Given the unsorted list, sort the list using Range Sort. [151, 110, 171, 119, 181, 131, 111, 141, 201, 121, ]

The minimum value in the list is 110.
The maximum value in the list is 201.

The range of values is $max\_value - min\_value + 1$.

Create a counting array (or frequency array) of size 92, initialized with zeros. Each index $i$ in this array will correspond to the value $i + min\_value$.
For example, index 0 corresponds to 110, index 1 to 111, and so on, up to index 91 corresponding to 201.

Iterate through the original list. For each element $x$, increment the count at index $x - min\_value$ in the counting array.

• For 151: increment count at index $151 - 110 = 41$.
• For 110: increment count at index $110 - 110 = 0$.
• For 171: increment count at index $171 - 110 = 61$.
• For 119: increment count at index $119 - 110 = 9$.
• For 181: increment count at index $181 - 110 = 71$.
• For 131: increment count at index $131 - 110 = 21$.
• For 111: increment count at index $111 - 110 = 1$.
• For 141: increment count at index $141 - 110 = 31$.
• For 201: increment count at index $201 - 110 = 91$.
• For 121: increment count at index $121 - 110 = 11$.

After this step, the counting array will have a 1 at indices $0, 1, 9, 11, 21, 31, 41, 61, 71, 91$, and 0 at all other indices.

Iterate through the counting array from index 0 to 91. For each index $i$ where the count is 1, add the value $i + min\_value$ to the sorted list.

• Index 0 has count $1 \implies 0 + 110 = 110$
• Index 1 has count $1 \implies 1 + 110 = 111$
• Index 9 has count $1 \implies 9 + 110 = 119$
• Index 11 has count $1 \implies 11 + 110 = 121$
• Index 21 has count $1 \implies 21 + 110 = 131$
• Index 31 has count $1 \implies 31 + 110 = 141$
• Index 41 has count $1 \implies 41 + 110 = 151$
• Index 61 has count $1 \implies 61 + 110 = 171$
• Index 71 has count $1 \implies 71 + 110 = 181$
• Index 91 has count $1 \implies 91 + 110 = 201$

The sorted list is: