Objective: Given an array write an algorithm to print all the possible sub subsequences.
Example:
int [] a = {1, 2, 3};
Output: Possible sub sequences –
{Empty}, {1}, {2}, {3}, {1, 2} ,{1,3}, {2, 3}, {1, 2, 3}
Approach:
- The approach will be similar to as discussed here Generate All Strings of n bits
- If we consider n= 3(same as the array size) then all possible combinations are [0, 0, 0] [1, 0, 0] [0, 1, 0] [1, 1, 0] [0, 0, 1] [1, 0, 1] [0, 1, 1] [1, 1, 1].
- So from the above combinations, wherever the bit is set to 1, place an array element at the position and wherever the bit is set to 0, ignore the array element.
- The above step will give the desired result.
- See the code below for better understanding.
Time Complexity: O(2^n)
Complete Code:
Output:
1 2 3
1 2
1 3
1
2 3
2
3
{Empty Set}
Much simpler code
public class ArraySubSequences {
public static void main(String[] args) {
int[] a = {1,2,3};
printSubSequences(a, 0, new ArrayList(), ” “);
}
static void printSubSequences(int[] arr, int start, List chosen, String space) {
if(start > arr.length) {
return;
}
else {
for (int i = start; i < arr.length; i++) {
//choose
chosen.add(arr[i]);
System.out.println(space + chosen);
//explore
printSubSequences(arr, i + 1, chosen, space + " ");
//un-choose
chosen.remove(chosen.size() – 1);
}
}
}
}