[Verse 1]
Started with a vision, balanced tree design
Every node holds keys in ascending line
Order matters here, we keep it tight
Minimum degree defines our height
Split when full, merge when light
B-tree structure, data's delight
Root to leaf, the path is clear
Search and find what we hold dear
[Chorus]
Insert split merge, that's the way we flow
Keep the balance, watch the B-tree grow
Half full minimum, that's the rule we know
Order property, from root below
Insert split merge, feel the rhythm go
Balance maintained, watch the data flow
[Verse 2]
Insertion starts with finding the right leaf
Add the key, but check for overflow grief
When a node gets too full, we split it clean
Median goes up, left and right between
Parent takes the middle, children divide
Recursive splits when nodes collide
All the way up to the root we climb
Keeping balance every single time
[Chorus]
Insert split merge, that's the way we flow
Keep the balance, watch the B-tree grow
Half full minimum, that's the rule we know
Order property, from root below
Insert split merge, feel the rhythm go
Balance maintained, watch the data flow
[Verse 3]
Deletion's trickier, three cases to know
Leaf node simple, just remove and go
Internal node, find the predecessor
Replace the key, then delete successor
Underflow means we need more keys
Borrow from siblings if you please
Merge with parent when borrowing fails
Recursive fixes, balance never pales
[Bridge]
Minimum degree t, children between
t minus one and two t minus one keys clean
Root exception, one key can survive
But every other node needs more to thrive
[Chorus]
Insert split merge, that's the way we flow
Keep the balance, watch the B-tree grow
Half full minimum, that's the rule we know
Order property, from root below
Insert split merge, feel the rhythm go
Balance maintained, watch the data flow
[Outro]
B-tree mastery, we conquered the game
Logarithmic height, performance the same
Disk access optimized, blocks align
Self-balancing beauty, by design