## Algorithm

Problem Name: 1096. Brace Expansion II

Under the grammar given below, strings can represent a set of lowercase words. Let `R(expr)` denote the set of words the expression represents.

The grammar can best be understood through simple examples:

• Single letters represent a singleton set containing that word.
• `R("a") = {"a"}`
• `R("w") = {"w"}`
• When we take a comma-delimited list of two or more expressions, we take the union of possibilities.
• `R("{a,b,c}") = {"a","b","c"}`
• `R("{{a,b},{b,c}}") = {"a","b","c"}` (notice the final set only contains each word at most once)
• When we concatenate two expressions, we take the set of possible concatenations between two words where the first word comes from the first expression and the second word comes from the second expression.
• `R("{a,b}{c,d}") = {"ac","ad","bc","bd"}`
• `R("a{b,c}{d,e}f{g,h}") = {"abdfg", "abdfh", "abefg", "abefh", "acdfg", "acdfh", "acefg", "acefh"}`

Formally, the three rules for our grammar:

• For every lowercase letter `x`, we have `R(x) = {x}`.
• For expressions `e1, e2, ... , ek` with `k >= 2`, we have `R({e1, e2, ...}) = R(e1) ∪ R(e2) ∪ ...`
• For expressions `e1` and `e2`, we have `R(e1 + e2) = {a + b for (a, b) in R(e1) × R(e2)}`, where `+` denotes concatenation, and `×` denotes the cartesian product.

Given an expression representing a set of words under the given grammar, return the sorted list of words that the expression represents.

Example 1:

```Input: expression = "{a,b}{c,{d,e}}"
```

Example 2:

```Input: expression = "{{a,z},a{b,c},{ab,z}}"
Output: ["a","ab","ac","z"]
Explanation: Each distinct word is written only once in the final answer.
```

Constraints:

• `1 <= expression.length <= 60`
• `expression[i]` consists of `'{'`, `'}'`, `','`or lowercase English letters.
• The given `expression` represents a set of words based on the grammar given in the description.

## Code Examples

### #1 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const braceExpansionII = function (expression) {
expression = expression.replace(/([a-z]){1}/g, '{\$1}')
const stk = new Array()
for (let char of expression) {
if (char !== '}') {
stk.push(char)
} else {
let str = '',
prev = '',
temp = ''
while (stk[stk.length - 1] != '{') {
prev = temp
temp = stk.pop()
if (temp == ',' || prev == ',' || str == '') str = temp + str
else {
str = str
.split(',')
.map((item) => {
let ar = new Array()
for (let ch of temp.split(',')) ar.push(ch + item)
return ar.join(',')
})
.join(',')
}
}
stk.pop()
while (
stk.length > 0 &&
stk[stk.length - 1] != ',' &&
stk[stk.length - 1] != '{'
) {
temp = stk.pop()
str = str
.split(',')
.map((item) => {
let ar = new Array()
for (let ch of temp.split(',')) ar.push(ch + item)
return ar.join(',')
})
.join(',')
}

if (str.length > 0) stk.push(str)
}
}

return [...new Set(stk[0].split(','))].sort()
}
``````
Copy The Code &

Input

cmd
expression = "{a,b}{c,{d,e}}"

Output

cmd

### #2 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def braceExpansionII(self, expression: str) -> List[str]:
stack,res,cur=[],[],[]
for i in range(len(expression)):
v=expression[i]
if v.isalpha():
cur=[c+v for c in cur or ['']]
elif v=='{':
stack.append(res)
stack.append(cur)
res,cur=[],[]
elif v=='}':
pre=stack.pop()
preRes=stack.pop()
cur=[p+c for c in res+cur for p in pre or ['']]
res=preRes
elif v==',':
res+=cur
cur=[]
return sorted(set(res+cur))

``````
Copy The Code &

Input

cmd
expression = "{a,b}{c,{d,e}}"

Output

cmd

### #3 Code Example with C# Programming

```Code - C# Programming```

``````
using System.Collections.Generic;
using System.Linq;

namespace LeetCode
{
public class _1096_BraceExpansionII
{
public IList BraceExpansionII(string expression)
{
var stack = new Stack>();
var union = new List();
var product = new List() { "" };

foreach (var ch in expression)
{
if (ch >= 'a' && ch <= 'z')
{
for (int i = 0; i < product.Count; i++)
product[i] += ch;
}
else if (ch == '{')
{
stack.Push(union);
stack.Push(product);
union = new List();
product = new List() { "" };
}
else if (ch == '}')
{
var pre_product = stack.Pop();
var pre_union = stack.Pop();

product = new List();
foreach (var str1 in pre_product)
foreach (var str2 in union)
union = pre_union;
}
else
{
product = new List() { "" };
}
}

return union.Distinct().OrderBy(s => s).ToList();
}
}
}
``````
Copy The Code &

Input

cmd
expression = "{{a,z},a{b,c},{ab,z}}"

Output

cmd
["a","ab","ac","z"]