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markdowns/_919. Complete Binary Tree Inserter.md

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> ```
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>
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> $$\left \lfloor{\log_{2}(1)}\right \rfloor = lvl = 0$$
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>
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> $$\left \lfloor{\log_{2}(2)}\right \rfloor = lvl = 1$$
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>
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> $$\left \lfloor{\log_{2}(3)}\right \rfloor = lvl = 1$$
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>
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> $$\left \lfloor{\log_{2}(4)}\right \rfloor = lvl = 2$$
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>
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> $$\left \lfloor{\log_{2}(5)}\right \rfloor = lvl = 2$$
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>
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> $$\left \lfloor{\log_{2}(6)}\right \rfloor = lvl = 2$$
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>
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> $$\left \lfloor{\log_{2}(7)}\right \rfloor = lvl = 2$$
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>
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>
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> Their remainders go as follows:
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>
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> $$Remainder(1) = 0 = 0b0$$
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>
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> $$Remainder(2) = 0 = 0b0$$
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>
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> $$Remainder(3) = 1 = 0b1$$
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>
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> $$Remainder(4) = 0 = 0b00$$
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>
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> $$Remainder(5) = 1 = 0b01$$
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>
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> $$Remainder(6) = 2 = 0b10$$
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>
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> $$Remainder(7) = 3 = 0b11$$
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>
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>
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> Ignoring the `root`, if we take the binary string and read it from
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> left to right (not including the `0b` binary indicator), we can
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> find the path to the proper index of the new node where `0` indicates

my-submissions/m919.md

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```
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$$\left \lfloor{\log_{2}(1)}\right \rfloor = lvl = 0$$
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$$\left \lfloor{\log_{2}(2)}\right \rfloor = lvl = 1$$
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$$\left \lfloor{\log_{2}(3)}\right \rfloor = lvl = 1$$
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$$\left \lfloor{\log_{2}(4)}\right \rfloor = lvl = 2$$
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$$\left \lfloor{\log_{2}(5)}\right \rfloor = lvl = 2$$
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$$\left \lfloor{\log_{2}(6)}\right \rfloor = lvl = 2$$
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$$\left \lfloor{\log_{2}(7)}\right \rfloor = lvl = 2$$
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Their remainders go as follows:
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$$Remainder(1) = 0 = 0b0$$
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$$Remainder(2) = 0 = 0b0$$
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$$Remainder(3) = 1 = 0b1$$
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$$Remainder(4) = 0 = 0b00$$
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$$Remainder(5) = 1 = 0b01$$
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$$Remainder(6) = 2 = 0b10$$
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$$Remainder(7) = 3 = 0b11$$
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Ignoring the `root`, if we take the binary string and read it from
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left to right (not including the `0b` binary indicator), we can
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find the path to the proper index of the new node where `0` indicates

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