# 2659. Make Array Empty

## Description

You are given an integer array nums containing distinct numbers, and you can perform the following operations until the array is empty:

• If the first element has the smallest value, remove it
• Otherwise, put the first element at the end of the array.

Return an integer denoting the number of operations it takes to make nums empty.

Example 1:

Input: nums = [3,4,-1]
Output: 5

Operation Array
1 [4, -1, 3]
2 [-1, 3, 4]
3 [3, 4]
4 [4]
5 []

Example 2:

Input: nums = [1,2,4,3]
Output: 5

Operation Array
1 [2, 4, 3]
2 [4, 3]
3 [3, 4]
4 [4]
5 []

Example 3:

Input: nums = [1,2,3]
Output: 3

Operation Array
1 [2, 3]
2 [3]
3 []

Constraints:

• 1 <= nums.length <= 105
• -109 <= nums[i] <= 109
• All values in nums are distinct.

## Solutions

• class BinaryIndexedTree {
private int n;
private int[] c;

public BinaryIndexedTree(int n) {
this.n = n;
c = new int[n + 1];
}

public void update(int x, int delta) {
while (x <= n) {
c[x] += delta;
x += x & -x;
}
}

public int query(int x) {
int s = 0;
while (x > 0) {
s += c[x];
x -= x & -x;
}
return s;
}
}

class Solution {
public long countOperationsToEmptyArray(int[] nums) {
int n = nums.length;
Map<Integer, Integer> pos = new HashMap<>();
for (int i = 0; i < n; ++i) {
pos.put(nums[i], i);
}
Arrays.sort(nums);
long ans = pos.get(nums[0]) + 1;
BinaryIndexedTree tree = new BinaryIndexedTree(n);
for (int k = 0; k < n - 1; ++k) {
int i = pos.get(nums[k]), j = pos.get(nums[k + 1]);
long d = j - i - (tree.query(j + 1) - tree.query(i + 1));
ans += d + (n - k) * (i > j ? 1 : 0);
tree.update(i + 1, 1);
}
return ans;
}
}

• class BinaryIndexedTree {
public:
BinaryIndexedTree(int _n)
: n(_n)
, c(_n + 1) {}

void update(int x, int delta) {
while (x <= n) {
c[x] += delta;
x += x & -x;
}
}

int query(int x) {
int s = 0;
while (x) {
s += c[x];
x -= x & -x;
}
return s;
}

private:
int n;
vector<int> c;
};

class Solution {
public:
long long countOperationsToEmptyArray(vector<int>& nums) {
unordered_map<int, int> pos;
int n = nums.size();
for (int i = 0; i < n; ++i) {
pos[nums[i]] = i;
}
sort(nums.begin(), nums.end());
BinaryIndexedTree tree(n);
long long ans = pos[nums[0]] + 1;
for (int k = 0; k < n - 1; ++k) {
int i = pos[nums[k]], j = pos[nums[k + 1]];
long long d = j - i - (tree.query(j + 1) - tree.query(i + 1));
ans += d + (n - k) * int(i > j);
tree.update(i + 1, 1);
}
return ans;
}
};

• from sortedcontainers import SortedList

class Solution:
def countOperationsToEmptyArray(self, nums: List[int]) -> int:
pos = {x: i for i, x in enumerate(nums)}
nums.sort()
sl = SortedList()
ans = pos[nums[0]] + 1
n = len(nums)
for k, (a, b) in enumerate(pairwise(nums)):
i, j = pos[a], pos[b]
d = j - i - sl.bisect(j) + sl.bisect(i)
ans += d + (n - k) * int(i > j)
return ans


• type BinaryIndexedTree struct {
n int
c []int
}

func newBinaryIndexedTree(n int) *BinaryIndexedTree {
c := make([]int, n+1)
return &BinaryIndexedTree{n, c}
}

func (this *BinaryIndexedTree) update(x, delta int) {
for x <= this.n {
this.c[x] += delta
x += x & -x
}
}

func (this *BinaryIndexedTree) query(x int) int {
s := 0
for x > 0 {
s += this.c[x]
x -= x & -x
}
return s
}

func countOperationsToEmptyArray(nums []int) int64 {
n := len(nums)
pos := map[int]int{}
for i, x := range nums {
pos[x] = i
}
sort.Ints(nums)
tree := newBinaryIndexedTree(n)
ans := pos[nums[0]] + 1
for k := 0; k < n-1; k++ {
i, j := pos[nums[k]], pos[nums[k+1]]
d := j - i - (tree.query(j+1) - tree.query(i+1))
if i > j {
d += n - k
}
ans += d
tree.update(i+1, 1)
}
return int64(ans)
}

• class BinaryIndexedTree {
private n: number;
private c: number[];

constructor(n: number) {
this.n = n;
this.c = Array(n + 1).fill(0);
}

public update(x: number, v: number): void {
while (x <= this.n) {
this.c[x] += v;
x += x & -x;
}
}

public query(x: number): number {
let s = 0;
while (x > 0) {
s += this.c[x];
x -= x & -x;
}
return s;
}
}

function countOperationsToEmptyArray(nums: number[]): number {
const pos: Map<number, number> = new Map();
const n = nums.length;
for (let i = 0; i < n; ++i) {
pos.set(nums[i], i);
}
nums.sort((a, b) => a - b);
const tree = new BinaryIndexedTree(n);
let ans = pos.get(nums[0])! + 1;
for (let k = 0; k < n - 1; ++k) {
const i = pos.get(nums[k])!;
const j = pos.get(nums[k + 1])!;
let d = j - i - (tree.query(j + 1) - tree.query(i + 1));
if (i > j) {
d += n - k;
}
ans += d;
tree.update(i + 1, 1);
}
return ans;
}