package q3510

import "container/heap"

type Node struct {
	val             int
	prev, next      *Node
	arrPos, heapPos int
}

type MinAdjSum []*Node

func (m *MinAdjSum) Len() int { return len(*m) }

func (m *MinAdjSum) Less(i int, j int) bool {
	if (*m)[i].next == nil {
		return false
	}
	if (*m)[j].next == nil {
		return true
	}
	s1, p1 := (*m)[i].val+(*m)[i].next.val, (*m)[i].arrPos
	s2, p2 := (*m)[j].val+(*m)[j].next.val, (*m)[j].arrPos
	if s1 == s2 {
		return p1 < p2
	}
	return s1 < s2
}

func (m *MinAdjSum) Push(x any) {
	elem := x.(*Node)
	elem.heapPos = len(*m)
	*m = append(*m, elem)
}

func (m *MinAdjSum) Pop() any {
	ret := (*m)[len(*m)-1]
	(*m) = (*m)[:len(*m)-1]
	return ret
}

func (m *MinAdjSum) Swap(i int, j int) {
	(*m)[i].heapPos = j
	(*m)[j].heapPos = i
	(*m)[i], (*m)[j] = (*m)[j], (*m)[i]
}

func minimumPairRemoval(nums []int) int {
	outOfOrder := 0
	for i := range len(nums) - 1 {
		if nums[i] > nums[i+1] {
			outOfOrder++
		}
	}
	if outOfOrder == 0 {
		return 0
	}

	nodes := make([]Node, len(nums))
	hp := make(MinAdjSum, len(nums))
	for i := range nums {
		nodes[i] = Node{val: nums[i], heapPos: i, arrPos: i}
		hp[i] = &nodes[i]

		if i > 0 {
			nodes[i].prev = &nodes[i-1]
		}
		if i+1 < len(nums) {
			nodes[i].next = &nodes[i+1]
		}
	}
	heap.Init(&hp)

	ops := 0
	for ; outOfOrder > 0; ops++ {
		node := hp[0]
		next, prev := node.next, node.prev

		heap.Remove(&hp, node.heapPos)
		heap.Remove(&hp, next.heapPos)
		if prev != nil {
			heap.Remove(&hp, prev.heapPos)
		}

		// Update outOfOrder
		if next.val < node.val {
			outOfOrder--
		}
		if next.next != nil && next.next.val < next.val {
			outOfOrder--
		}
		if prev != nil && node.val < prev.val {
			outOfOrder--
		}

		node.val += next.val
		if prev != nil && node.val < prev.val {
			outOfOrder++
		}
		if next.next != nil && next.next.val < node.val {
			outOfOrder++
		}

		// Update links & fix heap
		node.next = next.next
		if next.next != nil {
			next.next.prev = node
		}

		heap.Push(&hp, node)
		if prev != nil {
			heap.Push(&hp, prev)
		}
	}
	return ops
}

var _ = minimumPairRemoval