Stacks and Queues

Queue from Two Stacks

Implement queue behavior with an input stack and an output stack.

Algorithm

The replay uses the same three values in every language, so this R DSA implementation can be compared directly with the rest of the DSA track.

input stack Enqueue pushes new values onto the input stack.
output stack When the output stack is empty, transferring all input values reverses them into dequeue order.

Visual walkthrough

The two-stack queue keeps cheap enqueues in the input stack, then reverses that stack only when dequeue needs the output stack.

Step 1 - Enqueue pushes onto the input stack

After enqueueing 10, 20, 30, the newest input value is on top of the input stack.

After enqueues: input top is 30; output is empty.input stack top -> bottomoutput stack top -> bottomremoved30(empty)(empty)2010

Step 2 - Transfer reverses into output order

Moving every input value to the output stack turns 10 into the next pop.

After transfer: output top is 10, so dequeue returns the oldest value.input stackoutput stack top -> bottomremoved(empty)10(empty)2030

Step 3 - Dequeue pops from output

The output stack pops 10 first while 20 becomes the next front.

After one dequeue: removed is 10; output top is now 20.input stackoutput stack top -> bottomremoved(empty)201030

Basic Implementation

basic.R 
render <- function(values) {
  paste(values, collapse = " -> ")
}

in_stack <- c()
out_stack <- c()
for (value in c(10, 20, 30)) in_stack <- c(in_stack, value)
while (length(in_stack) > 0) {
  out_stack <- c(out_stack, in_stack[length(in_stack)])
  in_stack <- in_stack[-length(in_stack)]
}
removed <- c()
while (length(out_stack) > 0) {
  removed <- c(removed, out_stack[length(out_stack)])
  out_stack <- out_stack[-length(out_stack)]
}
cat(render(removed), "\n", sep = "")

Complexity

  • Time: O(1) amortized per operation
  • Space: O(n)

Implementation notes

  • in_stack <- c() and out_stack <- c() start as empty R vectors.
  • Enqueue appends onto the input stack with in_stack <- c(in_stack, value) for the pinned values 10, 20, and 30.
  • After enqueue, the trace shows in_stack = [10, 20, 30] and out_stack = [].
  • This source treats the right end of each vector as the stack top.
  • Transfer runs while length(in_stack) > 0.
  • in_stack[length(in_stack)] reads the top value from the input stack.
  • out_stack <- c(out_stack, in_stack[length(in_stack)]) pushes that value to the output stack.
  • in_stack <- in_stack[-length(in_stack)] removes the old top by negative indexing.
  • The transfer reverses the stack, producing out_stack = [30, 20, 10] and emptying in_stack.
  • Dequeue then pops from the right end of out_stack with out_stack[length(out_stack)].
  • Each popped scalar is appended to removed with removed <- c(removed, ...).

Replay steps

start:      in [], out [], removed []
enqueue:    in [10, 20, 30], out []
transfer:   in [], out [30, 20, 10]
dequeue:    out [], removed [10, 20, 30]
  • render(removed) uses paste(values, collapse = " -> "), and cat(render(removed), "\n", sep = "") prints 10 -> 20 -> 30.