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. @end @complexity

Time: O(log n)
Space: O(1) extra @end

sift up A new value starts at the end of the array and swaps with its parent while it is smaller.

C++ DSA Implementation

basic.cpp

#include <algorithm>
#include <iostream>
#include <sstream>
#include <vector>
using namespace std;
string listString(const vector<int>& values) {
    stringstream out; out << "[";
    for (size_t i = 0; i < values.size(); i++) { if (i) out << ", "; out << values[i]; }
    out << "]"; return out.str();
}
void heapInsert(vector<int>& heap, int value) {
    heap.push_back(value);
    size_t child = heap.size() - 1;
    while (child > 0) {
        size_t parent = (child - 1) / 2;
        if (heap[parent] <= heap[child]) break;
        swap(heap[parent], heap[child]);
        child = parent;
    }
}
int heapPop(vector<int>& heap) {
    int smallest = heap[0];
    heap[0] = heap.back(); heap.pop_back();
    size_t parent = 0;
    while (true) {
        size_t left = parent * 2 + 1, right = left + 1;
        if (left >= heap.size()) break;
        size_t child = left;
        if (right < heap.size() && heap[right] < heap[left]) child = right;
        if (heap[parent] <= heap[child]) break;
        swap(heap[parent], heap[child]);
        parent = child;
    }
    return smallest;
}
int main() { vector<int> heap = {2, 4, 7, 9, 6}; heapInsert(heap, 1); cout << listString(heap) << "\n"; }

@end @output [1, 4, 2, 9, 6, 7] @end