Min-Heap Insert (Sift Up)

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

Algorithm

Steps

Store the heap in an array.
Compare parent and child indexes instead of building explicit tree nodes.
Swap only when the heap order is violated.
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

C DSA Implementation

basic.c

#include <stdio.h>
void print_list(int* values, int n) {
    printf("[");
    for (int i = 0; i < n; i++) { if (i) printf(", "); printf("%d", values[i]); }
    printf("]");
}
void swap(int* a, int* b) { int t = *a; *a = *b; *b = t; }
void heap_insert(int* heap, int* n, int value) {
    heap[*n] = value; int child = *n; *n = *n + 1;
    while (child > 0) {
        int parent = (child - 1) / 2;
        if (heap[parent] <= heap[child]) break;
        swap(&heap[parent], &heap[child]);
        child = parent;
    }
}
int heap_pop(int* heap, int* n) {
    int smallest = heap[0]; heap[0] = heap[*n - 1]; *n = *n - 1;
    int parent = 0;
    while (1) {
        int left = parent * 2 + 1, right = left + 1;
        if (left >= *n) break;
        int child = left;
        if (right < *n && heap[right] < heap[left]) child = right;
        if (heap[parent] <= heap[child]) break;
        swap(&heap[parent], &heap[child]);
        parent = child;
    }
    return smallest;
}
int main(void) { int heap[16] = {2, 4, 7, 9, 6}; int n = 5; heap_insert(heap, &n, 1); print_list(heap, n); printf("\n"); }

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.

Step 2 - Swap with 7

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

Step 3 - Swap with 2

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

Output

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

Implementation notes

C stores the heap in stack array int heap[16] = {2, 4, 7, 9, 6} with scalar size int n = 5; the capacity is fixed by the array declaration, and this source does not add a bounds check before insertion.
heap_insert(int* heap, int* n, int value) receives the array as a pointer and the size by pointer, so heap[*n] = value and *n = *n + 1 mutate caller state.
Sift-up uses signed int indexes: child starts at the inserted slot and parent = (child - 1) / 2; the loop stops at the root or when heap[parent] <= heap[child].
swap(int* a, int* b) exchanges two heap slots through pointers using stack temporary int t; no second heap array is allocated.
The trace records [2, 4, 7, 9, 6], append to [2, 4, 7, 9, 6, 1], swap with parent 7 to [2, 4, 1, 9, 6, 7], then swap with parent 2 to [1, 4, 2, 9, 6, 7].
print_list(int* values, int n) receives the heap as a pointer after array decay and prints comma-separated integers with printf, followed by a newline in main.