【Letter Combinations of a Phone Number】cpp

题目：

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.

代码：

class Solution {
public:
    vector<string> letterCombinations(string digits) {
            vector<string> ret;
            if ( digits.empty() ) return ret; 
            map<int, string> digitLetters;
            digitLetters[0] = "";
            digitLetters[1] = "";
            digitLetters[2] = "abc";
            digitLetters[3] = "def";
            digitLetters[4] = "ghi";
            digitLetters[5] = "jkl";
            digitLetters[6] = "mno";
            digitLetters[7] = "pqrs";
            digitLetters[8] = "tuv";
            digitLetters[9] = "wxyz";
            vector<int> letterBegin(10,0);
            int index = 0;
            string tmp;
            Solution::combine(ret, tmp, index, digits, digitLetters, letterBegin);
            return ret;
    }
    static void combine(
        vector<string>& ret, 
        string& tmp, 
        int index, 
        string& digits, 
        map<int,string>& digitLetters, 
        vector<int>& letterBegin)
    {    
            if (index==digits.size())
            {
                ret.push_back(tmp);
                return;
            }
            int curr = digits[index]-'0';
            string letters = digitLetters[curr];
            for ( int i = 0; i < letters.size(); ++i )
            {
                letterBegin[curr] = i;
                tmp.push_back(letters[i]);
                Solution::combine(ret, tmp, index+1, digits, digitLetters, letterBegin);
                tmp.erase(tmp.end()-1);
            }
    }
};

tips：

上述的代码是AC的。思路也就是常规dfs的思路：

1. 终止条件是层级到了digits的长度

2. 每一层递归相当于根据该位置的数字选一个字母

但是，个人感觉这道题的题干要求没说清楚；既然是letter combinations，而不是letter permutation，那么“ac”和“ca”就应该算一个combination，但是OJ之后发现默认“ac”和“ca”算两个。加入“ac”和“ca”算一个，有没有解法呢？代码如下：

class Solution {
public:
    vector<string> letterCombinations(string digits) {
            vector<string> ret;
            if ( digits.empty() ) return ret; 
            map<int, string> digitLetters;
            digitLetters[0] = "";
            digitLetters[1] = "";
            digitLetters[2] = "abc";
            digitLetters[3] = "def";
            digitLetters[4] = "ghi";
            digitLetters[5] = "jkl";
            digitLetters[6] = "mno";
            digitLetters[7] = "pqrs";
            digitLetters[8] = "tuv";
            digitLetters[9] = "wxyz";
            vector<int> letterBegin(10,0);
            int index = 0;
            string tmp;
            Solution::combine(ret, tmp, index, digits, digitLetters, letterBegin);
            return ret;
    }
    static void combine(
        vector<string>& ret, 
        string& tmp, 
        int index, 
        string& digits, 
        map<int,string>& digitLetters, 
        vector<int>& letterBegin)
    {    
            if (index==digits.size())
            {
                ret.push_back(tmp);
                return;
            }
            int curr = digits[index]-'0';
            string letters = digitLetters[curr];
            for ( int i = letterBegin[curr]; i < letters.size(); ++i )
            {
                letterBegin[curr] = i;
                tmp.push_back(letters[i]);
                Solution::combine(ret, tmp, index+1, digits, digitLetters, letterBegin);
                tmp.erase(tmp.end()-1);
            }
    }
};

tips：

多维护一个letterBegin的数组，标记“当前的组合中，某个数字对应的字母序列中应该从第几个字母开始取”。

如果输入是“22”，那么给出的解集就是：

从这个例子可以看出来，算法的原理就是维护某一个数字对应字母序列：如果数字重复出现，那么对应的字母要保证字典序递增，这样就不会用重复的。

可惜题目并不是这么要求的。

===============================================

既然题目要求简单了，则再追求一个迭代的解法。AC的代码如下：

class Solution {
public:
    vector<string> letterCombinations(string digits) {
            vector<string> ret;
            if (digits.empty()) return ret;
            ret.push_back("");
            map<int, string> digitLetters;
            digitLetters[2] = "abc";
            digitLetters[3] = "def";
            digitLetters[4] = "ghi";
            digitLetters[5] = "jkl";
            digitLetters[6] = "mno";
            digitLetters[7] = "pqrs";
            digitLetters[8] = "tuv";
            digitLetters[9] = "wxyz";
            for ( size_t i = 0; i < digits.size(); ++i )
            {
                int curr = digits[i]-'0';
                string letters = digitLetters.find(curr)==digitLetters.end() ? "" : digitLetters[curr];
                vector<string> tmp = ret;
                ret.clear();
                for ( size_t j = 0; j < tmp.size(); ++j )
                {
                    for ( size_t k = 0; k < letters.size(); ++k )
                    {
                        string ori = tmp[j];
                        ori += letters[k];
                        ret.push_back(ori);
                    }
                }
            }
            return ret;
    }
};

完毕。

======================================

第二次过这道题，用dfs过的。注意如果原来的digits==""返回的也是空。

class Solution {
public:
        vector<string> letterCombinations(string digits)
        {    
            map<char, string> digit_letters;
            digit_letters['2'] = "abc";
            digit_letters['3'] = "def";
            digit_letters['4'] = "ghi";
            digit_letters['5'] = "jkl";
            digit_letters['6'] = "mno";
            digit_letters['7'] = "pqrs";
            digit_letters['8'] = "tuv";
            digit_letters['9'] = "wxyz";
            vector<string> ret;
            if ( digits=="" ) return ret;
            vector<char> tmp;
            Solution::dfs(ret, digits, tmp, digit_letters); 
            return ret;
        }
        static void dfs(
            vector<string>& ret, 
            string digits, 
            vector<char>& tmp,
            map<char,string>& digit_letters)
        {
            if ( tmp.size()==digits.size() )
            {
                ret.push_back(string(tmp.begin(),tmp.end()));
                return;
            }
            int index = tmp.size();
            for ( int i=0; i<digit_letters[digits[index]].size(); ++i )
            {
                tmp.push_back(digit_letters[digits[index]][i]);
                Solution::dfs(ret, digits, tmp, digit_letters);
                tmp.pop_back();
            }
        }
};