New Problem Solution "Perfect Rectangle"

README.md

@@ -8,6 +8,7 @@ LeetCode
 
 | # | Title | Solution | Difficulty |
 |---| ----- | -------- | ---------- |
+|391|[Perfect Rectangle](https://leetcode.com/problems/perfect-rectangle/) | [C++](./algorithms/cpp/perfectRectangle/PerfectRectangle.cpp)|Hard|
 |390|[Elimination Game](https://leetcode.com/contest/2/problems/elimination-game/) | [C++](./algorithms/cpp/eliminationGame/EliminationGame.cpp)|Medium|
 |389|[Find the Difference](https://leetcode.com/problems/find-the-difference/) | [C++](./algorithms/cpp/findTheDifference/FindTheDifference.cpp)|Easy|
 |388|[Longest Absolute File Path](https://leetcode.com/problems/longest-absolute-file-path/) | [C++](./algorithms/cpp/longestAbsoluteFilePath/LongestAbsoluteFilePath.cpp)|Medium|

algorithms/cpp/perfectRectangle/PerfectRectangle.cpp

@@ -0,0 +1,80 @@
+// Source : https://leetcode.com/problems/perfect-rectangle/
+// Author : Hao Chen
+// Date   : 2016-09-08
+
+/*************************************************************************************** 
+ *
+ * Given N axis-aligned rectangles where N > 0, determine if they all together form an 
+ * exact cover of a rectangular region.
+ * 
+ * Each rectangle is represented as a bottom-left point and a top-right point. For 
+ * example, a unit square is represented as [1,1,2,2]. (coordinate of bottom-left point 
+ * is (1, 1) and top-right point is (2, 2)).
+ * 
+ * Example 1:
+ * 
+ * rectangles = [
+ *   [1,1,3,3],
+ *   [3,1,4,2],
+ *   [3,2,4,4],
+ *   [1,3,2,4],
+ *   [2,3,3,4]
+ * ]
+ * 
+ * Return true. All 5 rectangles together form an exact cover of a rectangular region.
+ * 
+ * Example 2:
+ * 
+ * rectangles = [
+ *   [1,1,2,3],
+ *   [1,3,2,4],
+ *   [3,1,4,2],
+ *   [3,2,4,4]
+ * ]
+ * 
+ * Return false. Because there is a gap between the two rectangular regions.
+ * 
+ * Example 3:
+ * 
+ * rectangles = [
+ *   [1,1,3,3],
+ *   [3,1,4,2],
+ *   [1,3,2,4],
+ *   [3,2,4,4]
+ * ]
+ * 
+ * Return false. Because there is a gap in the top center.
+ * 
+ * Example 4:
+ * 
+ * rectangles = [
+ *   [1,1,3,3],
+ *   [3,1,4,2],
+ *   [1,3,2,4],
+ *   [2,2,4,4]
+ * ]
+ * 
+ * Return false. Because two of the rectangles overlap with each other.
+ ***************************************************************************************/
+
+
+class Solution {
+public:
+    bool isRectangleCover(vector<vector<int>>& rectangles) {
+        unordered_map<string,int> mp;
+        string corners[4];
+        for(auto v: rectangles)
+            for(int i = 0; i<4; ++i){
+                corners[i] = to_string(v[i/2*2]) + "," + to_string(v[(i%2)*2+1]);
+                if(mp[corners[i]] & int(pow(2,i))) return false;
+                else mp[corners[i]] |= int(pow(2,i));
+            }
+        int corner = 0;
+        for(auto i=mp.begin(); i!=mp.end(); ++i){
+            int val = i->second;
+            if(!(val & (val-1)) && (++corner >4)) return false;
+            if((val & (val-1)) && !(val == 3 || val==12 || val==10 || val==5 || val==15)) return false;
+        }
+        return true;        
+    }
+};