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/// Heapsort.
pub fn heapsort(arr: &mut [i32]) {
    // -- Heapify part --
    // This procedure would build a valid max-heap.
    // (or min-heap for sorting descendantly)
    let end = arr.len();
    for start in (0..end / 2).rev() {
        // Skip leaf nodes (end / 2).
        sift_down(arr, start, end - 1);
    }

    // -- Sorting part --
    // Iteratively sift down unsorted part (the heap).
    for end in (1..arr.len()).rev() {
        arr.swap(end, 0);
        sift_down(arr, 0, end - 1);
    }
}

/// Internal function for heap to fix itself to conform to heap definition.
/// Precondiition: all elements below `start` are in heap order
/// expect `start` itself.
fn sift_down(arr: &mut [i32], start: usize, end: usize) {
    let mut root = start;
    loop {
        let mut child = root * 2 + 1; // Get the left child
        if child > end {
            break;
        }
        if child < end && arr[child] < arr[child + 1] {
            // Right child exists and is greater.
            child += 1;
        }

        if arr[root] < arr[child] {
            // If child is greater than root, swap'em!
            arr.swap(root, child);
            root = child;
        } else {
            break;
        }
    }
}

#[cfg(test)]
mod base {
    use super::*;
    base_cases!(heapsort);
}