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.

Complexity

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

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

Visual walkthrough

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"; }

After popping the minimum, the last value moves to the root and sifts down by swapping with the smaller child.

Step 1 - Replace root

The saved minimum is 1; the last value 7 moves to the root before sifting down.

Step 2 - Swap with the smaller child

7 swaps with 2, producing the final heap [2, 4, 7, 9, 6].

Output

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

Implementation notes

In C++, the heap is a std::vector<int> initialized as {1, 4, 2, 9, 6, 7} and passed by non-const reference to heapPop(vector<int>& heap).
int smallest = heap[0] copies the root value for return, then heap[0] = heap.back(); heap.pop_back(); moves 7 into the root slot and shortens the same vector.
Sift-down indexes are size_t: left = parent * 2 + 1 and right = left + 1. The loop stops when the left child is outside heap.size() or the parent is already <= the selected child.
The right child is chosen only when it exists and heap[right] < heap[left]; swaps use std::swap on vector elements and then continue from that child index.
The trace records [1, 4, 2, 9, 6, 7], removes 1 and moves 7 to [7, 4, 2, 9, 6], then swaps with smaller child 2 to [2, 4, 7, 9, 6].
std::cout << popped << " -> " << listString(heap) << "\n" prints 1 -> [2, 4, 7, 9, 6]; listString builds that bracketed vector text with std::stringstream. Visible allocation is the heap vector storage and formatting buffer; mutation is root replacement, pop_back, and vector element swaps.