feat: support docs auto live-reload with sphinx-autobuild (#4111)

Signed-off-by: samzong <samzong.lu@gmail.com>
Co-authored-by: zhaochenyang20 <zhaochen20@outlook.com>

docs/Makefile

 # Minimal Makefile for Sphinx documentation
 SPHINXOPTS    ?=
 SPHINXBUILD   ?= sphinx-build
+SPHINXAUTOBUILD ?= sphinx-autobuild
 SOURCEDIR     = .
 BUILDDIR      = _build
+PORT          ?= 8003
 
 help:
 	@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+	@echo ""
+	@echo "Additional targets:"
+	@echo "  serve       to build and serve documentation with auto-build and live reload"
 
 # Compile Notebook files and record execution time
 compile:
@@ -32,8 +37,15 @@ compile:
 	echo "Total execution time: $${TOTAL_ELAPSED}s" >> logs/timing.log; \
 	echo "All Notebook execution timings:" && cat logs/timing.log
 
+# Serve documentation with auto-build and live reload
+serve:
+	@echo "Starting auto-build server at http://localhost:$(PORT)"
+	@$(SPHINXAUTOBUILD) "$(SOURCEDIR)" "$(BUILDDIR)/html" \
+		--port $(PORT) \
+		--watch $(SOURCEDIR) \
+		--re-ignore ".*\.(ipynb_checkpoints|pyc|pyo|pyd|git)"
 
-.PHONY: help Makefile compile clean
+.PHONY: help Makefile compile clean serve
 
 %: Makefile
 	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)

docs/README.md

 # SGLang Documentation
+
 We recommend new contributors start from writing documentation, which helps you quickly understand SGLang codebase. Most documentation files are located under the `docs/` folder. We prefer **Jupyter Notebooks** over Markdown so that all examples can be executed and validated by our docs CI pipeline.
 
 ## Docs Workflow
@@ -20,10 +21,17 @@ Update your Jupyter notebooks in the appropriate subdirectories under `docs/`. I
 # 1) Compile all Jupyter notebooks
 make compile
 
-# 2) Compile and Preview documentation locally
+# 2) Compile and Preview documentation locally with auto-build
+# This will automatically rebuild docs when files change
 # Open your browser at the displayed port to view the docs
 bash serve.sh
 
+# 2a) Alternative ways to serve documentation
+# Directly use make serve
+make serve
+# With custom port
+PORT=8080 make serve
+
 # 3) Clean notebook outputs
 # nbstripout removes notebook outputs so your PR stays clean
 pip install nbstripout
@@ -90,7 +98,7 @@ For demonstrations in the docs, **prefer smaller models** to reduce memory consu
 
 ### **Prompt Alignment Example**
 
-When designing prompts, ensure they align with SGLang’s structured formatting. For example:
+When designing prompts, ensure they align with SGLang's structured formatting. For example:
 
 ```python
 prompt = """You are an AI assistant. Answer concisely and accurately.

docs/requirements.txt

@@ -17,3 +17,4 @@ nbstripout
 sphinxcontrib-mermaid
 urllib3<2.0.0
 gguf>=0.10.0
+sphinx-autobuild

docs/serve.sh

+# Clean and serve documentation with auto-build
 make clean
-make html
-python3 -m http.server --d _build/html 8003
+make serve