leetcode_gym/_problems/longestCommonSubsequence.md

layout, title

layout	title
page	Longest Common Subsequence

Input: text1 = "abcde", text2 = "ace" 
Output: 3  
Explanation: The longest common subsequence is "ace" and its length is 

Gotchas

• look out for the dimension with which you build the grid (ie: m<->i, n<->j)
  • table=[[0]*(n+1) for x in range(m+1)]
  • otherwise you could run into a array out of bounds error

{% highlight python %}

str1 = "AAB" str2 = "AZB"

def lcs(text1, text2):

n= len(text1)
m= len(text2)

# creates an [m+1][n+1] matrix, filled with zeros
table=[[0]*(n+1) for x in range(m+1)]

for i in range(1, m+1):
    for j in range (1, n+1):

        # first char is the same, so add 1 to count
        if text2[i-1]==text1[j-1]:
            table[i][j]= 1+table[i-1][j-1]
        # first char is different, so break into subproblems and take the max
        else:
            table[i][j]=max(table[i-1][j],table[i][j-1])


print [0]*(n+1)
print range(m+1)
print table
print max(table)    # this get the last element at the end of the list
return max(max(table))  # this gets the last element at the bottom right corner (last element of both lists)

print lcs(str1, str2)

{% endhighlight %}