Question

391. 完美矩形

English Version

题目描述

给你一个数组 rectangles ，其中 rectangles[i] = [xi, yi, ai, bi] 表示一个坐标轴平行的矩形。这个矩形的左下顶点是 (xi, yi) ，右上顶点是 (ai, bi) 。

如果所有矩形一起精确覆盖了某个矩形区域，则返回 true ；否则，返回 false 。

 

示例 1：

输入：rectangles = [[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]
输出：true
解释：5 个矩形一起可以精确地覆盖一个矩形区域。 

示例 2：

输入：rectangles = [[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]
输出：false
解释：两个矩形之间有间隔，无法覆盖成一个矩形。

示例 3：

输入：rectangles = [[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]
输出：false
解释：因为中间有相交区域，虽然形成了矩形，但不是精确覆盖。

 

提示：

• 1 <= rectangles.length <= 2 * 104
• rectangles[i].length == 4
• -105 <= xi, yi, ai, bi <= 105

解法

方法一

class Solution:
  def isRectangleCover(self, rectangles: List[List[int]]) -> bool:
    area = 0
    minX, minY = rectangles[0][0], rectangles[0][1]
    maxX, maxY = rectangles[0][2], rectangles[0][3]
    cnt = defaultdict(int)

    for r in rectangles:
      area += (r[2] - r[0]) * (r[3] - r[1])

      minX = min(minX, r[0])
      minY = min(minY, r[1])
      maxX = max(maxX, r[2])
      maxY = max(maxY, r[3])

      cnt[(r[0], r[1])] += 1
      cnt[(r[0], r[3])] += 1
      cnt[(r[2], r[3])] += 1
      cnt[(r[2], r[1])] += 1

    if (
      area != (maxX - minX) * (maxY - minY)
      or cnt[(minX, minY)] != 1
      or cnt[(minX, maxY)] != 1
      or cnt[(maxX, maxY)] != 1
      or cnt[(maxX, minY)] != 1
    ):
      return False

    del cnt[(minX, minY)], cnt[(minX, maxY)], cnt[(maxX, maxY)], cnt[(maxX, minY)]

    return all(c == 2 or c == 4 for c in cnt.values())

class Solution {
  public boolean isRectangleCover(int[][] rectangles) {
    long area = 0;
    int minX = rectangles[0][0], minY = rectangles[0][1];
    int maxX = rectangles[0][2], maxY = rectangles[0][3];
    Map<Pair, Integer> cnt = new HashMap<>();

    for (int[] r : rectangles) {
      area += (r[2] - r[0]) * (r[3] - r[1]);

      minX = Math.min(minX, r[0]);
      minY = Math.min(minY, r[1]);
      maxX = Math.max(maxX, r[2]);
      maxY = Math.max(maxY, r[3]);

      cnt.merge(new Pair(r[0], r[1]), 1, Integer::sum);
      cnt.merge(new Pair(r[0], r[3]), 1, Integer::sum);
      cnt.merge(new Pair(r[2], r[3]), 1, Integer::sum);
      cnt.merge(new Pair(r[2], r[1]), 1, Integer::sum);
    }

    if (area != (long) (maxX - minX) * (maxY - minY)
      || cnt.getOrDefault(new Pair(minX, minY), 0) != 1
      || cnt.getOrDefault(new Pair(minX, maxY), 0) != 1
      || cnt.getOrDefault(new Pair(maxX, maxY), 0) != 1
      || cnt.getOrDefault(new Pair(maxX, minY), 0) != 1) {
      return false;
    }

    cnt.remove(new Pair(minX, minY));
    cnt.remove(new Pair(minX, maxY));
    cnt.remove(new Pair(maxX, maxY));
    cnt.remove(new Pair(maxX, minY));

    return cnt.values().stream().allMatch(c -> c == 2 || c == 4);
  }

  private static class Pair {
    final int first;
    final int second;

    Pair(int first, int second) {
      this.first = first;
      this.second = second;
    }

    @Override
    public boolean equals(Object o) {
      if (this == o) {
        return true;
      }
      if (o == null || getClass() != o.getClass()) {
        return false;
      }
      Pair pair = (Pair) o;
      return first == pair.first && second == pair.second;
    }

    @Override
    public int hashCode() {
      return Objects.hash(first, second);
    }
  }
}

#include <bits/stdc++.h>
using namespace std;

class Solution {
public:
  bool isRectangleCover(vector<vector<int>>& rectangles) {
    long long area = 0;
    int minX = rectangles[0][0], minY = rectangles[0][1];
    int maxX = rectangles[0][2], maxY = rectangles[0][3];

    using pii = pair<int, int>;
    map<pii, int> cnt;

    for (auto& r : rectangles) {
      area += (r[2] - r[0]) * (r[3] - r[1]);

      minX = min(minX, r[0]);
      minY = min(minY, r[1]);
      maxX = max(maxX, r[2]);
      maxY = max(maxY, r[3]);

      ++cnt[{r[0], r[1]}];
      ++cnt[{r[0], r[3]}];
      ++cnt[{r[2], r[3]}];
      ++cnt[{r[2], r[1]}];
    }

    if (area != (long long) (maxX - minX) * (maxY - minY) || cnt[{minX, minY}] != 1 || cnt[{minX, maxY}] != 1 || cnt[{maxX, maxY}] != 1 || cnt[{maxX, minY}] != 1) {
      return false;
    }

    cnt.erase({minX, minY});
    cnt.erase({minX, maxY});
    cnt.erase({maxX, maxY});
    cnt.erase({maxX, minY});

    return all_of(cnt.begin(), cnt.end(), [](pair<pii, int> e) {
      return e.second == 2 || e.second == 4;
    });
  }
};

type pair struct {
  first  int
  second int
}

func isRectangleCover(rectangles [][]int) bool {
  area := 0
  minX, minY := rectangles[0][0], rectangles[0][1]
  maxX, maxY := rectangles[0][2], rectangles[0][3]

  cnt := make(map[pair]int)
  for _, r := range rectangles {
    area += (r[2] - r[0]) * (r[3] - r[1])

    minX = min(minX, r[0])
    minY = min(minY, r[1])
    maxX = max(maxX, r[2])
    maxY = max(maxY, r[3])

    cnt[pair{r[0], r[1]}]++
    cnt[pair{r[0], r[3]}]++
    cnt[pair{r[2], r[3]}]++
    cnt[pair{r[2], r[1]}]++
  }

  if area != (maxX-minX)*(maxY-minY) ||
    cnt[pair{minX, minY}] != 1 ||
    cnt[pair{minX, maxY}] != 1 ||
    cnt[pair{maxX, maxY}] != 1 ||
    cnt[pair{maxX, minY}] != 1 {
    return false
  }

  delete(cnt, pair{minX, minY})
  delete(cnt, pair{minX, maxY})
  delete(cnt, pair{maxX, maxY})
  delete(cnt, pair{maxX, minY})

  for _, c := range cnt {
    if c != 2 && c != 4 {
      return false
    }
  }
  return true
}