add official sol

Author: keineahnung2345

969. Pancake Sorting.cpp

@@ -35,3 +35,42 @@ class Solution {
         return ans;
     }
 };
+
+//without actually flipping
+//official solution
+//time: O(N^2), space: O(N)
+//Runtime: 8 ms, faster than 69.75% of C++ online submissions for Pancake Sorting.
+//Memory Usage: 8.8 MB, less than 83.33% of C++ online submissions for Pancake Sorting.
+class Solution {
+public:
+    vector<int> pancakeSort(vector<int>& A) {
+        vector<int> ans;
+        int N = A.size();
+        
+        vector<int> indices(N);
+        iota(indices.begin(), indices.end(), 1);
+        //the larget the former
+        sort(indices.begin(), indices.end(), 
+             [&A](const int i, const int j){return A[i-1] > A[j-1];});
+        // copy(indices.begin(), indices.end(), ostream_iterator<int>(cout, " "));
+        // cout << endl;
+        
+        for(int index : indices){
+            //don't actually reverse the vector, but simulate it
+            // cout << index << "->";
+            for(int flip : ans){
+                if(index <= flip){
+                    //flip at flip'th position, so index'th position is affected
+                    //old position + new position = flipped vector's size + 1
+                    index = flip + 1 - index;
+                }
+            }
+            // cout << index << endl;
+            //now index becomes the true index after serveral flipping
+            ans.push_back(index);
+            ans.push_back(N--);
+        }
+        
+        return ans;
+    }
+};