minimum-subsequence-in-non-increasing-order_1403.py

# Given the array nums, obtain a subsequence of the array whose sum of elements is strictly greater than the sum of the non included elements in such subsequence.

# If there are multiple solutions, return the subsequence with minimum size and if there still exist multiple solutions, return the subsequence with the maximum total sum of all its elements. A subsequence of an array can be obtained by erasing some (possibly zero) elements from the array.

# Note that the solution with the given constraints is guaranteed to be unique. Also return the answer sorted in non-increasing order.


# Example 1:

# Input: nums = [4,3,10,9,8]
# Output: [10,9]
# Explanation: The subsequences [10,9] and [10,8] are minimal such that the sum of their elements is strictly greater than the sum of elements not included. However, the subsequence [10,9] has the maximum total sum of its elements.
# Example 2:

# Input: nums = [4,4,7,6,7]
# Output: [7,7,6]
# Explanation: The subsequence [7,7] has the sum of its elements equal to 14 which is not strictly greater than the sum of elements not included (14 = 4 + 4 + 6). Therefore, the subsequence [7,6,7] is the minimal satisfying the conditions. Note the subsequence has to be returned in non-decreasing order.

# ---------------------------------------Runtime 69 ms Beats 63.39% Memory 16.4 MB Beats 51.45%---------------------------------------


# Time Complexity O(n2)
from typing import List


class Solution:
    def minSubsequence(self, nums: List[int]) -> List[int]:
        sortedNum, output = sorted(nums), []
        while True:
            output.append(sortedNum.pop())
            if sum(output) > sum(sortedNum):
                return output