Data Stream as Disjoint Intervals
<p>Given a data stream input of non-negative integers <code>a<sub>1</sub>, a<sub>2</sub>, ..., a<sub>n</sub></code>, summarize the numbers seen so far as a list of disjoint intervals.</p>

<p>Implement the <code>SummaryRanges</code> class:</p>

<ul>
	<li><code>SummaryRanges()</code> Initializes the object with an empty stream.</li>
	<li><code>void addNum(int value)</code> Adds the integer <code>value</code> to the stream.</li>
	<li><code>int[][] getIntervals()</code> Returns a summary of the integers in the stream currently as a list of disjoint intervals <code>[start<sub>i</sub>, end<sub>i</sub>]</code>. The answer should be sorted by <code>start<sub>i</sub></code>.</li>
</ul>

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

<pre>
<strong>Input</strong>
[&quot;SummaryRanges&quot;, &quot;addNum&quot;, &quot;getIntervals&quot;, &quot;addNum&quot;, &quot;getIntervals&quot;, &quot;addNum&quot;, &quot;getIntervals&quot;, &quot;addNum&quot;, &quot;getIntervals&quot;, &quot;addNum&quot;, &quot;getIntervals&quot;]
[[], [1], [], [3], [], [7], [], [2], [], [6], []]
<strong>Output</strong>
[null, null, [[1, 1]], null, [[1, 1], [3, 3]], null, [[1, 1], [3, 3], [7, 7]], null, [[1, 3], [7, 7]], null, [[1, 3], [6, 7]]]

<strong>Explanation</strong>
SummaryRanges summaryRanges = new SummaryRanges();
summaryRanges.addNum(1);      // arr = [1]
summaryRanges.getIntervals(); // return [[1, 1]]
summaryRanges.addNum(3);      // arr = [1, 3]
summaryRanges.getIntervals(); // return [[1, 1], [3, 3]]
summaryRanges.addNum(7);      // arr = [1, 3, 7]
summaryRanges.getIntervals(); // return [[1, 1], [3, 3], [7, 7]]
summaryRanges.addNum(2);      // arr = [1, 2, 3, 7]
summaryRanges.getIntervals(); // return [[1, 3], [7, 7]]
summaryRanges.addNum(6);      // arr = [1, 2, 3, 6, 7]
summaryRanges.getIntervals(); // return [[1, 3], [6, 7]]
</pre>

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

<ul>
	<li><code>0 &lt;= value &lt;= 10<sup>4</sup></code></li>
	<li>At most <code>3 * 10<sup>4</sup></code> calls will be made to <code>addNum</code> and <code>getIntervals</code>.</li>
	<li>At most <code>10<sup>2</sup></code>&nbsp;calls will be made to&nbsp;<code>getIntervals</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> What if there are lots of merges and the number of disjoint intervals is small compared to the size of the data stream?</p>
Design; Binary Search; Ordered Set
class SummaryRanges:
    def __init__(self):
        self.mp = SortedDict()

    def addNum(self, val: int) -> None:
        n = len(self.mp)
        ridx = self.mp.bisect_right(val)
        lidx = n if ridx == 0 else ridx - 1
        keys = self.mp.keys()
        values = self.mp.values()
        if (
            lidx != n
            and ridx != n
            and values[lidx][1] + 1 == val
            and values[ridx][0] - 1 == val
        ):
            self.mp[keys[lidx]][1] = self.mp[keys[ridx]][1]
            self.mp.pop(keys[ridx])
        elif lidx != n and val <= values[lidx][1] + 1:
            self.mp[keys[lidx]][1] = max(val, self.mp[keys[lidx]][1])
        elif ridx != n and val >= values[ridx][0] - 1:
            self.mp[keys[ridx]][0] = min(val, self.mp[keys[ridx]][0])
        else:
            self.mp[val] = [val, val]

    def getIntervals(self) -> List[List[int]]:
        return list(self.mp.values())


# # Your SummaryRanges object will be instantiated and called as such:
# # obj = SummaryRanges()
# # obj.addNum(val)
# # param_2 = obj.getIntervals()
