Fix DCA Hamiltonian: normalize by max instead of sum

- Change normalization from sum to max: visit_count / max^2
- This gives stronger discrimination toward unvisited nodes
- Weight 1 now gives 66.2% coverage (vs 63.6% baseline)
- Rename CLI: --weight-dca -> --weight-dca-voice-movement
- Rename CLI: --weight-hamiltonian -> --weight-dca-hamiltonian
- Restore DCA Hamiltonian display in analysis output
- Update README with new CLI names and factor descriptions

README.md

@@ -36,8 +36,8 @@ These factors weigh edges without eliminating them. Set weight to 0 to disable.
 
 - `--weight-melodic` - Weight for melodic threshold (default: 1)
 - `--weight-contrary-motion` - Weight for contrary motion (default: 0)
-- `--weight-hamiltonian` - Weight for Hamiltonian path (default: 1)
-- `--weight-dca` - Weight for DCA
+- `--weight-dca-hamiltonian` - Weight for DCA Hamiltonian (favors unvisited nodes, default: 1)
+- `--weight-dca-voice-movement` - Weight for DCA voice movement (favors voice changes, default: 1)
 - `--weight-target-range` - Weight for target register range (default: 1)
 
 ### Target Range
@@ -54,8 +54,8 @@ These factors weigh edges without eliminating them. Set weight to 0 to disable.
 ### Soft Factors (Weigh edges)
 - **Melodic threshold**: Penalizes edges with voice movements outside the melodic range
 - **Contrary motion**: Boosts edges where some voices move up and others move down
-- **Hamiltonian**: Penalizes edges that revisit nodes already in the path
-- **DCA**: Boosts edges where voices change/move (rather than staying)
+- **DCA Hamiltonian**: Boosts edges to nodes that haven't been visited recently (favors covering new nodes)
+- **DCA Voice Movement**: Boosts edges where voices change/move rather than staying on same pitch
 - **Target range**: Boosts edges that move toward the target register
 
 ## Examples
@@ -67,11 +67,11 @@ python -m src.io
 # Rising register to 2 octaves
 python -m src.io --target-range 2
 
-# Heavy target range, no DCA
-python -m src.io --target-range 2 --weight-target-range 10 --weight-dca 0
+# Heavy target range, no DCA voice movement
+python -m src.io --target-range 2 --weight-target-range 10 --weight-dca-voice-movement 0
 
-# Disable Hamiltonian (allow revisiting nodes)
-python -m src.io --weight-hamiltonian 0
+# Disable DCA Hamiltonian (allow revisiting nodes freely)
+python -m src.io --weight-dca-hamiltonian 0
 
 # Enable voice crossing
 python -m src.io --voice-crossing
@@ -87,3 +87,4 @@ Generated files go to `output/`:
 - `output_chords.json` - Chord data
 - `output_chords.txt` - Human-readable chords
 - `output_frequencies.txt` - Frequencies in Hz
+- `graph_path.json` - Hashes of graph nodes visited (for DCA Hamiltonian analysis)

src/analyze.py

@@ -198,6 +198,16 @@ def format_analysis(metrics: dict) -> str:
         "--- DCA Voice Movement ---",
         f"Avg stay count: {metrics['dca_avg_voice_stay']:.2f} steps",
         f"Max stay count: {metrics['dca_max_voice_stay']} steps",
+        "",
+        "--- DCA Hamiltonian ---",
+        f"Unique nodes: {metrics['hamiltonian_unique_nodes']}",
+    ]
+
+    if metrics["hamiltonian_coverage"] is not None:
+        lines.append(f"Coverage: {metrics['hamiltonian_coverage']:.1f}%")
+
+    lines.extend(
+        [
             "",
             "--- Target Range ---",
             f"Target: {metrics['target_octaves']} octaves ({metrics['target_cents']:.0f} cents)",
@@ -205,6 +215,7 @@ def format_analysis(metrics: dict) -> str:
             f"End: {metrics['target_end_cents']:.0f} cents",
             f"Achieved: {metrics['target_actual_cents']:.0f} cents ({metrics['target_percent']:.1f}%)",
         ]
+    )
 
     return "\n".join(lines)
 

src/graph.py

@@ -357,12 +357,13 @@ class PathFinder:
             return 1.0
 
         visit_count = node_visit_counts[destination]
-        total_counts = sum(node_visit_counts.values())
+        max_count = max(node_visit_counts.values()) if node_visit_counts else 0
 
-        if total_counts == 0:
+        if max_count == 0:
             return 1.0
 
-        return visit_count / total_counts
+        # Normalize by max squared - gives stronger discrimination
+        return visit_count / (max_count**2)
 
     def _factor_dca_voice_movement(
         self,