diff --git a/hw5/xzgao/.gitignore b/hw5/xzgao/.gitignore
new file mode 100644
index 0000000..2251642
--- /dev/null
+++ b/hw5/xzgao/.gitignore
@@ -0,0 +1 @@
+Manifest.toml
\ No newline at end of file
diff --git a/hw5/xzgao/Project.toml b/hw5/xzgao/Project.toml
new file mode 100644
index 0000000..c6c200e
--- /dev/null
+++ b/hw5/xzgao/Project.toml
@@ -0,0 +1,10 @@
+[deps]
+CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
+CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
+DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+GenericMessagePassing = "09522ef3-fe1e-4698-a056-61d75781c616"
+GenericTensorNetworks = "3521c873-ad32-4bb4-b63d-f4f178f42b49"
+ProblemReductions = "899c297d-f7d2-4ebf-8815-a35996def416"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+TensorInference = "c2297e78-99bd-40ad-871d-f50e56b81012"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/hw5/xzgao/README.md b/hw5/xzgao/README.md
new file mode 100644
index 0000000..b2a9c82
--- /dev/null
+++ b/hw5/xzgao/README.md
@@ -0,0 +1,11 @@
+# BP for K-SAT
+
+Backend: GenericMessagePassing.jl at https://github.com/ArrogantGao/GenericMessagePassing.jl, it implements the bp algorithm, random K-SAT instances, and its tensor network model.
+
+In `entropy_density.jl`, we run BP on random K-SAT instances with (n = 100, k = 3) and plot the entropy density.
+
+![](data/entropy_density_n100_k3.png)
+
+The one from the book:
+
+![](data/entropy_density_book.png)
\ No newline at end of file
diff --git a/hw5/xzgao/data/entropy_density_book.png b/hw5/xzgao/data/entropy_density_book.png
new file mode 100644
index 0000000..a6feeed
Binary files /dev/null and b/hw5/xzgao/data/entropy_density_book.png differ
diff --git a/hw5/xzgao/data/entropy_density_n100_k3.csv b/hw5/xzgao/data/entropy_density_n100_k3.csv
new file mode 100644
index 0000000..25f87ce
--- /dev/null
+++ b/hw5/xzgao/data/entropy_density_n100_k3.csv
@@ -0,0 +1,274 @@
+alpha,i,s
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diff --git a/hw5/xzgao/data/entropy_density_n100_k3.png b/hw5/xzgao/data/entropy_density_n100_k3.png
new file mode 100644
index 0000000..01a4334
Binary files /dev/null and b/hw5/xzgao/data/entropy_density_n100_k3.png differ
diff --git a/hw5/xzgao/entropy_density.jl b/hw5/xzgao/entropy_density.jl
new file mode 100644
index 0000000..34accc7
--- /dev/null
+++ b/hw5/xzgao/entropy_density.jl
@@ -0,0 +1,16 @@
+using GenericMessagePassing
+using CSV, DataFrames
+
+function main(n, k, ms, n_samples)
+    df = CSV.write("data/entropy_density_n$(n)_k$(k).csv", DataFrame(alpha=Float64[], i = Int[], s=Float64[]))
+    for m in ms
+        for i in 1:n_samples
+            k_sat = random_k_sat(n, k, m)
+            tn = tn_model(k_sat)
+            S = entropy_bp(tn.code, tn.tensors, BPConfig())
+            CSV.write(df, DataFrame(alpha=m/n, i = i, s=S/n), append=true)
+        end
+    end
+end
+
+main(100, 3, 10:10:450, 10)
\ No newline at end of file
diff --git a/hw5/xzgao/plot.jl b/hw5/xzgao/plot.jl
new file mode 100644
index 0000000..3008ea3
--- /dev/null
+++ b/hw5/xzgao/plot.jl
@@ -0,0 +1,15 @@
+using CSV, DataFrames, CairoMakie
+using Statistics
+
+df = CSV.read("data/entropy_density_n100_k3.csv", DataFrame)
+
+fig = Figure()
+ax = Axis(fig[1, 1], xlabel="α", ylabel="s")
+
+alphas = unique(df.alpha)
+lines!(ax, alphas, [mean(df.s[df.alpha .== alpha]) for alpha in alphas], label="BP entropy density")
+
+xlims!(ax, 0.0, 5.0)
+ylims!(ax, 0.0, 0.7)
+
+save("data/entropy_density_n100_k3.png", fig)
\ No newline at end of file