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
func goodIndices(nums []int, k int) []int {
	n := len(nums)
	decr := make([]int, n)
	incr := make([]int, n)
	for i := range decr {
		decr[i] = 1
		incr[i] = 1
	}
	for i := 2; i < n; i++ {
		if nums[i-1] <= nums[i-2] {
			decr[i] = decr[i-1] + 1
		}
	}
	for i := n - 3; i >= 0; i-- {
		if nums[i+1] <= nums[i+2] {
			incr[i] = incr[i+1] + 1
		}
	}
	ans := []int{}
	for i := k; i < n-k; i++ {
		if decr[i] >= k && incr[i] >= k {
			ans = append(ans, i)
		}
	}
	return ans
}