Maximum Number Of Groups Entering A Competition - Leetcode Solution

Problem Statement: You are given an integer n and an integer array nums of length n. A group of k consecutive elements in nums is called a continuous block. Each continuous block is assigned a score equal to the sum of the elements in the block. A group can only enter the competition if its score is not negative.

Return the maximum number of continuous blocks that can be entered into the competition.

Solution: To find the maximum number of contiguous groups we can use a greedy approach. We will start with the first element of the array and check if the sum is non-negative. If the sum is non-negative, we will extend our current group by one and check if the new sum is non-negative. If the new sum is also non-negative, we will keep extending our group until the sum becomes negative. At this point, we will start a new group with the currently pointed element, since extending the previous group will result in a negative sum.

Let's say we are at index i and we want to start a new group. We will check if the sum of nums[i] is non-negative. If it is, we can start a new group with a score of nums[i]. If the sum is negative, we cannot start a new group with this element, and we will move to the next element.

We will repeat this process until we reach the end of the array. At each step, we will compare the length of the current group with the maximum length we have seen so far.

Time Complexity: The time complexity of this algorithm is O(n) since we will visit each element once.

Space Complexity: The space complexity of this algorithm is O(1) since we are only storing a few variables.

Python Code:

class Solution: def maxNumberOfGroups(self, n: int, nums: List[int]) -> int: """ :type n: int :type nums: List[int] :rtype: int """ # We start at index 0 with a group of score 0 and length 0. max_groups = 0 curr_group_sum = 0 curr_group_len = 0

    for i in range(n):
        # Check if we can extend the current group.
        if (curr_group_sum + nums[i]) >= 0:
            curr_group_sum += nums[i]
            curr_group_len += 1
        else:
            # Start a new group.
            curr_group_sum = nums[i] if nums[i] >= 0 else 0
            curr_group_len = 1 if nums[i] >= 0 else 0
        
        # Update the maximum number of groups so far.
        max_groups = max(max_groups, curr_group_len)
    
    return max_groups

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