Print all subsequences in an array with sum = K and no repitition of elements

Backtrack with duplicate control

Sort the values so equal candidates are adjacent. DFS with a start index, remaining sum, and current combination. At each depth, iterate candidates from start; skip a value when it equals the prior candidate at that same depth, choose it once, recurse with the next index so an element is not reused, then backtrack. Emit a copy when remaining sum is zero.

The same-depth skip removes duplicate combinations while still allowing equal values from different positions when enough copies exist. With nonnegative sorted values, stop when a candidate exceeds remaining sum; do not apply that pruning if negatives are allowed. The search is output-sensitive and can be O(2^n) time in the worst case, plus the cost of writing answers, with O(n) recursion/path space. Test duplicates, target zero, no solution, one solution using repeated equal values, and negative-number semantics. Clarify whether order creates distinct subsequences; if it does, sorting and deduplication change the requested result.