From 783f726820d8612f24afa90b87bec9edc94aabed Mon Sep 17 00:00:00 2001
From: Kevin Du <kevinkldu@gmail.com>
Date: Wed, 3 May 2017 12:05:16 -0700
Subject: [PATCH] Create Viterbi_algorithm.py

---
 Viterbi_algorithm.py | 39 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 39 insertions(+)
 create mode 100644 Viterbi_algorithm.py

diff --git a/Viterbi_algorithm.py b/Viterbi_algorithm.py
new file mode 100644
index 0000000..bd8c6ca
--- /dev/null
+++ b/Viterbi_algorithm.py
@@ -0,0 +1,39 @@
+# https://en.wikipedia.org/wiki/Viterbi_algorithm
+
+def viterbi(obs, states, start_p, trans_p, emit_p):
+    V = [{}]
+    for st in states:
+        V[0][st] = {"prob": start_p[st] * emit_p[st][obs[0]], "prev": None}
+    # Run Viterbi when t > 0
+    for t in range(1, len(obs)):
+        V.append({})
+        for st in states:
+            max_tr_prob = max(V[t-1][prev_st]["prob"]*trans_p[prev_st][st] for prev_st in states)
+            for prev_st in states:
+                if V[t-1][prev_st]["prob"] * trans_p[prev_st][st] == max_tr_prob:
+                    max_prob = max_tr_prob * emit_p[st][obs[t]]
+                    V[t][st] = {"prob": max_prob, "prev": prev_st}
+                    break
+    for line in dptable(V):
+        print line
+    opt = []
+    # The highest probability
+    max_prob = max(value["prob"] for value in V[-1].values())
+    previous = None
+    # Get most probable state and its backtrack
+    for st, data in V[-1].items():
+        if data["prob"] == max_prob:
+            opt.append(st)
+            previous = st
+            break
+    # Follow the backtrack till the first observation
+    for t in range(len(V) - 2, -1, -1):
+        opt.insert(0, V[t + 1][previous]["prev"])
+        previous = V[t + 1][previous]["prev"]
+    print 'The steps of states are ' + ' '.join(opt) + ' with highest probability of %s' % max_prob
+    
+def dptable(V):
+    # Print a table of steps from dictionary
+    yield " ".join(("%12d" % i) for i in range(len(V)))
+    for state in V[0]:
+        yield "%.7s: " % state + " ".join("%.7s" % ("%f" % v[state]["prob"]) for v in V