: _shgo.SHGO.minimizers() xl_maps list → xl_maps_set O(V×L) → O(V)%n");
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System.out.printf("Hotpath: every SHGO optimizer iteration; O(N²) per run on large sample sets%n");
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}
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}
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