哈希表中碰撞与探测长度的区别及追踪方法咨询

Hey there! Let's break down your problem step by step—great job getting this far with your linear probing hash table as a Python newbie! First, let's lock in the core definitions to make sure we're aligned, then we'll dive into your code and fix the gaps.

Key Definitions Recap #

First, let's clarify exactly what we're tracking:

• Collision Count: This increments only when the initial (or subsequent) hash position is occupied by an unrelated key (a key different from the one you're inserting/looking up). Finding the same key with a different value isn't a collision—it's just an existing key that needs an update.
• Probe Length: This is the total number of positions you check (including the initial hash position) to find an empty slot or the target key. Some definitions count only extra attempts after a collision, but the most common interpretation is total probe attempts.

Issues in Your Original & Modified Code #

Let's walk through the problems in your code:

1. Python Syntax Errors: Python uses or and and for logical operations, not || and &&—those are C-style operators and will throw syntax errors.
2. Incorrect Collision Detection: Your code counts a "collision" when it finds the same key with a different value. That's not a hash collision—it's an existing key that needs an update. Collisions only happen when a position is taken by a different key.
3. Broken Probe Length Calculation: Your modified code sets probeLength = collision-1, which doesn't make sense. Probe length should track every position you check, not just derive it from collision count.

Corrected Implementation #

Here's a revised version of your function with comments explaining each step:

def getCollisionAndProbeLength(self, key, value):
    position = self.hash_value(key)
    collision_count = 0
    probe_length = 1  # Start at 1—initial position counts as first probe

    for _ in range(self.table_size):
        if self.array[position] is None:
            # Found an empty slot, done probing
            break
        
        current_key, current_val = self.array[position]
        if current_key == key:
            # Found the target key—no collision here, even if value differs
            break
        
        # Reaching here means current position is taken by a different key: COLLISION
        collision_count += 1
        probe_length += 1
        # Move to next position (wrap around with modulo)
        position = (position + 1) % self.table_size

    return [collision_count, probe_length]

Why This Works #

• Collision Count: We only increment this when we hit a position occupied by a different key—this is the true definition of a hash collision in linear probing.
• Probe Length: We start at 1 (since the initial hash position is our first check) and increment it every time we have to move to a new position. This gives the total number of positions we probed to find a spot or the target key.
• Edge Cases Handled: If the initial position is empty or has the target key, probe length stays 1 and collision count stays 0—exactly what we want.

What Was Wrong With Your Modified Code? #

Your line probeLength = collision-1 would give incorrect values:

• If there are 0 collisions, probe length would be -1 (impossible)
• If there's 1 collision, probe length would be 0, but we actually probed 2 positions (initial + 1 extra)

The correct relationship is probe_length = collision_count + 1 when collisions occur, but tracking probe length independently avoids edge case bugs entirely.

内容的提问来源于stack exchange，提问作者Sook Lim