Problem 172: letter combinations of digits of a dialpad

Author: mandliya

README.md

@@ -6,7 +6,7 @@
 
 | Current Status|     Stats     |
 | :------------: | :----------: |
-| Total Problems | 171 |
+| Total Problems | 172 |
 
 </center>
 
@@ -206,6 +206,11 @@ Include contains single header implementation of data structures and some algori
 | Given two integer arrays, A and B, each containing N integers. You are free to permute the order of the elements in the arrays. Is there an permutation A', B' possible of A and B, such that, A'<sub>i</sub>+B'<sub>i</sub> ≥ K for all i, where A'<sub>i</sub> denotes the i<sup>th</sup> element in the array A' and B'<sub>i</sub> denotes i<sup>th</sup> element in the array B'.| [two_arrays.cpp](greedy_problems/two_arrays.cpp)|
 | John is taking orders. The i<sup>th</sup> order is placed by the i<sup>th</sup> customer at t<sub>i</sub> time and it takes d<sub>i</sub> time to procees. What is the order in which the customers will get their orders? (see more details in solutions's comments)|[orders_order.cpp](greedy_problems/orders_order.cpp)|
 
+### Backtracking Problems
+| Problem | Solution |
+| :------------ | :----------: |
+| You are given a digit string (e.g "1234", "567" etc), provide all possible letter combinations we could generate from this digit string, based on the mapping we see on the telphone/mobile dialpad. If you have typed SMS in old style phones, you would know. For e.g. "1" is mapped to "abc", 2 is mapped to "def". You can refer to the <a href="http://techotv.com/wp-content/uploads/2013/03/Lumia-620-dial-pad-screen-1.jpg" target="_blank">image.</a>. <ul><li> Example: "34" will give output: {"dg","dh","di","eg","eh","ei","fg","fh","fi"} </li></ul> Note that order does not matter in result set.|[dialpad_combinations.cpp](backtracking_problems/dialpad_combinations.cpp)|
+
 
 ### Leet code Problems
 | Problem | Solution |

backtracking_problems/dialpad_combinations.cpp

@@ -0,0 +1,80 @@
+/*
+ * You are given a digit string (e.g "1234", "567" etc), 
+ * provide all possible letter combinations we could generate from this digit string,
+ * based on the mapping we see on the telphone/mobile dialpad. 
+ * If you have typed SMS in old style phones, you would know. For e.g. "1" is mapped to "abc", 
+ * 2 is mapped to "def". 
+ * Example: "34" will give output: {"dg","dh","di","eg","eh","ei","fg","fh","fi"}
+ * Note that order does not matter in result set.
+ * 
+ * Approach:
+ * 
+ * We can use a simple backtracking approach. Since each digit letter could be mapped to multiple characters,
+ * for example '1' is mapped to 'a', 'b' and 'c'. As we move along in the digit string, for an index i, we will
+ * add all possible letters to the string and recursively move ahead to i+1, 
+ * i.e. we will choose say 'a' as our choice for the iteration, we map '1' to 'a' and then move to next
+ * digit letter (i+1) and recurse, then we will make 'b' as our choice for position i, and then 'c'
+ * This way we do it for all the letters at all the positions. 
+ * The idea is to generate all possible subsets of the string, keeping in mind the order.
+ */
+
+#include <iostream>
+#include <string>
+#include <unordered_map>
+#include <vector>
+
+std::unordered_map<char, std::string> dict {
+    {'1' , "" },
+    {'2' , "abc"},
+    {'3' , "def"},
+    {'4' , "ghi"},
+    {'5' , "jkl"},
+    {'6' , "mno"},
+    {'7' , "pqrs"},
+    {'8' , "tuv"},
+    {'9' , "wxyz"},
+    {'0' , " "},
+    {'*' , "*"},
+    {'#' , "#"}
+};
+
+void helper(const std::string& digits, std::string rs,
+    std::vector<std::string>& result, int index)
+{
+    if (index == digits.length()) {
+        result.push_back(rs);
+        return;
+    }
+    
+    char c = digits[index];
+    std::string ps = dict[c];
+    for (int i = 0; i < ps.length(); ++i) {
+        helper(digits, rs + ps[i], result, index + 1);
+    }
+}
+
+std::vector<std::string> letter_combinations(const std::string& digits)
+{
+    std::vector<std::string> result;
+        if (digits.size() == 0) {
+            return result;
+        }
+        std::string rs("");
+        helper(digits, rs, result,  0);
+        return result;
+}
+
+void print_vec(const std::vector<std::string>& vec)
+{
+    for(auto v: vec) {
+        std::cout << v << " ";
+    }
+    std::cout << std::endl;
+}
+int main()
+{
+    std::string digits{"34"};
+    std::cout << "All possible combinations of digits " << digits << " are: \n";
+    print_vec(letter_combinations(digits));
+    return 0;
+}