Min-Heap Pop (Sift Down)

Remove the minimum value, move the last item to the root, and sift downward.

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 down After removing the root, the last value moves to the root and swaps with the smaller child until order is restored.

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 = {1, 4, 2, 9, 6, 7}; int popped = heapPop(heap); cout << popped << " -> " << listString(heap) << "\n"; }

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