Suppose we have a string s. We have to check whether we can split s into three palindromic substring or not.
So, if the input is like s = "levelpopracecar", then the output will be True because we can split it like "level", "pop", "racecar", all are palindromes.
To solve this, we will follow these steps −
n := size of s
dp := a matrix of order n x n and fill with false
for i in range n-1 to 0, decrease by 1, do
for j in range 0 to n - 1, do
if i >= j, then
dp[i, j] := True
otherwise when s[i] is same as s[j], then
dp[i, j] := dp[i+1, j-1]
for i in range 1 to n - 1, do
for j in range i+1 to n - 1, do
if dp[0, i-1] and dp[i, j-1] and dp[j, n-1] all are true, then
return True
return False
Example
Let us see the following implementation to get better understanding
def solve(s):
n = len(s)
dp = [[False] * n for _ in range(n)]
for i in range(n-1, -1, -1):
for j in range(n):
if i >= j:
dp[i][j] = True
elif s[i] == s[j]:
dp[i][j] = dp[i+1][j-1]
for i in range(1, n):
for j in range(i+1, n):
if dp[0][i-1] and dp[i][j-1] and dp[j][n-1]:
return True
return False
s = "levelpopracecar"
print(solve(s))Input
"levelpopracecar"
Output
True