September Morn Update

Task/Longest-common-subsequence/Python/longest-common-subsequence-3.py

@@ -1,23 +1,18 @@
 def lcs(a, b):
-    lengths = [[0 for j in range(len(b)+1)] for i in range(len(a)+1)]
-    # row 0 and column 0 are initialized to 0 already
+    # generate matrix of length of longest common subsequence for substrings of both words
+    lengths = [[0] * (len(b)+1) for _ in range(len(a)+1)]
     for i, x in enumerate(a):
         for j, y in enumerate(b):
             if x == y:
                 lengths[i+1][j+1] = lengths[i][j] + 1
             else:
                 lengths[i+1][j+1] = max(lengths[i+1][j], lengths[i][j+1])
-    # read the substring out from the matrix
-    result = ""
-    x, y = len(a), len(b)
-    while x != 0 and y != 0:
-        if lengths[x][y] == lengths[x-1][y]:
-            x -= 1
-        elif lengths[x][y] == lengths[x][y-1]:
-            y -= 1
-        else:
-            assert a[x-1] == b[y-1]
-            result = a[x-1] + result
-            x -= 1
-            y -= 1
+
+    # read a substring from the matrix
+    result = ''
+    j = len(b)
+    for i in range(1, len(a)+1):
+        if lengths[i][j] != lengths[i-1][j]:
+            result += a[i-1]
+
     return result