Question

1649. Create Sorted Array through Instructions

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Description

Given an integer array instructions, you are asked to create a sorted array from the elements in instructions. You start with an empty container nums. For each element from left to right in instructions, insert it into nums. The cost of each insertion is the minimum of the following:

• The number of elements currently in nums that are strictly less than instructions[i].
• The number of elements currently in nums that are strictly greater than instructions[i].

For example, if inserting element 3 into nums = [1,2,3,5], the cost of insertion is min(2, 1) (elements 1 and 2 are less than 3, element 5 is greater than 3) and nums will become [1,2,3,3,5].

Return _the total cost to insert all elements from _instructions_ into _nums. Since the answer may be large, return it modulo 109 + 7

 

Example 1:

Input: instructions = [1,5,6,2]

Output: 1

Explanation: Begin with nums = [].

Insert 1 with cost min(0, 0) = 0, now nums = [1].

Insert 5 with cost min(1, 0) = 0, now nums = [1,5].

Insert 6 with cost min(2, 0) = 0, now nums = [1,5,6].

Insert 2 with cost min(1, 2) = 1, now nums = [1,2,5,6].

The total cost is 0 + 0 + 0 + 1 = 1.

Example 2:

Input: instructions = [1,2,3,6,5,4]

Output: 3

Explanation: Begin with nums = [].

Insert 1 with cost min(0, 0) = 0, now nums = [1].

Insert 2 with cost min(1, 0) = 0, now nums = [1,2].

Insert 3 with cost min(2, 0) = 0, now nums = [1,2,3].

Insert 6 with cost min(3, 0) = 0, now nums = [1,2,3,6].

Insert 5 with cost min(3, 1) = 1, now nums = [1,2,3,5,6].

Insert 4 with cost min(3, 2) = 2, now nums = [1,2,3,4,5,6].

The total cost is 0 + 0 + 0 + 0 + 1 + 2 = 3.

Example 3:

Input: instructions = [1,3,3,3,2,4,2,1,2]

Output: 4

Explanation: Begin with nums = [].

Insert 1 with cost min(0, 0) = 0, now nums = [1].

Insert 3 with cost min(1, 0) = 0, now nums = [1,3].

Insert 3 with cost min(1, 0) = 0, now nums = [1,3,3].

Insert 3 with cost min(1, 0) = 0, now nums = [1,3,3,3].

Insert 2 with cost min(1, 3) = 1, now nums = [1,2,3,3,3].

Insert 4 with cost min(5, 0) = 0, now nums = [1,2,3,3,3,4].

​​​​​​​Insert 2 with cost min(1, 4) = 1, now nums = [1,2,2,3,3,3,4].

​​​​​​​Insert 1 with cost min(0, 6) = 0, now nums = [1,1,2,2,3,3,3,4].

​​​​​​​Insert 2 with cost min(2, 4) = 2, now nums = [1,1,2,2,2,3,3,3,4].

The total cost is 0 + 0 + 0 + 0 + 1 + 0 + 1 + 0 + 2 = 4.

 

Constraints:

• 1 <= instructions.length <= 105
• 1 <= instructions[i] <= 105

Solutions

Solution 1

class BinaryIndexedTree:
  def __init__(self, n):
    self.n = n
    self.c = [0] * (n + 1)

  def update(self, x: int, v: int):
    while x <= self.n:
      self.c[x] += v
      x += x & -x

  def query(self, x: int) -> int:
    s = 0
    while x:
      s += self.c[x]
      x -= x & -x
    return s


class Solution:
  def createSortedArray(self, instructions: List[int]) -> int:
    m = max(instructions)
    tree = BinaryIndexedTree(m)
    ans = 0
    mod = 10**9 + 7
    for i, x in enumerate(instructions):
      cost = min(tree.query(x - 1), i - tree.query(x))
      ans += cost
      tree.update(x, 1)
    return ans % mod

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

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

  public void update(int x, int v) {
    while (x <= n) {
      c[x] += v;
      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 int createSortedArray(int[] instructions) {
    int m = 0;
    for (int x : instructions) {
      m = Math.max(m, x);
    }
    BinaryIndexedTree tree = new BinaryIndexedTree(m);
    int ans = 0;
    final int mod = (int) 1e9 + 7;
    for (int i = 0; i < instructions.length; ++i) {
      int x = instructions[i];
      int cost = Math.min(tree.query(x - 1), i - tree.query(x));
      ans = (ans + cost) % mod;
      tree.update(x, 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:
  int createSortedArray(vector<int>& instructions) {
    int m = *max_element(instructions.begin(), instructions.end());
    BinaryIndexedTree tree(m);
    const int mod = 1e9 + 7;
    int ans = 0;
    for (int i = 0; i < instructions.size(); ++i) {
      int x = instructions[i];
      int cost = min(tree.query(x - 1), i - tree.query(x));
      ans = (ans + cost) % mod;
      tree.update(x, 1);
    }
    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 createSortedArray(instructions []int) (ans int) {
  m := slices.Max(instructions)
  tree := newBinaryIndexedTree(m)
  const mod = 1e9 + 7
  for i, x := range instructions {
    cost := min(tree.query(x-1), i-tree.query(x))
    ans = (ans + cost) % mod
    tree.update(x, 1)
  }
  return
}

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

  constructor(n: number) {
    this.n = n;
    this.c = new 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 createSortedArray(instructions: number[]): number {
  const m = Math.max(...instructions);
  const tree = new BinaryIndexedTree(m);
  let ans = 0;
  const mod = 10 ** 9 + 7;
  for (let i = 0; i < instructions.length; ++i) {
    const x = instructions[i];
    const cost = Math.min(tree.query(x - 1), i - tree.query(x));
    ans = (ans + cost) % mod;
    tree.update(x, 1);
  }
  return ans;
}

Solution 2

class Node:
  def __init__(self):
    self.l = 0
    self.r = 0
    self.v = 0


class SegmentTree:
  def __init__(self, n):
    self.tr = [Node() for _ in range(4 * n)]
    self.build(1, 1, n)

  def build(self, u, l, r):
    self.tr[u].l = l
    self.tr[u].r = r
    if l == r:
      return
    mid = (l + r) >> 1
    self.build(u << 1, l, mid)
    self.build(u << 1 | 1, mid + 1, r)

  def modify(self, u, x, v):
    if self.tr[u].l == x and self.tr[u].r == x:
      self.tr[u].v += v
      return
    mid = (self.tr[u].l + self.tr[u].r) >> 1
    if x <= mid:
      self.modify(u << 1, x, v)
    else:
      self.modify(u << 1 | 1, x, v)
    self.pushup(u)

  def pushup(self, u):
    self.tr[u].v = self.tr[u << 1].v + self.tr[u << 1 | 1].v

  def query(self, u, l, r):
    if self.tr[u].l >= l and self.tr[u].r <= r:
      return self.tr[u].v
    mid = (self.tr[u].l + self.tr[u].r) >> 1
    v = 0
    if l <= mid:
      v = self.query(u << 1, l, r)
    if r > mid:
      v += self.query(u << 1 | 1, l, r)
    return v


class Solution:
  def createSortedArray(self, instructions: List[int]) -> int:
    n = max(instructions)
    tree = SegmentTree(n)
    ans = 0
    for num in instructions:
      a = tree.query(1, 1, num - 1)
      b = tree.query(1, 1, n) - tree.query(1, 1, num)
      ans += min(a, b)
      tree.modify(1, num, 1)
    return ans % int((1e9 + 7))

class Solution {
  public int createSortedArray(int[] instructions) {
    int n = 100010;
    int mod = (int) 1e9 + 7;
    SegmentTree tree = new SegmentTree(n);
    int ans = 0;
    for (int num : instructions) {
      int a = tree.query(1, 1, num - 1);
      int b = tree.query(1, 1, n) - tree.query(1, 1, num);
      ans += Math.min(a, b);
      ans %= mod;
      tree.modify(1, num, 1);
    }
    return ans;
  }
}

class Node {
  int l;
  int r;
  int v;
}

class SegmentTree {
  private Node[] tr;

  public SegmentTree(int n) {
    tr = new Node[4 * n];
    for (int i = 0; i < tr.length; ++i) {
      tr[i] = new Node();
    }
    build(1, 1, n);
  }

  public void build(int u, int l, int r) {
    tr[u].l = l;
    tr[u].r = r;
    if (l == r) {
      return;
    }
    int mid = (l + r) >> 1;
    build(u << 1, l, mid);
    build(u << 1 | 1, mid + 1, r);
  }

  public void modify(int u, int x, int v) {
    if (tr[u].l == x && tr[u].r == x) {
      tr[u].v += v;
      return;
    }
    int mid = (tr[u].l + tr[u].r) >> 1;
    if (x <= mid) {
      modify(u << 1, x, v);
    } else {
      modify(u << 1 | 1, x, v);
    }
    pushup(u);
  }

  public void pushup(int u) {
    tr[u].v = tr[u << 1].v + tr[u << 1 | 1].v;
  }

  public int query(int u, int l, int r) {
    if (tr[u].l >= l && tr[u].r <= r) {
      return tr[u].v;
    }
    int mid = (tr[u].l + tr[u].r) >> 1;
    int v = 0;
    if (l <= mid) {
      v += query(u << 1, l, r);
    }
    if (r > mid) {
      v += query(u << 1 | 1, l, r);
    }
    return v;
  }
}

class Node {
public:
  int l;
  int r;
  int v;
};

class SegmentTree {
public:
  vector<Node*> tr;

  SegmentTree(int n) {
    tr.resize(4 * n);
    for (int i = 0; i < tr.size(); ++i) tr[i] = new Node();
    build(1, 1, n);
  }

  void build(int u, int l, int r) {
    tr[u]->l = l;
    tr[u]->r = r;
    if (l == r) return;
    int mid = (l + r) >> 1;
    build(u << 1, l, mid);
    build(u << 1 | 1, mid + 1, r);
  }

  void modify(int u, int x, int v) {
    if (tr[u]->l == x && tr[u]->r == x) {
      tr[u]->v += v;
      return;
    }
    int mid = (tr[u]->l + tr[u]->r) >> 1;
    if (x <= mid)
      modify(u << 1, x, v);
    else
      modify(u << 1 | 1, x, v);
    pushup(u);
  }

  void pushup(int u) {
    tr[u]->v = tr[u << 1]->v + tr[u << 1 | 1]->v;
  }

  int query(int u, int l, int r) {
    if (tr[u]->l >= l && tr[u]->r <= r) return tr[u]->v;
    int mid = (tr[u]->l + tr[u]->r) >> 1;
    int v = 0;
    if (l <= mid) v = query(u << 1, l, r);
    if (r > mid) v += query(u << 1 | 1, l, r);
    return v;
  }
};

class Solution {
public:
  int createSortedArray(vector<int>& instructions) {
    int n = *max_element(instructions.begin(), instructions.end());
    int mod = 1e9 + 7;
    SegmentTree* tree = new SegmentTree(n);
    int ans = 0;
    for (int num : instructions) {
      int a = tree->query(1, 1, num - 1);
      int b = tree->query(1, 1, n) - tree->query(1, 1, num);
      ans += min(a, b);
      ans %= mod;
      tree->modify(1, num, 1);
    }
    return ans;
  }
};