08-heaps

Min-Heap Insert (Sift Up)

Insert one value into a min-heap and restore the parent-child order by sifting upward.

Algorithm

Steps

  1. Store the heap in an array.
  2. Compare parent and child indexes instead of building explicit tree nodes.
  3. Swap only when the heap order is violated.
  4. Print the deterministic final heap state for replay comparison.

Complexity

  • Time: O(log n)
  • Space: O(1) extra
sift up A new value starts at the end of the array and swaps with its parent while it is smaller.

Visual walkthrough

R DSA Implementation

basic.R 
list_string <- function(values) paste0("[", paste(values, collapse = ", "), "]")
heap_insert <- function(heap, value) {
  heap <- c(heap, value)
  child <- length(heap)
  while (child > 1) {
    parent <- floor(child / 2)
    if (heap[parent] <= heap[child]) break
    tmp <- heap[parent]; heap[parent] <- heap[child]; heap[child] <- tmp
    child <- parent
  }
  heap
}
heap_pop <- function(heap) {
  smallest <- heap[1]
  heap[1] <- heap[length(heap)]
  heap <- heap[-length(heap)]
  parent <- 1
  while (TRUE) {
    left <- parent * 2
    right <- left + 1
    if (left > length(heap)) break
    child <- left
    if (right <= length(heap) && heap[right] < heap[left]) child <- right
    if (heap[parent] <= heap[child]) break
    tmp <- heap[parent]; heap[parent] <- heap[child]; heap[child] <- tmp
    parent <- child
  }
  list(value = smallest, heap = heap)
}
heap <- c(2, 4, 7, 9, 6)
heap <- heap_insert(heap, 1)
cat(list_string(heap), "\n", sep = "")

The heap is still an array, but the tree view makes parent-child swaps visible. The labels use the pinned replay states from the lesson.

Step 1 - Append 1

The new value 1 starts at index 5 and compares with its parent value 7.

Array state [2, 4, 7, 9, 6, 1] as a heap-shaped tree.2i04i17parent9i36i41new

Step 2 - Swap with 7

Because 1 is smaller than 7, those array slots swap.

After the first sift-up swap: [2, 4, 1, 9, 6, 7].2parent4i11child9i36i47i5

Step 3 - Swap with 2

1 is also smaller than 2, so it moves to the root and the heap order is restored.

Final heap after insert: [1, 4, 2, 9, 6, 7].1root4i12i29i36i47i5

Implementation notes

  • heap <- c(2, 4, 7, 9, 6) is the starting min-heap vector. This lesson uses R's 1-based indexes.
  • The output path calls heap <- heap_insert(heap, 1). heap_pop() is present in the shared file, but it is not used for this lesson's printed result.
  • heap_insert() appends with heap <- c(heap, value), producing [2, 4, 7, 9, 6, 1], then starts child <- length(heap) at index 6.
  • parent <- floor(child / 2) follows the 1-based heap relationship: child 6 has parent 3, then child 3 has parent 1.
  • if (heap[parent] <= heap[child]) break stops when min-heap order is already valid. Otherwise the tmp line swaps the parent and child values.

Replay steps

start:       [2, 4, 7, 9, 6]
append 1:    [2, 4, 7, 9, 6, 1]
swap 1/7:    [2, 4, 1, 9, 6, 7]
swap 1/2:    [1, 4, 2, 9, 6, 7]
  • list_string(heap) formats [1, 4, 2, 9, 6, 7], and cat(..., "\n", sep = "") prints that exact line.

Output

[1, 4, 2, 9, 6, 7]