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困难
数组
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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

Python3

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())

Java

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);
        }
    }
}

C++

#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;
        });
    }
};

Go

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
}