# is that for every node

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#### taraa

##### Senior Member
Is "that" redundant?
“There are two kinds of binary heaps: max-heaps and min-heaps. In both kinds, the values in the nodes satisfy a heap property, the specifics of which depend on the kind of heap. In a max-heap, the max-heap property is that for every node i other than the root,”

• #### grassy

##### Senior Member
Please give us the complete sentence, tara.

#### entangledbank

##### Senior Member
'That' is usually redundant, but is needed when something comes in front of the subject. In what you've quoted, the 'for' phrase does, and we haven't seen the subject yet. So 'that' is required to show where the 'that'-clause begins.

#### taraa

##### Senior Member
Please give us the complete sentence, tara.
It's:
"There are two kinds of binary heaps: max-heaps and min-heaps. In both kinds, the values in the nodes satisfy a heap property, the specifics of which depend on the kind of heap. In a max-heap, the max-heap property is that for every node i other than the root,

A[PARENT(i)] >=A ;

that is, the value of a node is at most the value of its parent."

'That' is usually redundant, but is needed when something comes in front of the subject. In what you've quoted, the 'for' phrase does, and we haven't seen the subject yet. So 'that' is required to show where the 'that'-clause begins.
Thanks a lot

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#### PaulQ

##### Senior Member
In a max-heap, the max-heap property is that for every node i other than the root,”
To me, "that" is a pronoun = the property.

My accent is that of all the people in this village.

In my wardrobe, the size of the shoes is that for every member of the family other than my wife.

#### Myridon

##### Senior Member
In a max-heap, the max-heap property is that for every node i other than the root, A[Parent(i)] >= A, that is, the value of a node is at most the value of its parent.

ie

In a max-heap, the max-heap property is the property "for every node i other than the root, A[Parent(i)] >= A", that is, the value of a node is at most the value of its parent.

max-heap property = for every node i other than the root, A[Parent(i)] >= A

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#### grassy

##### Senior Member
In a max-heap, the max-heap property is that for every node i other than the root,

A[PARENT(i)] >=A ;

that is, the value of a node is at most the value of its parent."
Thanks for providing the complete sentence, Tara.
I think I agree with ETB that "that" introduces a 'that'-clause there.

#### kentix

##### Senior Member
I agree. It's not a pronoun, it's introducing an explanation of an idea.

The max-heap property fits this criteria:

For every node i other than the root <the following is true>

Combining that into one sentence it becomes:
The max-heap property fits the criteria that, for every node i other than the root, <the following is true>

#### taraa

##### Senior Member
Thank you all so much
Sorry I've written that wrong. It's
A[PARENT(i)] >=A(i)

#### PaulQ

##### Senior Member
National Institute of Standards and Technology: max-heap property

max-heap property
Definition: Each node in a tree has a key (i.e. 'number) which is less than or equal to the key of its parent.

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