data structures array and sparse matrics

data structures array and sparse matrics

• 1.
  ARRAYS  Array isa consecutive set of memory locations and it's mainly used to store similar data.  It is a particular method of storing elements of indexed data. Elements of data are stored sequentially in blocks within the array.  Each element is referenced by an index, or subscript. The index is usually a number used to address an element in the array.  An array is a set of pairs, index and a value.  For each index which is defined, there is a value associated with that index.  In mathematical terms it is called as correspondence or mapping.
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  ARRAYS...
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  ARRAYS... Simply, declaration ofarray is as follows: int arr[10] Where int specifies the data type or type of elements arrays stores. “arr” is the name of array & the number specified inside the square brackets is the number of elements an array can store, this is also called sized or length of array.
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  ARRAYS... Following are someof the concepts to be remembered about arrays: The individual element of an array can be accessed by specifying name of the array, following by index or subscript inside square brackets. The first element of the array has index zero[0]. It means the first element and last element will be specified as:arr[0] & arr[9] Respectively.
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  ARRAYS... The elements ofarray will always be stored in the consecutive (continues) memory location. The number of elements that can be stored in an array, that is the size of array or its length is given by the following equation: (Upperbound-lowerbound)+1
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  ARRAYS... For the abovearray it would be (9-0)+1=10,where 0 is the lower bound of array and 9 is the upper bound of array. Array can always be read or written through loop. If we read a one-dimensional array it require one loop for reading and other for writing the array.
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  ARRAYS... For example: Readingan array For(i=0;i<=9;i++) scanf(“%d”,&arr[i]); For example: Writing an array For(i=0;i<=9;i++) printf(“%d”,arr[i]);
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  ARRAYS... If we arereading or writing two-dimensional array it would require two loops. And similarly the array of a N dimension would required N loops. Some common operation performed on array are: Creation of an array Traversing an array
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  ARRAYS... Insertion of newelement Deletion of required element Modification of an element Merging of arrays
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  SPARSE MATRICES  Amatrix is a two-dimensional data object made of m rows and n columns, therefore having total m x n values.  If most of the elements of the matrix have 0 value, then it is called a sparse matrix. Why to use Sparse Matrix instead of simple matrix ?  Storage: There are lesser non-zero elements than zeros and thus lesser memory can be used to store only those elements.  Computing time: Computing time can be saved by logically designing a data structure traversing only non-zero elements..
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  SPARSE MATRICES......  Example 00 3 0 4 0 0 5 7 0 0 0 0 0 0 0 2 6 0 0  Representing a sparse matrix by a 2D array leads to wastage of lots of memory as zeroes in the matrix are of no use in most of the cases.  So, instead of storing zeroes with non-zero elements, we only store non-zero elements.  This means storing non-zero elements with triples- (Row, Column, value).
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  SPARSE MATRICES...  Thesame time they are sparse: say only 1000 out of one million possible elements are nonzero.  On most computers today it would be impossible to store a full 1000 X 1000 matrix in the memory at once.  Sparse Matrix Representations can be done in many ways following are two common representations:  Array representation  Linked list representation
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  Array Representation  2Darray is used to represent a sparse matrix in which there are three rows named as  Row: Index of row, where non-zero element is located  Column: Index of column, where non-zero element is located  Value: Value of the non zero element located at index - (row,column)
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  Linked List Representation In linked list, each node has four fields. These four fields are defined as:  Row: Index of row, where non-zero element is located  Column: Index of column, where non-zero element is located  Value: Value of the non zero element located at index - (row,column)  Next node: Address of the next node