adding the word search code

lectures/12_advanced_recursion/README.md

@@ -116,15 +116,17 @@ daldruetryrt
 ```
 - If you can start from any location of this grid, and go forward, backward, up and down. Can you find the word **computer** in this grid?  (**Note**: The same letter cell may not be used more than once.)
 - A sketch of the solution is as follows:
-  – The grid of letters is represented as vector<vector<char>> grid; Each vector<char> represents a row. We can treat this as a two-dimensional array.
+  – The grid of letters is represented as vector<vector<char>> grid; Each vector<char> represents a row. We can treat this as a two-dimensional array.  
-  – A word to be sought, such as “computer” is read as a string.
+  – A word to be sought, such as “computer” is read as a string.  
-  – A pair of nested for loops searches the grid for occurrences of the first letter in the string. Call such a location (r, c).
+  – A pair of nested for loops searches the grid for occurrences of the first letter in the string. Call such a location (r, c).  
-  – At each such location, the occurrences of the second letter are sought in the 4 locations surrounding (r, c).
+  - At each location where the first letter is found, a search of the second letter is initiated in the 4 neighboring locations of location (r, c).  
-  - At each location where the second letter is found, a search is initiated in the 4 locations surrouding this second letter.
+  - Make this process recursive: at each location where the *ith* letter is found, a search of the *(i+1)th* letter is initiated in the 4 neighboring locations. 
+  - The search can stop when all letters of the string are found - this is the base case of the recursion.
+  - Question: how to make sure we do not use the same letter more than once on our success path?
 
 ## 12.8 Exercise: Complete the implementation
 
-- [Leetcode problem 79: Word Search](https://leetcode.com/problems/word-search/). Solution: To be added.
+- [Leetcode problem 79: Word Search](https://leetcode.com/problems/word-search/). Solution: [p79_wordsearch.cpp](p79_wordsearch.cpp).
 - [Leetcode problem 212: Word Search II](https://leetcode.com/problems/word-search-ii/). Solution: To be added.
 
 ## 12.9 Summary of Nonlinear Word Search Recursion

leetcode/p79_wordsearch.cpp

@@ -0,0 +1,58 @@
+class Solution {
+public:
+    // search word[index] at locations (i,j)
+    bool search(vector<vector<char>>& board, string word, int i, int j, int index){
+        // base case
+        if(index>=word.length()){
+            // when index is equal to word length, it means our search job is done.
+            // and in this case, we don't care if i or j is out of bounds of not.
+            return true;
+        }
+
+        // boundary checking
+        if(i<0 || i>=board.size()){
+            return false;
+        }
+        if(j<0 || j>=board[0].size()){
+            return false;
+        }
+
+        // if not equal, then this is not the path we are looking for.
+        if(board[i][j] != word[index]){
+            return false;
+        }
+
+        char c = board[i][j];
+        // if it's found, we change it to '0' so we can guarantee to not reuse it while we are still on this path.
+        board[i][j]='0';
+
+        // general case
+        // if search job is still incomplete, then let's continue searching letter i in all four directions, and if we can find the word in any of these four directions, then we are good.
+        if( (search(board, word, i, j+1, index+1) ||
+            search(board, word, i, j-1, index+1) ||
+            search(board, word, i-1, j, index+1) ||
+            search(board, word, i+1, j, index+1) ) == true ){
+                return true;
+        }else{
+            // restore board[i][j] to its original value
+            board[i][j] = c;
+            return false;
+        }
+    }
+
+    bool exist(vector<vector<char>>& board, string word) {
+        int m=board.size();
+        int n=board[0].size();
+        // find the first letter of this word
+        for(int i=0;i<m;i++){
+            for(int j=0;j<n;j++){
+                // if it's true, return true; if not, continue search at next (i,j)
+                if(search(board, word, i, j, 0) == true){
+                    return true;
+                }
+            }
+        }
+        // if we reach here, then the word can't be found.
+        return false;
+    }
+};