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.
这个题我甚至不知道该怎么总结。
难就难在从这个题抽象出一种解法,看了别人的答案和思路= =然而没有归类总结到某种类型,这题相当于背了个题。。。
简单的说,除了最外面的4个点,所有的点都会2次2次的出现,如果有覆盖,覆盖进去的点就不是成对出现了。
最外面4个点围的面积等于所有小矩形面积的和。
就用这2个判断就行了。
判断成对的点用的SET,单次出现添加,第二次出现删除。。这样最后应该都删掉,SET里只剩下4个最外面的点。
剩下的就是判断最外点,不停地更新。。
Consider how the corners of all rectangles appear in the large rectangle if there's a perfect rectangular cover.
Rule1: The local shape of the corner has to follow one of the three following patterns
- Corner of the large rectangle (blue): it occurs only once among all rectangles
- T-junctions (green): it occurs twice among all rectangles
- Cross (red): it occurs four times among all rectangles
For each point being a corner of any rectangle, it should appear even times except the 4 corners of the large rectangle. So we can put those points into a hash map and remove them if they appear one more time.
At the end, we should only get 4 points.
Rule2: the large rectangle area should be equal to the sum of small rectangles
public class Solution { public boolean isRectangleCover(int[][] rectangles) { if (rectangles==null || rectangles.length==0 || rectangles[0].length==0) return false; int subrecAreaSum = 0; //sum of subrectangle's area int x1 = Integer.MAX_VALUE; //large rectangle bottom left x-axis int y1 = Integer.MAX_VALUE; //large rectangle bottom left y-axis int x2 = Integer.MIN_VALUE; //large rectangle top right x-axis int y2 = Integer.MIN_VALUE; //large rectangle top right y-axis HashSet<String> set = new HashSet<String>(); // store points for(int[] rec : rectangles) { //check if it has large rectangle's 4 points x1 = Math.min(x1, rec[0]); y1 = Math.min(y1, rec[1]); x2 = Math.max(x2, rec[2]); y2 = Math.max(y2, rec[3]); //calculate sum of subrectangles subrecAreaSum += (rec[2]-rec[0]) * (rec[3] - rec[1]); //store this rectangle's 4 points into hashSet String p1 = Integer.toString(rec[0]) + "" + Integer.toString(rec[1]); String p2 = Integer.toString(rec[0]) + "" + Integer.toString(rec[3]); String p3 = Integer.toString(rec[2]) + "" + Integer.toString(rec[1]); String p4 = Integer.toString(rec[2]) + "" + Integer.toString(rec[3]); if (!set.add(p1)) set.remove(p1); if (!set.add(p2)) set.remove(p2); if (!set.add(p3)) set.remove(p3); if (!set.add(p4)) set.remove(p4); } if (set.size()!=4 || !set.contains(x1+""+y1) || !set.contains(x1+""+y2) || !set.contains(x2+""+y1) || !set.contains(x2+""+y2)) return false; return subrecAreaSum == (x2-x1) * (y2-y1); } }
矩阵的题不光会heap, bfs,dfs, 还有单纯的找规律, 遍历四周, 01编码, 求和, map存边角为字符串
存为字符串 //store this rectangle's 4 points into hashSet String p1 = Integer.toString(rec[0]) + "" + Integer.toString(rec[1]);
boolean |
add(E e) 如果此 set 中尚未包含指定元素,则添加指定元素。 |
如果此 set 已经包含该元素,则该调用不改变此 set 并返回 false。结合构造方法上的限制,这就可以确保 set 永远不包含重复的元素