Use a prefix sum approach to find the partition points in one pass to split an array into three parts with equal sums.

To split an array into three contiguous parts with equal sums, first compute the total sum. If it is not divisible by 3, return false. Let target = total / 3. Iterate through the array, maintaining a running sum. When the running sum equals target, record the index as the first cut. Continue; when the running sum equals 2 * target, record the second cut. If both cuts are found before the end of the array, the array can be partitioned. Complexity is O(n) time and O(1) extra space. Example in Python:

def can_split(nums):
    total = sum(nums)
    if total % 3 != 0:
        return False
    target = total // 3
    cur = 0
    first = second = -1
    for i, v in enumerate(nums):
        cur += v
        if first == -1 and cur == target:
            first = i
        elif first != -1 and second == -1 and cur == 2 * target:
            second = i
            break
    return first != -1 and second != -1 and second < len(nums) - 1

This algorithm handles negative numbers and zeros correctly and runs in linear time.