Package g2801_2900.s2826_sorting_three_groups

Class Solution

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public final class Solution

    2826 - Sorting Three Groups.

    Medium

    You are given a 0-indexed integer array nums of length n.

    The numbers from 0 to n - 1 are divided into three groups numbered from 1 to 3, where number i belongs to group nums[i]. Notice that some groups may be empty.

    You are allowed to perform this operation any number of times:

    • Pick number x and change its group. More formally, change nums[x] to any number from 1 to 3.

    A new array res is constructed using the following procedure:

    • Sort the numbers in each group independently.

    • Append the elements of groups 1, 2, and 3 to res in this order.

    Array nums is called a beautiful array if the constructed array res is sorted in non-decreasing order.

    Return the minimum number of operations to make nums a beautiful array.

    Example 1:

    Input: nums = 2,1,3,2,1

    Output: 3

    Explanation: It's optimal to perform three operations:

    • change nums0 to 1.

    • change nums2 to 1.

    • change nums3 to 1.

    After performing the operations and sorting the numbers in each group, group 1 becomes equal to 0,1,2,3,4 and group 2 and group 3 become empty. Hence, res is equal to 0,1,2,3,4 which is sorted in non-decreasing order.

    It can be proven that there is no valid sequence of less than three operations.

    Example 2:

    Input: nums = 1,3,2,1,3,3

    Output: 2

    Explanation: It's optimal to perform two operations:

    • change nums1 to 1.

    • change nums2 to 1.

    After performing the operations and sorting the numbers in each group, group 1 becomes equal to 0,1,2,3, group 2 becomes empty, and group 3 becomes equal to 4,5. Hence, res is equal to 0,1,2,3,4,5 which is sorted in non-decreasing order.

    It can be proven that there is no valid sequence of less than two operations.

    Example 3:

    Input: nums = 2,2,2,2,3,3

    Output: 0

    Explanation: It's optimal to not perform operations.

    After sorting the numbers in each group, group 1 becomes empty, group 2 becomes equal to 0,1,2,3 and group 3 becomes equal to 4,5. Hence, res is equal to 0,1,2,3,4,5 which is sorted in non-decreasing order.

    Constraints:

    • 1 <= nums.length <= 100

    • 1 <= nums[i] <= 3

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer minimumOperations(List<Integer> nums)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait