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391. Perfect Rectangle

Description

Given an array rectangles where rectangles[i] = [xi, yi, ai, bi] represents an axis-aligned rectangle. The bottom-left point of the rectangle is (xi, yi) and the top-right point of it is (ai, bi).

Return true if all the rectangles together form an exact cover of a rectangular region.

 

Example 1:

Input: rectangles = [[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]
Output: true
Explanation: All 5 rectangles together form an exact cover of a rectangular region.

Example 2:

Input: rectangles = [[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]
Output: false
Explanation: Because there is a gap between the two rectangular regions.

Example 3:

Input: rectangles = [[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]
Output: false
Explanation: Because two of the rectangles overlap with each other.

 

Constraints:

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

Solutions

Solution 1

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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())

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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);
        }
    }
}

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#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;
        });
    }
};

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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
}

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