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49 lines
1.3 KiB
Python
49 lines
1.3 KiB
Python
"""
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LCS Problem Statement: Given two sequences, find the length of longest subsequence present in both of them.
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A subsequence is a sequence that appears in the same relative order, but not necessarily continious.
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Example:"abc", "abg" are subsequences of "abcdefgh".
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"""
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def LCS(x,y):
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b=[[] for j in range(len(x)+1)]
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c=[[] for i in range(len(x))]
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for i in range(len(x)+1):
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b[i].append(0)
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for i in range(1,len(y)+1):
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b[0].append(0)
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for i in range(len(x)):
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for j in range(len(y)):
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if x[i]==y[j]:
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b[i+1].append(b[i][j]+1)
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c[i].append('/')
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elif b[i][j+1]>=b[i+1][j]:
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b[i+1].append(b[i][j+1])
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c[i].append('|')
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else :
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b[i+1].append(b[i+1][j])
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c[i].append('-')
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return b,c
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def print_lcs(x,c,n,m):
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n,m=n-1,m-1
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ans=[]
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while n>=0 and m>=0:
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if c[n][m]=='/':
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ans.append(x[n])
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n,m=n-1,m-1
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elif c[n][m]=='|':
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n=n-1
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else:
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m=m-1
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ans=ans[::-1]
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return ans
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if __name__=='__main__':
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x=['a','b','c','b','d','a','b']
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y=['b','d','c','a','b','a']
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b,c=LCS(x,y)
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print('Given \nX : ',x)
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print('Y : ',y)
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print('LCS : ',print_lcs(x,c,len(x),len(y)))
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