Arrays and Iteration

Two-Sum with Hash Lookup

Walk the array once, storing seen values in a lookup table. When the complement is already present, the result indices are known.

Algorithm

execution replay The checked-in replay follows the language-neutral state table for `array-two-sum-hash`.
cross-language comparison This Lua DSA version keeps the same data and final output as every other DSA book in this wave.

Basic Implementation

basic.lua
Replay: real traced execution (multi-file project)
arr = {2, 7, 11, 4, 5}
target = 9
seen = {}
first = -1
second = -1
for i = 1, #arr do
	value = arr[i]
	need = target - value
	if seen[need] ~= nil then
		first = seen[need]
		second = i - 1
		break
	end
	seen[value] = i - 1
end
print("[" .. first .. ", " .. second .. "]")

  1. arr ← [2, 7, 11, 4, 5], target ← 9, seen ← {}

    1arr = {2, 7, 11, 4, 5}2target = 9
    values this step[2, 7, 11, 4, 5]arr9target{}seen

  2. seen ← {2: 0}, hit ← no

    7value = arr[i]8need = target - value9if seen[need] ~= nil then
    values this step{} → {2: 0}seennohit0i2arr[i]7need

  3. hit ← yes, result ← [0, 1]

    7value = arr[i]8need = target - value9if seen[need] ~= nil then
    values this stepyeshit[0, 1]result1i7arr[i]2need{2: 0}seen

Complexity

  • Time: O(n) average
  • Space: O(n)

Implementation notes

  • arr = {2, 7, 11, 4, 5} is a Lua table used as an array, and target = 9.
  • The loop is for i = 1, #arr do, so the source reads values with Lua's 1-based table indexes.
  • The result indices are deliberately zero-based: stored positions use i - 1, and second = i - 1 when a match is found.
  • seen = {} is the lookup table from value to earlier zero-based index.
  • need = target - value computes the complement for the current value.
  • Lua table lookup returns nil for a missing key, so if seen[need] ~= nil then distinguishes a miss from a stored index such as 0.
  • The trace first reads value 2, needs 7, misses in {}, and records seen[2] = 0.
  • The next value is 7, needs 2, hits seen[2], and sets the result to [0, 1] before break.
  • print("[" .. first .. ", " .. second .. "]") prints [0, 1].