LWC 51：683. K Empty Slots

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本文介绍了一种算法解决方案，用于在一个连续的花园槽位中找出两个已开花植物间恰好相隔k个未开花植物的最早天数。通过维护有序集合，实现了高效查找。

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LWC 51：683. K Empty Slots

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Problem:

There is a garden with N slots. In each slot, there is a flower. The N flowers will bloom one by one in N days. In each day, there will be exactly one flower blooming and it will be in the status of blooming since then.

Given an array flowers consists of number from 1 to N. Each number in the array represents the place where the flower will open in that day.

For example, flowers[i] = x means that the unique flower that blooms at day i will be at position x, where i and x will be in the range from 1 to N.

Also given an integer k, you need to output in which day there exists two flowers in the status of blooming, and also the number of flowers between them is k and these flowers are not blooming.

If there isn’t such day, output -1.

Example 1:

Input:
flowers: [1,3,2]
k: 1
Output: 2
Explanation: In the second day, the first and the third flower have become blooming.

Example 2:

Input:
flowers: [1,2,3]
k: 1
Output: -1

Note:

The given array will be in the range [1, 20000].

题意：

题目要求满足开花的两个slot之间的间隙恰好为k个的天数。

很暴力，遍历每个位置i，因为在位置i的左侧一定都是开花的，而在位置i的右侧则都是还没开过的花。所以在左侧的位置中，找到两个相邻位置之差为k个即可，为了快速比较相邻slot之间的间隙，i在不断累加的同时，始终保持i左侧位置的有序性，在插入的同时，去比较它的左侧位置，和右侧位置，看是否符合间隙之差为k+1。

当然上述操作需要维护位置的有序性，于是采用了插入排序算法，并且输出插入对应的位置。这样就能方便的找寻当前位置的左侧位置和右侧位置。

代码如下：

    public int kEmptySlots(int[] flowers, int k) {
        int n = flowers.length;
        if (n == 1 && k == 0) return 1;
        sort = new int[n + 16];
        for (int i = 0; i < n; ++i) {
            int index = add(flowers[i]);
            int min = index - 1 < 0 ? -11111111 : sort[index - 1];
            int max = index + 1 >= tot ? -11111111 : sort[index + 1];
            if (valid(flowers[i], k, min, max)) return i + 1;
        }
        return -1;
    }

    boolean valid(int x, int k, int min, int max) {
        if (max - x == k + 1) return true;
        if (x - min == k + 1) return true;
        return false;
    }

    int[] sort;
    int tot = 0;
    public int add(int x) {
        int j = 0;
        while (j < tot && sort[j] < x) {
            ++j;
        }
        for (int i = tot - 1; i >= j; --i) {
            sort[i + 1] = sort[i];
        }
        sort[j] = x;
        tot++;
        return j;
    }

当然，你也可以使用JAVA自带的数据结构，TreeSet来实现，代码精简很多。

代码如下：

    public int kEmptySlots(int[] flowers, int k) {
        int n = flowers.length;
        if (n == 1 && k == 0) return 1;
        TreeSet<Integer> sort = new TreeSet<>();
        for (int i = 0; i < n; ++i) {
            sort.add(flowers[i]);
            Integer min = sort.lower(flowers[i]);
            Integer max = sort.higher(flowers[i]);
            int mi = min == null ? -1111111 : min;
            int ma = max == null ? -1111111 : max;
            if (valid(flowers[i], k, mi, ma)) return i + 1;
        }
        return -1;
    }

    boolean valid(int x, int k, int min, int max) {
        if (max - x == k + 1) return true;
        if (x - min == k + 1) return true;
        return false;
    }