Print LCS string using memoization

m,n=len(s1),len(s2)
dp={}
def lcs(i,j):
    if (i,j)in dp:return dp[i,j]
    if i==m or j==n:
        dp[i,j]=0
    else:
        if s1[i]==s2[j]:
            dp[i,j]=1+lcs(i+1,j+1)
        else:
            dp[i,j]=max(lcs(i+1,j),lcs(i,j+1))

    return dp[i,j]
for i in range(m+1):
    for j in range(n+1):
        if (i,j) not in dp:
            lcs(i,j)

i,j,item=0,0,[]
while i<m and j<n:
    if s1[i]==s2[j]:
        item.append(s1[i])
        i,j=i+1,j+1
    elif dp[i+1,j]>dp[i,j+1]:
        i=i+1
    else:
        j=j+1
print(item)