feat(letsplot): implement elbow-curve (#2353)

## Implementation: `elbow-curve` - letsplot

Implements the **letsplot** version of `elbow-curve`.

**File:** `plots/elbow-curve/implementations/letsplot.py`

---
:robot: *[impl-generate
workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/20528205832)*

---------

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Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

Author: github-actions[bot]

plots/elbow-curve/implementations/letsplot.py

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+""" pyplots.ai
+elbow-curve: Elbow Curve for K-Means Clustering
+Library: letsplot 4.8.2 | Python 3.13.11
+Quality: 92/100 | Created: 2025-12-26
+"""
+
+import numpy as np
+import pandas as pd
+from lets_plot import *
+
+
+LetsPlot.setup_html()
+
+# Simulated K-means inertia values showing typical elbow curve pattern
+# Data represents clustering analysis on customer segmentation dataset
+np.random.seed(42)
+
+k_values = list(range(1, 11))
+
+# Realistic inertia values that show clear elbow at k=4
+# Inertia decreases sharply until k=4, then diminishing returns
+inertias = [
+    12500,  # k=1: all points in one cluster
+    6800,  # k=2: significant drop
+    3900,  # k=3: still improving
+    2100,  # k=4: elbow point (optimal)
+    1800,  # k=5: diminishing returns start
+    1550,  # k=6
+    1380,  # k=7
+    1250,  # k=8
+    1150,  # k=9
+    1080,  # k=10
+]
+
+# Create DataFrame for plotting
+df = pd.DataFrame({"k": k_values, "Inertia": inertias})
+
+# Optimal k (elbow point)
+optimal_k = 4
+
+# Create elbow curve plot
+plot = (
+    ggplot(df, aes(x="k", y="Inertia"))
+    + geom_line(size=2, color="#306998")
+    + geom_point(size=6, color="#306998", alpha=0.9)
+    + geom_point(data=df[df["k"] == optimal_k], mapping=aes(x="k", y="Inertia"), size=10, color="#FFD43B", shape=18)
+    + geom_vline(xintercept=optimal_k, linetype="dashed", color="#FFD43B", size=1.5, alpha=0.7)
+    + labs(
+        title="elbow-curve · letsplot · pyplots.ai",
+        x="Number of Clusters (k)",
+        y="Inertia (Within-Cluster Sum of Squares)",
+    )
+    + scale_x_continuous(breaks=k_values)
+    + theme_minimal()
+    + theme(
+        plot_title=element_text(size=28, face="bold"),
+        axis_title=element_text(size=22),
+        axis_text=element_text(size=18),
+        panel_grid_major=element_line(color="#CCCCCC", size=0.5),
+        panel_grid_minor=element_blank(),
+    )
+    + ggsize(1600, 900)
+)
+
+# Save as PNG (scale 3x for 4800x2700)
+ggsave(plot, "plot.png", path=".", scale=3)
+
+# Save interactive HTML
+ggsave(plot, "plot.html", path=".")

plots/elbow-curve/metadata/letsplot.yaml

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+library: letsplot
+specification_id: elbow-curve
+created: '2025-12-26T19:36:50Z'
+updated: '2025-12-26T19:43:18Z'
+generated_by: claude-opus-4-5-20251101
+workflow_run: 20528205832
+issue: 0
+python_version: 3.13.11
+library_version: 4.8.2
+preview_url: https://storage.googleapis.com/pyplots-images/plots/elbow-curve/letsplot/plot.png
+preview_thumb: https://storage.googleapis.com/pyplots-images/plots/elbow-curve/letsplot/plot_thumb.png
+preview_html: https://storage.googleapis.com/pyplots-images/plots/elbow-curve/letsplot/plot.html
+quality_score: 92
+review:
+  strengths:
+  - Excellent visual clarity with properly scaled text elements for 4800x2700 resolution
+  - Clear elbow point highlighting using contrasting yellow diamond marker and vertical
+    dashed line
+  - Proper implementation of lets-plot grammar of graphics with layered geoms
+  - Clean KISS code structure following project guidelines
+  - Correct title format and descriptive axis labels
+  weaknesses:
+  - No legend or annotation text explaining what the yellow marker/line represents
+    (the optimal k value)
+  - Could use lets-plot interactive features like tooltips showing exact values on
+    hover
+  - Grid lines could be slightly more subtle (alpha currently at 0.5, could be 0.3)