Maximize Win From Two Segments
<p>There are some prizes on the <strong>X-axis</strong>. You are given an integer array <code>prizePositions</code> that is <strong>sorted in non-decreasing order</strong>, where <code>prizePositions[i]</code> is the position of the <code>i<sup>th</sup></code> prize. There could be different prizes at the same position on the line. You are also given an integer <code>k</code>.</p>

<p>You are allowed to select two segments with integer endpoints. The length of each segment must be <code>k</code>. You will collect all prizes whose position falls within at least one of the two selected segments (including the endpoints of the segments). The two selected segments may intersect.</p>

<ul>
	<li>For example if <code>k = 2</code>, you can choose segments <code>[1, 3]</code> and <code>[2, 4]</code>, and you will win any prize <font face="monospace">i</font> that satisfies <code>1 &lt;= prizePositions[i] &lt;= 3</code> or <code>2 &lt;= prizePositions[i] &lt;= 4</code>.</li>
</ul>

<p>Return <em>the <strong>maximum</strong> number of prizes you can win if you choose the two segments optimally</em>.</p>

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

<pre>
<strong>Input:</strong> prizePositions = [1,1,2,2,3,3,5], k = 2
<strong>Output:</strong> 7
<strong>Explanation:</strong> In this example, you can win all 7 prizes by selecting two segments [1, 3] and [3, 5].
</pre>

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

<pre>
<strong>Input:</strong> prizePositions = [1,2,3,4], k = 0
<strong>Output:</strong> 2
<strong>Explanation:</strong> For this example, <strong>one choice</strong> for the segments is <code>[3, 3]</code> and <code>[4, 4],</code> and you will be able to get <code>2</code> prizes. 
</pre>

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

<ul>
	<li><code>1 &lt;= prizePositions.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= prizePositions[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>0 &lt;= k &lt;= 10<sup>9</sup> </code></li>
	<li><code>prizePositions</code> is sorted in non-decreasing order.</li>
</ul>

<p>&nbsp;</p>
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Array; Binary Search; Sliding Window
func maximizeWin(prizePositions []int, k int) (ans int) {
	n := len(prizePositions)
	f := make([]int, n+1)
	for i, x := range prizePositions {
		j := sort.Search(n, func(h int) bool { return prizePositions[h] >= x-k })
		ans = max(ans, f[j]+i-j+1)
		f[i+1] = max(f[i], i-j+1)
	}
	return
}