add 391

Author: fishercoder1534

README.md

@@ -212,6 +212,7 @@ Your ideas/fixes/algorithms are more than welcome!
 |396|[Rotate Function](https://leetcode.com/problems/rotate-function/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_396.java)| O(n^2) could be optimized to O(n) | O(1) | Easy|
 |393|[UTF-8 Validation](https://leetcode.com/problems/utf-8-validation/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_393.java)| O(?)|O(?) | Medium| Bit Manipulation
 |392|[Is Subsequence](https://leetcode.com/problems/is-subsequence/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_392.java)| O(m*n)|O(1) | Medium| Array, String
+|391|[Perfect Rectangle](https://leetcode.com/problems/perfect-rectangle/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_391.java)| O(n)|O(1) | Hard| 
 |390|[Elimination Game](https://leetcode.com/problems/elimination-game/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_390.java)| O(logn)|O(1) | Medium|
 |389|[Find the Difference](https://leetcode.com/problems/find-the-difference/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_389.java)| O(n)|O(1) | Easy|
 |388|[Longest Absolute File Path](https://leetcode.com/problems/longest-absolute-file-path/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_388.java)| O(n)|O(d) | Medium| Stack

src/main/java/com/fishercoder/solutions/_391.java

@@ -0,0 +1,96 @@
+package com.fishercoder.solutions;
+
+import java.util.HashSet;
+import java.util.Set;
+
+/**
+ * 391. Perfect Rectangle
+ *
+ * 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.
+ */
+public class _391 {
+    /**reference: https://discuss.leetcode.com/topic/56052/really-easy-understanding-solution-o-n-java*/
+    public boolean isRectangleCover(int[][] rectangles) {
+        if (rectangles.length == 0 || rectangles[0].length == 0) return false;
+
+        int x1 = Integer.MAX_VALUE;
+        int x2 = Integer.MIN_VALUE;
+        int y1 = Integer.MAX_VALUE;
+        int y2 = Integer.MIN_VALUE;
+
+        Set<String> set = new HashSet<>();
+        int area = 0;
+
+        for (int[] rect : rectangles) {
+            x1 = Math.min(rect[0], x1);
+            y1 = Math.min(rect[1], y1);
+            x2 = Math.max(rect[2], x2);
+            y2 = Math.max(rect[3], y2);
+
+            area += (rect[2] - rect[0]) * (rect[3] - rect[1]);
+
+            String s1 = rect[0] + " " + rect[1];
+            String s2 = rect[0] + " " + rect[3];
+            String s3 = rect[2] + " " + rect[3];
+            String s4 = rect[2] + " " + rect[1];
+
+            if (!set.add(s1)) set.remove(s1);
+            if (!set.add(s2)) set.remove(s2);
+            if (!set.add(s3)) set.remove(s3);
+            if (!set.add(s4)) set.remove(s4);
+        }
+
+        if (!set.contains(x1 + " " + y1) || !set.contains(x1 + " " + y2) || !set.contains(x2 + " " + y1) || !set.contains(x2 + " " + y2) || set.size() != 4) {
+            return false;
+        }
+
+        return area == (x2 - x1) * (y2 - y1);
+    }
+}