## Saturday, February 6, 2016

### Subarray/Substring vs Subsequence and Programs to Generate them - GeeksforGeeks

Subarray/Substring vs Subsequence and Programs to Generate them - GeeksforGeeks
A subbarray is a contiguous part of array. An array that is inside another array. For example, consider the array [1, 2, 3, 4], There are 10 non-empty sub-arrays. The subbarays are (1), (2), (3), (4), (1,2), (2,3), (3,4), (1,2,3), (2,3,4) and (1,2,3,4). In general, for an array/string of size n, there are n*(n+1)/2 non-empty subarrays/subsrings.
How to generate all subarrays?
We can run two nested loops, the outer loop picks starting element and inner loop considers all elements on right of the picked elements as ending element of subarray.
`void` `subArray(``int` `arr[], ``int` `n)`
`{`
`    ``// Pick starting point`
`    ``for` `(``int` `i=0; i <n; i++)`
`    ``{`
`        ``// Pick ending point`
`        ``for` `(``int` `j=i; j<n; j++)`
`        ``{`
`            ``// Print subarray between current starting`
`            ``// and ending points`
`            ``for` `(``int` `k=i; k<=j; k++)`
`                ``cout << arr[k] << ``" "``;`

`            ``cout << endl;`
`        ``}`
`    ``}`
`}`

A subsequence is a sequence that can be derived from another sequence by zero or more elements, without changing the order of the remaining elements.
For the same example, there are 15 sub-sequences. They are (1), (2), (3), (4), (1,2), (1,3),(1,4), (2,3), (2,4), (3,4), (1,2,3), (1,2,4), (1,3,4), (2,3,4), (1,2,3,4). More generally, we can say that for a sequence of size n, we can have (2n-1) non-empty sub-sequences in total.

`void` `printSubsequences(``int` `arr[], ``int` `n)`
`{`
`    ``/* Number of subsequences is (2**n -1)*/`
`    ``unsigned ``int` `opsize = ``pow``(2, n);`

`    ``/* Run from counter 000..0 to 111..1*/`
`    ``for` `(``int` `counter = 1; counter < opsize; counter++)`
`    ``{`
`        ``for` `(``int` `j = 0; j < n; j++)`
`        ``{`
`            ``/* Check if jth bit in the counter is set`
`                ``If set then print jth element from arr[] */`
`            ``if` `(counter & (1<<j))`
`                ``cout << arr[j] << ``" "``;`
`        ``}`
`        ``cout << endl;`
`    ``}`
`}`