**Problem:** Given an input string s and a pattern p, implement regular expression matching with support for '.' and '*' where:

**'.' Matches any single character.**

**'*' Matches zero or more of the preceding element.**

*The matching should cover the entire input string (not partial).*

Can anyone help me with this ?

i tried two pointers and it failed, then I looked at the solution. It was DP but I could not get the idea on how to think and understand that, Can anyone explain in easiest words to me please ?

Thanks

**Spoiler**

I'd be happy to help you understand the dynamic programming approach for regular expression matching.

Key idea:The problem can be broken down into two main cases:

The goal is to determine whether the entire pattern matches the entire input string.

Dynamic Programming (DP) approach:Create a 2D array

`dp`

with dimensions`(len(s) + 1) x (len(p) + 1)`

where`dp[i][j]`

represents whether the first`i`

characters in`s`

match the first`j`

characters in`p`

.Initialization:`dp[0][0] = true`

(empty pattern matches empty string)`dp[0][j] = false`

for`j > 0`

(pattern is not empty, but string is empty)`dp[i][0] = false`

for`i > 0`

(string is not empty, but pattern is empty)Transition rules:`p[j - 1] == '.'`

, then`dp[i][j] = dp[i - 1][j - 1]`

(dot matches any single character)`p[j - 1] == s[i - 1]`

, then`dp[i][j] = dp[i - 1][j - 1]`

(match if characters match)`p[j - 1] == '*'`

, then:`dp[i][j - 2]`

is true, then`dp[i][j] = true`

(zero or more of the preceding element)`p[j - 2] == s[i - 1] || p[j - 2] == '.'`

, then`dp[i][j] = dp[i][j - 2] || dp[i - 1][j]`

(match if zero or more preceding elements match)Return value:`dp[len(s)][len(p)]`

represents whether the entire pattern matches the entire input string.Example:Let's consider the input string "aab" and pattern "c*a*b".

The final result is

`dp[3][4] = true`

, indicating that the pattern "c*a*b" matches the input string "aab".Why it works:The DP approach ensures that we consider all possible combinations of matching and non-matching characters in both the input string and the pattern. By using the transition rules and initialization values, we can efficiently determine whether the entire pattern matches the entire input string.

I hope this explanation helps you understand the dynamic programming approach for regular expression matching!

this is chat gpt, I bet you didnt right it yourself

wow, this coming from a self-proclaimed cheater is

crazyAuto comment: topic has been updated by StellarSpecter (previous revision, new revision, compare).Let me explain:

IF CHARACTER IS "."then. string must have single character at some indexelse

IF CHARACTER IS "*"therefore: it will equal previous or not element.THEREFORE "." character will always work because it matches any character.SIMILARLY "*" character wiill always work because it need not be equal previous characterTherefore need for dynamic programming is unnecessary. I think entire string works.