Cycle Sort can be used to handle special case input, which is consecutive integers, it's a decrease and conquers approach:

The name came from how it approaches the inputs: starting from the leftmost spot and figuring out which number goes there, then recursive call on the remaining elements, which looks like a cycle.

The general template looks like this:

for (let i = 0; i < nums.length; i++) {
  while (nums[i] !== i) {
    const destinationIndex = nums[i]

    if (nums[destinationIndex] !== nums[i]) {
      [nums[i], nums[destinationIndex]] = [nums[destinationIndex], nums[i]]
    } else {
      break
    }
  }
}

it can reach O(n) on time complexity instead of O(n2) and without the need to use extra space.

To practice on it, you can check the following questions shown on Leetcode:

• Missing Number
• Find All Numbers Disappeared in an Array
• Find the Duplicate Number
• Set Mismatch
• Find All Duplicates in an Array
• First Missing Positive
• Couples Holding Hands