Balance Factor Calculator
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The Balance Factor Calculator is essential for identifying imbalances in binary trees and AVL trees, in order to ensure height-balanced structures. By calculating the difference between the heights of left and right subtrees, it maintains optimal search and operation times.
Formula:
The formula is:
To calculate the Balance Factor (BF), subtract the right weight (RW) from the left weight (LW), then divide the result by the sum of the left weight and right weight.
| Variable | Meaning |
|---|---|
| BF | Balance Factor (a measure of balance between two weights) |
| LW | Left Weight (the weight on the left side) |
| RW | Right Weight (the weight on the right side) |
Solved Calculations :
Example 1:
Given:
- Left Weight (LW) = 100 kg
- Right Weight (RW) = 80 kg
| Calculation | Instructions |
|---|---|
| Step 1: BF = | Start with the formula. |
| Step 2: BF = | Replace LW with 100 kg and RW with 80 kg. |
| Step 3: BF = | Subtract 80 from 100 and add the weights together. |
| Step 4: BF = 0.11 | Divide 20 by 180 to get the balance factor. |
Answer:
The balance factor is 0.11.
Example 2:
Given:
- Left Weight (LW) = 150 kg
- Right Weight (RW) = 120 kg
| Calculation | Instructions |
|---|---|
| Step 1: BF = | Start with the formula. |
| Step 2: BF = | Replace LW with 150 kg and RW with 120 kg. |
| Step 3: BF = | Subtract 120 from 150 and add the weights together. |
| Step 4: BF = 0.11 | Divide 30 by 270 to get the balance factor. |
Answer:
The balance factor is 0.11.
Final Words:
It also has practical applications in mechanical systems like crankshaft balancing, helping to maintain smooth engine function.
