Subsequence sum

Question

Given an array of integers eg [1, 2, -3, 1] find whether there is a sub-sequence that sums to 0 and return it (eg [1, 2, -3] or [2,

Answer 1

Do a running sum, storing sum values in a hash table along with array index

If you ever get a sum value you’ve already seen, return 1+the index in the hash table, and the current index. This solution is O(n) time complexity.

No need for a new array. Space complexity is O(N) because of the hash.

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A Python implementation:

input = [1, 4, -3, -4, 6, -7, 8, -5]
map = {}
sum = 0
for i in range(len(input)):
    sum += input[i]
    if sum in map:
        print map[sum][0] + 1, "to", i
    map[sum] = (i, sum)

Notice that repeated subsequences are not shown, example: If (1 to 2) is a subsequence and (3 to 4), (1 to 4) won't be shown. You can achieve this behavior by storing lists in each position of the map:

for x in map[sum]:
    print x[0]+1, "to", i
map[sum].append((i, sum))