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Algorithms to performing "split" operations without any need for additional memory:

function $split\left(a\left[1,...,n\right],v\right)$

$$\begin{gathered} hira=1 \\ fori=1ton: \\ ifa\left(i\right)<v: \\ swapa\left[i\right]anda\left[hira\right] \\ hira=hira+1 \\ fori=hiraton: \\ ifa\left(i\right)v: \\ swapa\left[i\right]anda\left[hira\right] \\ hira=hira+1 \end{gathered}$$

鈥� 鈥渟plit 鈥� is the function which accepts the array 鈥�$s\left[1,...,n\right]$鈥� and a value 鈥溾�� as the input parameters.

鈥� Initially, the variable 鈥� count鈥� is assigned with the value.

鈥� The function has 2 鈥渇or 鈥� loops. In the first 鈥� for鈥� loop,

o Process all the elements in the array and brings the elements that are smaller than the value 2 鈥� 鈥� to front of the array by swapping.

o Thus, the array is split into sub-array by moving all the smaller elements in the array to front.

鈥� It first checks if the value in the k鈥渢h鈥� element of the array is less than the value of 鈥� val鈥�.

鈥� If it is true, it swaps the k鈥渢h鈥� element of the array 鈥� s鈥� with the position of the array element which has the value of count.

鈥� Then, the value of the 鈥渃ount鈥� is incremented.

鈥� In the second 鈥渇or鈥� loop,

o Find the position of the value 鈥� val鈥� and move it next to the sub-array by swapping.

鈥� It first checks if the value in the k鈥渢h鈥� element of the array is equal to the value of 鈥渧al 鈥�.

鈥� If it is true, it swaps the k鈥渢h鈥� element of the array 鈥� s鈥� with the position of the array element which has the value of count.

鈥� Then, the value of the 鈥� count鈥� is incremented.

o Here, both the 鈥� for鈥� loops require constant time.

Therefore, it takes the running time of $慰\left(n\right)$.