<p>You are given an integer array <code>nums</code> and two integers <code>indexDiff</code> and <code>valueDiff</code>.</p>

<p>Find a pair of indices <code>(i, j)</code> such that:</p>

<ul>
	<li><code>i != j</code>,</li>
	<li><code>abs(i - j) &lt;= indexDiff</code>.</li>
	<li><code>abs(nums[i] - nums[j]) &lt;= valueDiff</code>, and</li>
</ul>

<p>Return <code>true</code><em> if such pair exists or </em><code>false</code><em> otherwise</em>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,1], indexDiff = 3, valueDiff = 0
<strong>Output:</strong> true
<strong>Explanation:</strong> We can choose (i, j) = (0, 3).
We satisfy the three conditions:
i != j --&gt; 0 != 3
abs(i - j) &lt;= indexDiff --&gt; abs(0 - 3) &lt;= 3
abs(nums[i] - nums[j]) &lt;= valueDiff --&gt; abs(1 - 1) &lt;= 0
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,5,9,1,5,9], indexDiff = 2, valueDiff = 3
<strong>Output:</strong> false
<strong>Explanation:</strong> After trying all the possible pairs (i, j), we cannot satisfy the three conditions, so we return false.
</pre>

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

<ul>
	<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= indexDiff &lt;= nums.length</code></li>
	<li><code>0 &lt;= valueDiff &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def containsNearbyAlmostDuplicate(self, nums: List[int], indexDiff: int, valueDiff: int) -> bool:
        
        index_width = indexDiff + 1
        value_width = valueDiff + 1

        buckets = {}

        def get_bucket(num):
            return num // value_width

        def has_dupe(num, bucket):
            if bucket in buckets:
                # Has dupe bucket
                return True

            for next_bucket in (bucket - 1, bucket + 1):
                if next_bucket in buckets:
                    next_num = buckets[next_bucket]
                    if abs(next_num - num) <= valueDiff:
                        return True

            return False

        # Build the initial window
        for num in nums[:index_width]:
            bucket = get_bucket(num)
            if has_dupe(num, bucket):
                # Found dupe in initial window
                return True
            buckets[bucket] = num

        for i in range(len(nums) - index_width):
            remnum = nums[i]
            addnum = nums[i + index_width]

            rembucket = get_bucket(remnum)
            del buckets[rembucket]

            addbucket = get_bucket(addnum)
            if has_dupe(addnum, addbucket):
                return True

            buckets[addbucket] = addnum

        return False

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