#169 is completed with DP + buttom-up approach

Author: Hamid Gasmi

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence.py

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+import sys
+
+# 1. Express a solution mathematically:
+#       Let's A be a matrix of alignments of (|s| + 1) x (|t| + 1)
+#       A[0,0] = 0
+#       A[0,c] = 0 for 1 <= c <= |s|
+#       A[r,0] = 0 for 1 <= r <= |t|
+#       A[r,c] = max(A[r-1,c-1] + 1 if s[c] = t[r] else 0, A[r-1,c] + 0, A[r,c-1] + 0) for 1 <= c <= |s| and 1 <= r <= |t|
+# 2. Proof:
+# 3. Implementation: buttom up solution
+#    Running time: O(nm)
+#    Space Complexity: O(nm)
+class Solution:
+    def __init__(self, s, t):
+        self.rows_count = len(t) + 1
+        self.columns_count = len(s) + 1
+
+        A = self.built_lcs_matrix(s, t)
+        self.lcs = self.get_lcs(A)
+
+    def built_lcs_matrix(self, s, t):
+        A = [ [0 for _ in range(self.columns_count)] for _ in range(self.rows_count)]
+
+        for r in range(1, self.rows_count, 1):
+            for c in range(1, self.columns_count, 1):
+                alignment_score = A[r-1][c-1] + 1 if t[r-1] == s[c-1] else 0
+                delete_score = A[r][c-1]
+                insert_score = A[r-1][c]
+                A[r][c] = max(alignment_score, delete_score, insert_score)
+
+        return A
+
+    def get_lcs(self, A):
+        lcs_inverse_list = []
+
+        r = self.rows_count - 1
+        c = self.columns_count - 1
+        while r > 0 and c > 0:
+            
+            if A[r][c] == A[r - 1][c - 1] + 1 and s[c - 1] == t[r - 1]:
+                lcs_inverse_list.append(s[c - 1])
+                c = c - 1
+                r = r - 1
+
+            elif A[r][c] == A[r - 1][c - 1]:
+                c = c - 1
+                r = r - 1
+
+            elif A[r][c] == A[r][c - 1]:
+                c = c - 1
+
+            elif A[r][c] == A[r - 1][c]:
+                r = r - 1
+        
+        return ''.join(lcs_inverse_list[::-1])
+
+
+if __name__ == "__main__":
+    s,t = sys.stdin.read().strip().splitlines()
+    
+    lcs_solution = Solution(s,t)
+
+    print(lcs_solution.lcs)

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/01

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+GACT
+ATG

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/01e

@@ -0,0 +1 @@
+AT

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/01r

@@ -0,0 +1 @@
+AT

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/02

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+ACTGAG
+GACTGG

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/02e

@@ -0,0 +1 @@
+ACTGG

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/02r

@@ -0,0 +1 @@
+ACTGG

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/03

@@ -0,0 +1,2 @@
+AC
+AC

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/03e

@@ -0,0 +1 @@
+AC

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/03r

@@ -0,0 +1 @@
+AC

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/04

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+GGGGT
+CCCCT

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/04e

@@ -0,0 +1 @@
+T

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/04r

@@ -0,0 +1 @@
+T

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/05

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+TCCCC
+TGGGG

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/05e

@@ -0,0 +1 @@
+T

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/05r

@@ -0,0 +1 @@
+T

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/06

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+AA
+CGTGGAT

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/06e

@@ -0,0 +1 @@
+A

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/06r

@@ -0,0 +1 @@
+A

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/07

@@ -0,0 +1,2 @@
+GGTGACGT
+CT

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/07e

@@ -0,0 +1 @@
+CT

6-dynamic-programming-applications-in-machine-learning-and-genomics/1-sequence-alignment-1/longest_common_subsequence_tests/07r

@@ -0,0 +1 @@
+CT