Find All Good Indices
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of size <code>n</code> and a positive integer <code>k</code>.</p>

<p>We call an index <code>i</code> in the range <code>k &lt;= i &lt; n - k</code> <strong>good</strong> if the following conditions are satisfied:</p>

<ul>
	<li>The <code>k</code> elements that are just <strong>before</strong> the index <code>i</code> are in <strong>non-increasing</strong> order.</li>
	<li>The <code>k</code> elements that are just <strong>after</strong> the index <code>i</code> are in <strong>non-decreasing</strong> order.</li>
</ul>

<p>Return <em>an array of all good indices sorted in <strong>increasing</strong> order</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,1,1,1,3,4,1], k = 2
<strong>Output:</strong> [2,3]
<strong>Explanation:</strong> There are two good indices in the array:
- Index 2. The subarray [2,1] is in non-increasing order, and the subarray [1,3] is in non-decreasing order.
- Index 3. The subarray [1,1] is in non-increasing order, and the subarray [3,4] is in non-decreasing order.
Note that the index 4 is not good because [4,1] is not non-decreasing.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,1,1,2], k = 2
<strong>Output:</strong> []
<strong>Explanation:</strong> There are no good indices in this array.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>3 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= k &lt;= n / 2</code></li>
</ul>
Array; Dynamic Programming; Prefix Sum
class Solution {
    public List<Integer> goodIndices(int[] nums, int k) {
        int n = nums.length;
        int[] decr = new int[n];
        int[] incr = new int[n];
        Arrays.fill(decr, 1);
        Arrays.fill(incr, 1);
        for (int i = 2; i < n - 1; ++i) {
            if (nums[i - 1] <= nums[i - 2]) {
                decr[i] = decr[i - 1] + 1;
            }
        }
        for (int i = n - 3; i >= 0; --i) {
            if (nums[i + 1] <= nums[i + 2]) {
                incr[i] = incr[i + 1] + 1;
            }
        }
        List<Integer> ans = new ArrayList<>();
        for (int i = k; i < n - k; ++i) {
            if (decr[i] >= k && incr[i] >= k) {
                ans.add(i);
            }
        }
        return ans;
    }
}