# Program to find length of longest common subsequence of three strings in Python

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Suppose we have three strings s1, s2, and s3, we have to find the length of their longest common subsequence.

So, if the input is like s1 = "ababchemxde" s2 = "pyakcimde" s3 = "oauctime", then the output will be 4, as the longest common subsequence is "acme".

To solve this, we will follow these steps −

• m := size of s1, n := size of s2, o := size of s3
• dp := a 3D matrix of size (o + 1) x (n + 1) x (m + 1)
• for i in range 1 to m, do
• for j in range 1 to n, do
• for k in range 1 to o, do
• if s1[i - 1], s2[j - 1], s3[k - 1] are same, then
• dp[i, j, k] := 1 + dp[i - 1, j - 1, k - 1]
• otherwise,
• dp[i, j, k] = maximum of (dp[i - 1, j, k], dp[i, j - 1, k] and dp[i,j, k - 1])
• return dp[m, n, o]

## Example (Python)

Let us see the following implementation to get better understanding −

Live Demo

class Solution:
def solve(self, s1, s2, s3):
m = len(s1)
n = len(s2)
o = len(s3)
dp = [[[0 for i in range(o + 1)] for j in range(n + 1)] for k in range(m + 1)]
for i in range(1, m + 1):
for j in range(1, n + 1):
for k in range(1, o + 1):
if s1[i - 1] == s2[j - 1] == s3[k - 1]:
dp[i][j][k] = 1 + dp[i - 1][j - 1][k - 1]
else:
dp[i][j][k] = max(dp[i - 1][j][k], dp[i][j - 1][k], dp[i][j][k - 1])
return dp[m][n][o]
ob = Solution()
s1 = "ababchemxde"
s2 = "pyakcimde"
s3 = "oauctime"
print(ob.solve(s1, s2, s3))

## Input

"ababchemxde", "pyakcimde", "oauctime"

## Output

4
Updated on 12-Dec-2020 10:36:12