[LeetCode] 17. Letter Combinations of a Phone Number *的字母组合

Given a digit string, return all possible letter combinations that the number could represent.

A mapping of digit to letters (just like on the telephone buttons) is given below.

Input:Digit string "23"
Output: ["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"].

Note:
Although the above answer is in lexicographical order, your answer could be in any order you want.

给一串数字，按电话键盘上数字可代表的字母，求出所有可能的组合。

解法1: 递归Recursion，和subset, combination问题类似的DFS+backtracking。先要用HashMap或者数组建立一个从数字到字母的转换表，然后每一层递归遍历当前digits[i]所对应的所有字母，并加入当前combination中传到下一层递归。

解法2: 迭代Iteration。

Java: Recursion, Time: O(3^n), Space: O(n)

public class Solution {
    private static final String[] keyboard =
            new String[]{ " ", "", "abc", "def", // '0','1','2',...
            "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz" };

    public List<String> letterCombinations(String digits) {
        List<String> result = new ArrayList<>();
        if (digits.isEmpty()) return result;
        dfs(digits, 0, "", result);
        return result;
    }

    private static void dfs(String digits, int cur, String path,
                            List<String> result) {
        if (cur == digits.length()) {
            result.add(path);
            return;
        }
        final String str = keyboard[digits.charAt(cur) - '0'];

        for (char c : keyboard[digits.charAt(cur) - '0'].toCharArray()) {
            dfs(digits, cur + 1, path + c, result);
        }
    }
}

Java: Iteration, Time: O(3^n), Space: O(1)

public class Solution {
    private static final String[] keyboard =
            new String[]{ " ", "", "abc", "def", // '0','1','2',...
                    "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz" };

    public List<String> letterCombinations(String digits) {
        if (digits.isEmpty()) return new ArrayList<>();
        List<String> result = new ArrayList<>();
        result.add("");
        for (char d : digits.toCharArray()) {
            final int n = result.size();
            final int m = keyboard[d - '0'].length();

            // resize to n * m
            for (int i = 1; i < m; ++i) {
                for (int j = 0; j < n; ++j) {
                    result.add(result.get(j));
                }
            }

            for (int i = 0; i < result.size(); ++i) {
                result.set(i, result.get(i) + keyboard[d - '0'].charAt(i/n));
            }
        }
        return result;
    }
}

Java: BFS, LinkedList

public class Solution {
    public List<String> letterCombinations(String digits) {
        LinkedList<String> res = new LinkedList<>();
        if (digits == null || digits.length() == 0) return res;
        String[] map = new String[] {"", "", "abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"};
        res.add("");
        for (int i = 0; i < digits.length(); i++) {
            int index = digits.charAt(i) - '0';
            while (res.peek().length() == i) {
                String t = res.remove();
                for (char c : map[index].toCharArray()) {
                    res.add(t + c);
                }
            }
        }
        return res;
    }
}

Java: Recursion, HashMap, Time: O(3^n), Space: O(n)

public class Solution {
    public ArrayList<String> letterCombinations(String digits) {
        ArrayList<String> result = new ArrayList<String>();

        if (digits == null || digits.equals("")) {
            return result;
        }

        Map<Character, char[]> map = new HashMap<Character, char[]>();
        map.put('0', new char[] {});
        map.put('1', new char[] {});
        map.put('2', new char[] { 'a', 'b', 'c' });
        map.put('3', new char[] { 'd', 'e', 'f' });
        map.put('4', new char[] { 'g', 'h', 'i' });
        map.put('5', new char[] { 'j', 'k', 'l' });
        map.put('6', new char[] { 'm', 'n', 'o' });
        map.put('7', new char[] { 'p', 'q', 'r', 's' });
        map.put('8', new char[] { 't', 'u', 'v'});
        map.put('9', new char[] { 'w', 'x', 'y', 'z' });

        StringBuilder sb = new StringBuilder();
        helper(map, digits, sb, result);

        return result;
    }

    private void helper(Map<Character, char[]> map, String digits, 
        StringBuilder sb, ArrayList<String> result) {
        if (sb.length() == digits.length()) {
            result.add(sb.toString());
            return;
        }

        for (char c : map.get(digits.charAt(sb.length()))) {
            sb.append(c);
            helper(map, digits, sb, result);
            sb.deleteCharAt(sb.length() - 1);
        }
    }
}

Java: Iteration, FIFO queue

public class Solution {
    private String[] mapping = new String[] {"0", "1", "abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"};
    public List<String> letterCombinations(String digits) {
    LinkedList<String> ans = new LinkedList<String>();
    if(digits.length()<1) return ans;
    ans.add("");
    for(int i =0; i<digits.length();i++){
        int x = digits.charAt(i) - '0';
        while(ans.peek().length()==i){
            String t = ans.remove();
            for(char s : mapping[x].toCharArray())
                ans.add(t+s);
        }
    }
    return ans;
    }
}　　

Python: Recursion

class Solution:
    def letterCombinations(self, digits):
        if not digits:
            return []
        lookup, result = ["", "", "abc", "def", "ghi", "jkl", "mno", 
                          "pqrs", "tuv", "wxyz"], []
        self.letterCombinationsRecu(result, digits, lookup, "", 0)
        return result
    
    def letterCombinationsRecu(self, result, digits, lookup, cur, n):
        if n == len(digits):
            result.append(cur)
        else:
            for choice in lookup[int(digits[n])]:
                self.letterCombinationsRecu(result, digits, lookup, cur + choice, n + 1)

Python: Iteration

class Solution:
    def letterCombinations(self, digits):
        if not digits:
            return []
            
        lookup, result = ["", "", "abc", "def", "ghi", "jkl", "mno", 
                          "pqrs", "tuv", "wxyz"], [""]

        for digit in reversed(digits):
            choices = lookup[int(digit)]
            m, n = len(choices), len(result)
            result += [result[i % n] for i in xrange(n, m * n)]    

            for i in xrange(m * n):
                result[i] = choices[i / n] + result[i] 
            
        return result　　

C++: Recursion

class Solution {
public:
    vector<string> letterCombinations(string digits) {
        vector<string> lettComb;
        string dict[] = {" ", "", "abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"};
        string comb(digits.size(),'');
        findLettComb(digits, 0, dict, comb, lettComb);
        return lettComb;
    }
    
    void findLettComb(string &digits, int index, string dict[], string &comb, vector<string> &lettComb) {
        if(index==digits.size()) {
            lettComb.push_back(comb);
            return;
        }
        
        string lett= dict[digits[index] - '0'];
        for(int i=0; i<lett.size(); i++) {
            comb[index] = lett[i];
            findLettComb(digits, index+1, dict, comb, lettComb);
        }
    }
};　

 C++：Iteration

class Solution {
public:
    vector<string> letterCombinations(string digits) {
        vector<string> res;
        if (digits.empty()) return res;
        string dict[] = {"abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"};
        res.push_back("");
        for (int i = 0; i < digits.size(); ++i) {
            int n = res.size();
            string str = dict[digits[i] - '2'];
            for (int j = 0; j < n; ++j) {
                string tmp = res.front();
                res.erase(res.begin());
                for (int k = 0; k < str.size(); ++k) {
                    res.push_back(tmp + str[k]);
                }
            }
        }
        return res;
    }
};

　　

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