adding merge sort array problem

lectures/12_advanced_recursion/README.md

@@ -71,8 +71,10 @@ are you going to do with the result of the recursive call?)
 
 ## 12.4 Another Recursion Example: Merge Sort
 
-- Idea: 1) Split a vector in half, 2) Recursively sort each half, and 3) Merge the two sorted halves into a single
-sorted vector.
+- Idea:
+  - 1) Split a vector in half,  
+  - 2) Recursively sort each half, and  
+  - 3) Merge the two sorted halves into a single sorted vector.  
 - Suppose we have a vector called values having two halves that are each already sorted. In particular, the
 values in subscript ranges [low..mid] (the lower interval) and [mid+1..high] (the upper interval) are each
 in increasing order.
@@ -87,6 +89,7 @@ into the scratch vector. Finally, the entire scratch vector is copied back.
 ## 12.5 Thinking About Merge Sort
 
 - It exploits the power of recursion! We only need to think about  
+
   – Base case (intervals of size 1)  
   – Splitting the vector  
   – Merging the results
@@ -96,7 +99,7 @@ Count the number of pairwise comparisons that are required.
 
 ## 12.6 Merge Sort Exercises
 
-<!--- [Leetcode problem 912: Sort an Array](https://leetcode.com/problems/sort-an-array/). Solution: [p912_sortarray.cpp](../../leetcode/p912_sortarray.cpp)-->
+- [Leetcode problem 912: Sort an Array](https://leetcode.com/problems/sort-an-array/). Solution: [p912_sortarray.cpp](../../leetcode/p912_sortarray.cpp)
 - [Leetcode problem 148: Sort List](https://leetcode.com/problems/sort-list/). Solution: [p148_sortlist.cpp](../../leetcode/p148_sortlist.cpp)
 
 ## 12.7 Example: Word Search

leetcode/p912_sortarray.cpp

@@ -0,0 +1,63 @@
+class Solution {
+public:
+    vector<int> mergeArrays(vector<int>& v1, vector<int>& v2){
+        int size1 = v1.size();
+        int size2 = v2.size();
+        vector<int> v(size1+size2, 0);
+        int index1 = 0;
+        int index2 = 0;
+        int index = 0;
+        // scan and compare, whoever is smaller goes to v.
+        while(index1<size1 && index2<size2){
+            if(v1[index1]<v2[index2]){
+                v[index] = v1[index1];
+                index1 = index1 + 1;
+            }else{
+                v[index] = v2[index2];
+                index2 = index2 + 1;
+            }
+            index = index + 1;
+        }
+
+        // if v1 is done, let's now deal with v2 left overs
+        if(index1>=size1){
+            while(index2<size2){
+                v[index] = v2[index2];
+                index++;
+                index2++;
+            }
+        }else{
+            // else means v2 is done. let's now deal with v1 left overs
+            while(index1<size1){
+                v[index] = v1[index1];
+                index++;
+                index1++;
+            }
+        }
+        return v;
+    }
+    vector<int> sortArray(vector<int>& nums) {
+        int size = nums.size();
+        // base case
+        if(size==1){
+            return nums;
+        }
+        // general case
+        // split evenly or not evenly does not matter that much in this case
+        int mid = size/2;
+        vector<int> nums1(mid, 0);
+        vector<int> nums2(size-mid, 0);
+        for(int i=0;i<mid;i++){
+            nums1[i]=nums[i];
+        }
+        for(int i=mid;i<size;i++){
+            // caution: here the index in nums2 has to be i-mid, rather than i; and if we use i here, it will cause a heap buffer overflow issue.
+            nums2[i-mid]=nums[i];
+        }
+        // sort the left half
+        nums1 = sortArray(nums1);
+        // sort the right half
+        nums2 = sortArray(nums2);
+        return mergeArrays(nums1, nums2);
+    }
+};