647-palindromic-substrings

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Description

Given a string s, return the number of palindromic substrings in it.

A string is a palindrome when it reads the same backward as forward.

A substring is a contiguous sequence of characters within the string.

 

Example 1:

Input: s = "abc"
Output: 3
Explanation: Three palindromic strings: "a", "b", "c".

Example 2:

Input: s = "aaa"
Output: 6
Explanation: Six palindromic strings: "a", "a", "a", "aa", "aa", "aaa".

 

Constraints:

• 1 <= s.length <= 1000
• s consists of lowercase English letters.

Solution(Python)

class Solution:
    def countSubstrings(self, s: str) -> int:
        return self.dptable(s)

    # Time Complexity: O(n^3)
    # Space Complexity: O(1)
    def bruteforce(self, s: str) -> int:
        n = len(s)
        cnt = 0
        for i in range(n):
            for j in range(i, n):
                if self.ispalindrome(s[i: j + 1]):
                    cnt += 1
        return cnt

    # Time Complexity: O(n^2)
    # Space Complexity: O(n^2)
    def topdown(self, s: str) -> int:
        n = len(s)
        cnt = 0
        dp = [[-1 for _ in range(n)] for _ in range(n)]

        def solve(i, j):
            if i >= j:
                return 1

            if dp[i][j] != -1:
                return dp[i][j]

            dp[i][j] = solve(i + 1, j - 1) if s[i] == s[j] else 0
            return dp[i][j]

        for i in range(n):
            for j in range(i, n):
                cnt += solve(i, j)
        return cnt

    # Time Complexity: O(n^2)
    # Space Complexity: O(n^2)
    def dptable(self, s: str) -> int:
        n = len(s)
        dp = [[False] * n for _ in range(n)]

        ans = 0
        for i in range(n - 1, -1, -1):
            for j in range(i, n):
                if s[i] == s[j]:
                    if i + 1 >= j:
                        dp[i][j] = True
                    else:
                        dp[i][j] = dp[i + 1][j - 1]

                if dp[i][j]:
                    ans += 1
        return ans

    def ispalindrome(self, string):
        s, e = 0, len(string) - 1

        while s <= e:
            if string[s] != string[e]:
                return False
            s += 1
            e -= 1

        return True