From 1fbe751b7b82bdc948e8339beb60cab84d4f0a66 Mon Sep 17 00:00:00 2001
From: Moria <moria@moria-research.(none)>
Date: Wed, 14 Oct 2015 14:00:53 -0400
Subject: [PATCH] Done

---
 centerstar.py | 121 +++++++++++++++++++++++++++++++++++++++++++++-----
 input.txt     |   1 -
 2 files changed, 109 insertions(+), 13 deletions(-)

diff --git a/centerstar.py b/centerstar.py
index 4134938..f130978 100644
--- a/centerstar.py
+++ b/centerstar.py
@@ -3,12 +3,55 @@ import os
 import itertools
 import numpy as np
 
+def backtrack(v, w, dir_graph):
+    '''
+    Backtracks through dir_graph to find v_p, w_p
+    '''
+
+    # Init prime strings, and the indel char
+    v_p = ""
+    w_p = ""
+    indel = "-"
+    
+    # get our starting index
+    i = len(v)
+    j = len(w)
+
+    # until we reach 0,0 go through the direction graph and work backwards
+    while i != 0 and j != 0:
+        
+        direction = dir_graph[i,j]
+        
+        if direction == 0:  
+            # We go up, add letter to v_p, add indel to w_p
+            v_p += v[i-1]
+            w_p += indel
+            i -= 1
+        elif direction == 1:
+            # We go left, add indel to v_p, add letter to w_p
+            v_p += indel
+            w_p += w[j-1]
+            j -= 1
+        else:
+            # We go up/left (diag), add letter to v_p, w_p
+            v_p += v[i-1]
+            w_p += w[j-1]
+            i -= 1
+            j -= 1
+
+    # Reverse the strings since we added from the end first
+    v_p = v_p[::-1]
+    w_p = w_p[::-1]
+
+    return v_p, w_p
+
+
 
 def find_edit_distance(v,w):
     '''
     Finds the edit distance between w and v
     Returns the distance between the two strings
-    Edit graph is set up as w along y axis (left), v along x axis (top)
+    Edit graph is set up as v along y axis (left), w along x axis (top)
     Score 0 for match, 1 for mistmatch or indel
     '''
     # n, m are number of rows, cols
@@ -20,9 +63,10 @@ def find_edit_distance(v,w):
 
     # Init graph
     edit_graph = np.zeros((n, m)) 
-    
+    dir_graph = np.zeros((n,m))
+
     # Add distances along x, y axis
-    # +1 at every step because indels -> +1
+    # +1 at every step along 0th row, col because indels -> +1
     for i in range(n):
         edit_graph[i,0] = i
     for j in range(m):
@@ -39,19 +83,47 @@ def find_edit_distance(v,w):
                 diag = edit_graph[i-1,j-1] + 1
             
             # Update
-            edit_graph[i,j] = min(edit_graph[i-1, j]+1, edit_graph[i,j-1]+1, diag)
+            min_index, min_score = min(enumerate([edit_graph[i-1, j]+1, edit_graph[i,j-1]+1, diag]), key=lambda p: p[1])
+            edit_graph[i,j] = min_score
+            
+            # Store direction, backtrack later
+            # 0 = Up, 1 = left, 2 = diag up left
+            dir_graph[i,j] = min_index
+
+    # Backtrack to get aligned strings (primes)
+    v_p, w_p = backtrack(v, w, dir_graph)
     
-    # Return n,m 
-    distance = edit_graph[n-1,m-1]
-    return distance
+    # Get distance and return it all
+    distance = edit_graph[n-1,m-1]  # Remember we index at 0 so -1
+    
+    return distance, v_p, w_p
+
 
+def align_strings(S, min_index):
+    '''
+    Aligns strings S around center string min_index
+    '''
 
+    # Pop out our center string from the string list
+    Sc = S.pop(min_index)
+
+    # Loop through and align, going back and changing as needed
+    for i in range(len(S)):
+        while i >= 0:
+            distance, v_p, w_p = find_edit_distance(Sc, S[i])
+            Sc = v_p
+            S[i] = w_p
+            i -= 1
+
+    return Sc, S
 
 def main():
     '''
     Main Function
     '''
 
+    print "Center Star Algorithm\nStephen Lincoln\nProgramming Assignment 2\n\n\n"
+   
     # Try to get file as input
     try:
         input_file = sys.argv[1]
@@ -59,13 +131,13 @@ def main():
         print "Please supply an input file"
         sys.exit()
 
-
+    # Assuming that the input file is correct, for sake of brevity
     # Read in n, strings to S
     with open(input_file, 'r') as f:
         content = f.readlines()
     
     n = int(content[0].strip())
-    S = [s.strip() for s in content[1:]]
+    S = [s.strip() for s in content[1:]]    # Dont forget to strip newlines and such
 
     # Init scoring table to find center string candidate
     scores = [0 for i in range(n)]
@@ -75,16 +147,41 @@ def main():
     
     # Iterate and score
     for pair in string_pairs:
-        w = S[pair[0]]
-        v = S[pair[1]]
-        distance = find_edit_distance(w,v)
+        v = S[pair[0]]
+        w = S[pair[1]]
+        distance, v_p, w_p = find_edit_distance(v, w)
         
         # Update scores
         for i in range(n):
             if i in pair:
                 scores[i] += distance
 
+    # get the string number and score of the best candidate
+    min_index, min_score = min(enumerate(scores), key=lambda p: p[1]) 
+
+    # Now align all the strings with the center string
+    Sc, S = align_strings(S, min_index)
+
+    # Recombine into a list
+    new_S = [Sc] + S
+   
+    # Init total cost
+    total_cost = 0
+
+    # Find the total cost
+    string_pairs = itertools.combinations(range(n), 2)
+    for pair in string_pairs:
+        v = new_S[pair[0]]
+        w = new_S[pair[1]]
+        for i in range(len(v)):
+            if v[i] != w[i]:
+                total_cost += 1
     
+    print "Sequences aligned\nmin star cost: %d\ntotal cost: %d" % (min_score, total_cost)
+    for s in new_S:
+        print s
+
+    # End main
 
 if __name__ == '__main__':
     main()
diff --git a/input.txt b/input.txt
index 44af585..7ee1f94 100644
--- a/input.txt
+++ b/input.txt
@@ -3,4 +3,3 @@ AXZ
 AXXZ
 AYXYZ
 AYZ
-