How hard is LeetCode 730. Count Different Palindromic Subsequences?

LeetCode 730. Count Different Palindromic Subsequences is rated Hard on LeetCode.

What topics does LeetCode 730. Count Different Palindromic Subsequences cover?

LeetCode 730. Count Different Palindromic Subsequences is tagged String and Dynamic Programming on LeetCode.

Count Different Palindromic Subsequences — LeetCode 730 Python Solution

HardStringDynamic Programming

Problem: #730
Pattern: Dynamic Programming
Reading time: 4 min
Source: leetcode.com

The problem

Given a string s, return the number of different non-empty palindromic subsequences in s. Since the answer may be very large, return it modulo 109 + 7.

Example

Input: s = "bccb"
Output: 6
Explanation: The 6 different non-empty palindromic subsequences are 'b', 'c', 'bb', 'cc', 'bcb', 'bccb'.

Python solution

Python

class Solution:
    def countPalindromicSubsequences(self, s: str) -> int:
        mod = 10**9 + 7
        n = len(s)
        dp = [[[0] * 4 for _ in range(n)] for _ in range(n)]
        for i, c in enumerate(s):
            dp[i][i][ord(c) - ord('a')] = 1
        for l in range(2, n + 1):
            for i in range(n - l + 1):
                j = i + l - 1
                for c in 'abcd':
                    k = ord(c) - ord('a')
                    if s[i] == s[j] == c:
                        dp[i][j][k] = 2 + sum(dp[i + 1][j - 1])
                    elif s[i] == c:
                        dp[i][j][k] = dp[i][j - 1][k]
                    elif s[j] == c:
                        dp[i][j][k] = dp[i + 1][j][k]
                    else:
                        dp[i][j][k] = dp[i + 1][j - 1][k]
        return sum(dp[0][-1]) % mod

Complexity

Measure	Complexity
Time	O(n·m) (typical)
Space	O(n·m) or optimized auxiliary

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 730. Count Different Palindromic Subsequences is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 730. Count Different Palindromic Subsequences?: LeetCode 730. Count Different Palindromic Subsequences is rated Hard on LeetCode.
What topics does LeetCode 730. Count Different Palindromic Subsequences cover?: LeetCode 730. Count Different Palindromic Subsequences is tagged String and Dynamic Programming on LeetCode.