Order of choosing keys from the given sets to insert in B+ tree
The question is taken from web.stanford.edu.
Consider a B+ Tree where each node can have at most $3$ keys. Suppose the tree initially has a root node with two children leaf nodes, which contain keys ${1, 3, 5}$ and ${7, 9, 11}$ respectively. The root node has a single key $7$. Four distinct keys from the set ${0, 2, 4, 6, 8, 10, 12}$ are added to the tree in some order, which causes the tree to grow by one level. How many solutions are possible to insert the keys?
My Try:
Sequence of $4$ keys: Any set which has one or three of ${0, 2, 4, 6}$ and three or one of ${8, 10, 12}$.
$^4C_1 times ^3C_3 + ^4C_2 times ^3C_2 + ^4C_3 times ^3C_1$
$= 4 + 12 + 12$
$= 28$
But one of the my frieneds arguing that there should be permuatation instead of selection. But I don't see if order is matter here, as an example, numbers $0,8,10,12$ is a valid solution. We have take ${0}$ from the first set and ${8,10,12}$.
Will order of choosing keys from the set matter? Can you please explain?
combinatorics discrete-mathematics graph-theory permutations trees
asked Nov 29 '18 at 12:12
Mithlesh Upadhyay
2,90982864
add a comment |
The question is taken from web.stanford.edu.
Consider a B+ Tree where each node can have at most $3$ keys. Suppose the tree initially has a root node with two children leaf nodes, which contain keys ${1, 3, 5}$ and ${7, 9, 11}$ respectively. The root node has a single key $7$. Four distinct keys from the set ${0, 2, 4, 6, 8, 10, 12}$ are added to the tree in some order, which causes the tree to grow by one level. How many solutions are possible to insert the keys?
My Try:
Sequence of $4$ keys: Any set which has one or three of ${0, 2, 4, 6}$ and three or one of ${8, 10, 12}$.
$^4C_1 times ^3C_3 + ^4C_2 times ^3C_2 + ^4C_3 times ^3C_1$
$= 4 + 12 + 12$
$= 28$
But one of the my frieneds arguing that there should be permuatation instead of selection. But I don't see if order is matter here, as an example, numbers $0,8,10,12$ is a valid solution. We have take ${0}$ from the first set and ${8,10,12}$.
Will order of choosing keys from the set matter? Can you please explain?
combinatorics discrete-mathematics graph-theory permutations trees
asked Nov 29 '18 at 12:12
Mithlesh Upadhyay
2,90982864
add a comment |
The question is taken from web.stanford.edu.
Consider a B+ Tree where each node can have at most $3$ keys. Suppose the tree initially has a root node with two children leaf nodes, which contain keys ${1, 3, 5}$ and ${7, 9, 11}$ respectively. The root node has a single key $7$. Four distinct keys from the set ${0, 2, 4, 6, 8, 10, 12}$ are added to the tree in some order, which causes the tree to grow by one level. How many solutions are possible to insert the keys?
My Try:
Sequence of $4$ keys: Any set which has one or three of ${0, 2, 4, 6}$ and three or one of ${8, 10, 12}$.
$^4C_1 times ^3C_3 + ^4C_2 times ^3C_2 + ^4C_3 times ^3C_1$
$= 4 + 12 + 12$
$= 28$
But one of the my frieneds arguing that there should be permuatation instead of selection. But I don't see if order is matter here, as an example, numbers $0,8,10,12$ is a valid solution. We have take ${0}$ from the first set and ${8,10,12}$.
Will order of choosing keys from the set matter? Can you please explain?
combinatorics discrete-mathematics graph-theory permutations trees
asked Nov 29 '18 at 12:12
Mithlesh Upadhyay
2,90982864
The question is taken from web.stanford.edu.
Consider a B+ Tree where each node can have at most $3$ keys. Suppose the tree initially has a root node with two children leaf nodes, which contain keys ${1, 3, 5}$ and ${7, 9, 11}$ respectively. The root node has a single key $7$. Four distinct keys from the set ${0, 2, 4, 6, 8, 10, 12}$ are added to the tree in some order, which causes the tree to grow by one level. How many solutions are possible to insert the keys?
My Try:
Sequence of $4$ keys: Any set which has one or three of ${0, 2, 4, 6}$ and three or one of ${8, 10, 12}$.
$^4C_1 times ^3C_3 + ^4C_2 times ^3C_2 + ^4C_3 times ^3C_1$
$= 4 + 12 + 12$
$= 28$
But one of the my frieneds arguing that there should be permuatation instead of selection. But I don't see if order is matter here, as an example, numbers $0,8,10,12$ is a valid solution. We have take ${0}$ from the first set and ${8,10,12}$.
Will order of choosing keys from the set matter? Can you please explain?
combinatorics discrete-mathematics graph-theory permutations trees
combinatorics discrete-mathematics graph-theory permutations trees
asked Nov 29 '18 at 12:12
Mithlesh Upadhyay
2,90982864
asked Nov 29 '18 at 12:12
Mithlesh Upadhyay
2,90982864
edited Dec 17 '18 at 8:09
asked Nov 29 '18 at 12:12
Mithlesh Upadhyay
2,90982864
asked Nov 29 '18 at 12:12
Mithlesh Upadhyay
2,90982864
asked Nov 29 '18 at 12:12
Mithlesh Upadhyay
2,90982864
2,90982864
add a comment |
add a comment |
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