### Brackets

January 31, 2020

A string S consisting of N characters is considered to be properly nested if any of the following conditions is true:

• S is empty;

• S has the form "(U)" or "[U]" or "{U}" where U is a properly nested string;

• S has the form "VW" where V and W are properly nested strings.

For example, the string **"{[()()]}"** is properly nested but **"([)()]"** is not.

**Write a function:**

function solution(S);

that, given a string S consisting of N characters, returns 1 if S is properly nested and 0 otherwise.

For example, given S = "{[()()]}", the function should return 1 and given S = "([)()]", the function should return 0, as explained above.

Write an efficient algorithm for the following assumptions:

• N is an integer within the range [0..200,000];

• string S consists only of the following characters: "(", "{", "[", "]", "}" and/or ")".

**Hints**

• push left brackets into an array L1

• compare non-left brackets with L1.pop()

```
function isPair(c1, c2){
if( c1=='(' && c2==')' ) return true
if( c1=='{' && c2=='}' ) return true
if( c1=='[' && c2==']' ) return true
return false
}
function solution(S) {
// write your code in JavaScript (Node.js 8.9.4)
if(S.length < 1) return 1
let L = ['(', '{', '[']
let L1 = []
let c
for(let i=0; i<S.length; i++){
if( L.includes(S[i])){ // Left brackets
L1.push(S[i])
} else { // Right brackets
if(L1.length < 1) return 0 // no left barckets for matching
c = L1.pop()
if( !isPair(c, S[i])) return 0
}
}
if( L1.length < 1) return 1 // all popped out
else return 0 // Let brackets remaining
}
```