HardNo. 2484
Count Palindromic Subsequences — LeetCode 2484 Python Solution
- Pattern
- Dynamic Programming
- Topics
- String, Dynamic Programming
- Reading time
- 5 min
- Source
- leetcode.com
The problem
Given a string of digits s, return the number of palindromic subsequences of s having length 5. Since the answer may be very large, return it modulo 109 + 7.
Example
- Input
- s = "103301"
- Output
- 2
- Explanation
- There are 6 possible subsequences of length 5: "10330","10331","10301","10301","13301","03301".
Python solution
class Solution:
def countPalindromes(self, s: str) -> int:
mod = 10**9 + 7
n = len(s)
pre = [[[0] * 10 for _ in range(10)] for _ in range(n + 2)]
suf = [[[0] * 10 for _ in range(10)] for _ in range(n + 2)]
t = list(map(int, s))
c = [0] * 10
for i, v in enumerate(t, 1):
for j in range(10):
for k in range(10):
pre[i][j][k] = pre[i - 1][j][k]
for j in range(10):
pre[i][j][v] += c[j]
c[v] += 1
c = [0] * 10
for i in range(n, 0, -1):
v = t[i - 1]
for j in range(10):
for k in range(10):
suf[i][j][k] = suf[i + 1][j][k]
for j in range(10):
suf[i][j][v] += c[j]
c[v] += 1
ans = 0
for i in range(1, n + 1):
for j in range(10):
for k in range(10):
ans += pre[i - 1][j][k] * suf[i + 1][j][k]
ans %= mod
return ansComplexity
- Time
- O(100 × n)
- Space · auxiliary
- O(100 × n)
Pattern: Dynamic Programming
Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2484. Count 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.
Related problems
| No. | Problem | Difficulty |
|---|---|---|
| 2478 | Number of Beautiful Partitions | Hard |
| 0010 | Regular Expression Matching | Hard |
| 0022 | Generate Parentheses | Medium |
| 0032 | Longest Valid Parentheses | Hard |
| 0044 | Wildcard Matching | Hard |
| 0072 | Edit Distance | Medium |
Frequently asked questions
- How hard is LeetCode 2484. Count Palindromic Subsequences?
LeetCode 2484. Count Palindromic Subsequences is rated Hard on LeetCode.
- What is the time complexity of LeetCode 2484. Count Palindromic Subsequences?
The Python solution on this page runs in O(100 × n).
- What is the space complexity of LeetCode 2484. Count Palindromic Subsequences?
The Python solution on this page uses O(100 × n) auxiliary space.
- What topics does LeetCode 2484. Count Palindromic Subsequences cover?
LeetCode 2484. Count Palindromic Subsequences is tagged String and Dynamic Programming on LeetCode.