# Program to find length longest prefix sequence of a word array in Python

Suppose we have a list of words called w, with lowercase strings. We have to find the length of the longest sequence of w where each previous word is the prefix of the next word and the next word has just one new character appended.

So, if the input is like w = ["pqr", "pq", "m", "mn", "pqrs"], then the output will be 3 because we can get the sequence: ["pq", "pqr", "pqrs"], whose length is 3.

To solve this, we will follow these steps −

• sort the list w
• dp := a map, where default value for a key is 0
• res := 0
• for each word in w, do
• dp[word] := dp[substring of word up to second last element] + 1
• res := maximum of res and dp[word]
• return res

## Example

Let us see the following implementation to get better understanding −

from collections import defaultdict
def solve(w):
w.sort()
dp = defaultdict(int)
res = 0
for word in w:
dp[word] = dp[word[:-1]] + 1
res = max(res, dp[word])
return res

w = ["pqr", "pq", "m", "mn", "pqrs"]
print(solve(w))

## Input

["pqr", "pq", "m", "mn", "pqrs"]

## Output

3