Generate Parentheses

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Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

For example, given n = 3, a solution set is:

"((()))", "(()())", "(())()", "()(())", "()()()"

Java Solution 1 – DFS

This solution is simple and clear. In the dfs() method, left stands for the remaining number of (, right stands for the remaining number of ).

public List<String> generateParenthesis(int n) {
    ArrayList<String> result = new ArrayList<String>();
    dfs(result, "", n, n);
    return result;
}
/*
left and right represents the remaining number of ( and ) that need to be added. 
When left > right, there are more ")" placed than "(". Such cases are wrong and the method stops. 
*/
public void dfs(ArrayList<String> result, String s, int left, int right){
    if(left > right)
        return;
 
    if(left==0&amp;&amp;right==0){
        result.add(s);
        return;
    }
 
    if(left>0){
        dfs(result, s+"(", left-1, right);
    }
 
    if(right>0){
        dfs(result, s+")", left, right-1);
    }
}

Generate Parentheses Java Solution 2

This solution looks more complicated. You can use n=2 to walk through the code.

public List<String> generateParenthesis(int n) {
	ArrayList<String> result = new ArrayList<String>();
	ArrayList<Integer> diff = new ArrayList<Integer>();
 
	result.add("");
	diff.add(0);
 
	for (int i = 0; i < 2 * n; i++) {
		ArrayList<String> temp1 = new ArrayList<String>();
		ArrayList<Integer> temp2 = new ArrayList<Integer>();
 
		for (int j = 0; j < result.size(); j++) {
			String s = result.get(j);
			int k = diff.get(j);
 
			if (i < 2 * n - 1) {
				temp1.add(s + "(");
				temp2.add(k + 1);
			}
 
			if (k > 0 &amp;&amp; i < 2 * n - 1 || k == 1 &amp;&amp; i == 2 * n - 1) {
				temp1.add(s + ")");
				temp2.add(k - 1);
			}
		}
 
		result = new ArrayList<String>(temp1);
		diff = new ArrayList<Integer>(temp2);
	}
 
	return result;
}


Object-oriented programming offers a sustainable way to write spaghetti code. It lets you accrete programs as a series of patches.” 
― Paul Graham, Hackers & Painters: Big Ideas from the Computer Age

You can also check out Longest Valid Parentheses

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