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Better right-click detection: Halving method

Esan Sang Sang Sang

Let’s look at a performance improvement solution for right-click detection:

Right-click detection (halving method)

Before we start, let’s do an experiment: If a scoreboard value initially is$0$, add it first every time$4$, then divided by$2$, and see what happens:

• initial:$0$
• $0+4=4$，$4÷2=2$
• $2+4=6$，$6÷2=3$
• $3+4=7$，$7÷2=3$
• $3+4=7$，$7÷2=3$
• ...

You'll notice that the last value always seems to be$3$。
If we don't continue to add$4$, what will happen?

• initial:$0$
• $0+4=4$，$4÷2=2$
• $2+4=6$，$6÷2=3$
• $3+4=7$，$7÷2=3$
• $3+4=7$，$7÷2=3$
• $3÷2=1$
• $1÷2=0$
• $0÷2=0$
• ...

If we don't continue to add$4$, this value will change from$3$become$1$, and then return to the initial$0$ Did you notice anything strange?
Let’s look directly at the resulting numbers:

$0$
$2$
$3$
$3$
$3$
$1$
$0$
$0$

You will find that when the value is added$4$During this period of time, the value will look like$23331$, that is, starting with$2$, the middle is$3$, ending with$1$。 In other words, we only need to add$4$, and then continue to divide by$2$, you can get the right-click status. This is where the name "halving method" comes from.

However, players who are familiar with command will say that right-click advancement detection is very unstable and often disconnects. In this way, during a long press, the detection will start immediately after the end due to disconnection. So this method cannot be used? No, we can add it to the process$4$Change to plus$6$：

$0$
$3$
$4$
$5$
$5$
$2$
$1$
$0$

If the value is$3$, it means starting to press and hold the right button If the value is$1$, it means release the right button Otherwise as long as it is not$0$, indicating that you are pressing and holding the right button But some people will say, what will happen if I press and release it immediately?

$0$
$0$
$3$ 🕹️
$1$
$0$
$0$

What if you press it longer?

$0$
$0$
$3$ 🕹️
$4$ 🕹️
$2$
$1$
$0$
$0$

What if contact is discontinued?

$0$
$0$
$3$ 🕹️
$4$ 🕹️
$5$ 🕹️
$2$
$5$ 🕹️
$2$
$1$
$0$

You will find that as long as$+4$or$+6$back$÷2$, no matter how you do it, this value is based on$2$or$3$Start with$1$ended. This property can only be satisfied by dividing by 2, which is why it is called the "halving method".
Why is this? In this process, only$3$and$2$Divide by$2$will get$1$, other numbers will not. And other numbers are divided multiple times by$2$After that, you will eventually come back to$2$。
Due to space limitations, this video does not carry out strict mathematical proofs. If you are interested you can prove it yourself.

Next, I will post the complete code without further explanation.

# example:rmb/using_item
# ...右键运行example:rmb/run的进度

# example:load
scoreboard objectives add rmb_flag dummy
scoreboard objectives add example dummy
scoreboard players set 2 example 2

# example:rmb/run
scoreboard players add @s rmb_flag 4
advancement revoke @s only example:rmb/using_item

# example:tick
execute as @a at @s run function example:rmb/player_tick

# example:rmb/player_tick
scoreboard players operation @s rmb_flag /= 2 example
execute if score @s rmb_flag matches 2 run say 开始长按右键
execute if score @s rmb_flag matches 3 run say 正在长按右键
execute if score @s rmb_flag matches 1 run say 松开右键

summary

In this tutorial, we learned a high-performance right-click detection scheme-the halving method. The knowledge points involved are:

• Halving method:

  • Taking advantage of the properties of integer division, by$(currentvalue+inputvalue)÷2$The formula of , completes the state flow within a variable
  • If you need touch-off protection, you only need to modify the numbers and do not need to add new logic.

• State mapping table

| Scheme | Value | Meaning | |----------|----|----------------| | $+4$Halving |$2$|Start by right-clicking | | | $3$| Long pressing the right button | | | $1$| Release the right button | | | $0$| No operation | | $+6$Halving |$3$|Start by right-clicking | | | $1$| Release the right button | | | $0$| No operation | | |Other values| Long pressing the right button |

• scoreboard operations
  • Constant setting: The scoreboard operation does not support direct division by numbers. A "constant score" must be set first (such as settingexampleThe score is2) as the divisor.
  • Operation instructions:
    • Input signal:scoreboard players add @s rmb_flag 4(Executed in the function triggered by advancement)
    • Status decay:scoreboard players operation @s rmb_flag /= 2 example(Executed in Tickfunction)