Question

2044. Count Number of Maximum Bitwise-OR Subsets

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Description

Given an integer array nums, find the maximum possible bitwise OR of a subset of nums and return _the number of different non-empty subsets with the maximum bitwise OR_.

An array a is a subset of an array b if a can be obtained from b by deleting some (possibly zero) elements of b. Two subsets are considered different if the indices of the elements chosen are different.

The bitwise OR of an array a is equal to a[0] OR a[1] OR ... OR a[a.length - 1] (0-indexed).

 

Example 1:

Input: nums = [3,1]
Output: 2
Explanation: The maximum possible bitwise OR of a subset is 3. There are 2 subsets with a bitwise OR of 3:
- [3]
- [3,1]

Example 2:

Input: nums = [2,2,2]
Output: 7
Explanation: All non-empty subsets of [2,2,2] have a bitwise OR of 2. There are 23 - 1 = 7 total subsets.

Example 3:

Input: nums = [3,2,1,5]
Output: 6
Explanation: The maximum possible bitwise OR of a subset is 7. There are 6 subsets with a bitwise OR of 7:
- [3,5]
- [3,1,5]
- [3,2,5]
- [3,2,1,5]
- [2,5]
- [2,1,5]

 

Constraints:

• 1 <= nums.length <= 16
• 1 <= nums[i] <= 105

Solutions

Solution 1

class Solution:
  def countMaxOrSubsets(self, nums: List[int]) -> int:
    mx = ans = 0
    for x in nums:
      mx |= x

    def dfs(i, t):
      nonlocal mx, ans
      if i == len(nums):
        if t == mx:
          ans += 1
        return
      dfs(i + 1, t)
      dfs(i + 1, t | nums[i])

    dfs(0, 0)
    return ans

class Solution {
  private int mx;
  private int ans;
  private int[] nums;

  public int countMaxOrSubsets(int[] nums) {
    mx = 0;
    for (int x : nums) {
      mx |= x;
    }
    this.nums = nums;
    dfs(0, 0);
    return ans;
  }

  private void dfs(int i, int t) {
    if (i == nums.length) {
      if (t == mx) {
        ++ans;
      }
      return;
    }
    dfs(i + 1, t);
    dfs(i + 1, t | nums[i]);
  }
}

class Solution {
public:
  int mx;
  int ans;
  vector<int> nums;

  int countMaxOrSubsets(vector<int>& nums) {
    this->nums = nums;
    mx = 0;
    ans = 0;
    for (int x : nums) mx |= x;
    dfs(0, 0);
    return ans;
  }

  void dfs(int i, int t) {
    if (i == nums.size()) {
      if (t == mx) ++ans;
      return;
    }
    dfs(i + 1, t);
    dfs(i + 1, t | nums[i]);
  }
};

func countMaxOrSubsets(nums []int) int {
  mx, ans := 0, 0
  for _, x := range nums {
    mx |= x
  }

  var dfs func(i, t int)
  dfs = func(i, t int) {
    if i == len(nums) {
      if t == mx {
        ans++
      }
      return
    }
    dfs(i+1, t)
    dfs(i+1, t|nums[i])
  }

  dfs(0, 0)
  return ans
}

function countMaxOrSubsets(nums: number[]): number {
  let n = nums.length;
  let max = 0;
  for (let i = 0; i < n; i++) {
    max |= nums[i];
  }
  let ans = 0;
  function dfs(pre: number, depth: number): void {
    if (depth == n) {
      if (pre == max) ++ans;
      return;
    }
    dfs(pre, depth + 1);
    dfs(pre | nums[depth], depth + 1);
  }
  dfs(0, 0);
  return ans;
}

impl Solution {
  fn dfs(nums: &Vec<i32>, i: usize, sum: i32) -> (i32, i32) {
    let n = nums.len();
    let mut max = i32::MIN;
    let mut res = 0;
    for j in i..n {
      let num = sum | nums[j];
      if num >= max {
        if num > max {
          max = num;
          res = 0;
        }
        res += 1;
      }
      let (r_max, r_res) = Self::dfs(nums, j + 1, num);
      if r_max >= max {
        if r_max > max {
          max = r_max;
          res = 0;
        }
        res += r_res;
      }
    }
    (max, res)
  }

  pub fn count_max_or_subsets(nums: Vec<i32>) -> i32 {
    Self::dfs(&nums, 0, 0).1
  }
}

Solution 2

class Solution:
  def countMaxOrSubsets(self, nums: List[int]) -> int:
    def dfs(u, t):
      nonlocal ans, mx
      if u == len(nums):
        if t > mx:
          mx, ans = t, 1
        elif t == mx:
          ans += 1
        return
      dfs(u + 1, t | nums[u])
      dfs(u + 1, t)

    ans = mx = 0
    dfs(0, 0)
    return ans

class Solution {
  private int mx;
  private int ans;
  private int[] nums;

  public int countMaxOrSubsets(int[] nums) {
    this.nums = nums;
    dfs(0, 0);
    return ans;
  }

  private void dfs(int u, int t) {
    if (u == nums.length) {
      if (t > mx) {
        mx = t;
        ans = 1;
      } else if (t == mx) {
        ++ans;
      }
      return;
    }
    dfs(u + 1, t);
    dfs(u + 1, t | nums[u]);
  }
}

class Solution {
public:
  int mx;
  int ans;

  int countMaxOrSubsets(vector<int>& nums) {
    dfs(0, 0, nums);
    return ans;
  }

  void dfs(int u, int t, vector<int>& nums) {
    if (u == nums.size()) {
      if (t > mx) {
        mx = t;
        ans = 1;
      } else if (t == mx)
        ++ans;
      return;
    }
    dfs(u + 1, t, nums);
    dfs(u + 1, t | nums[u], nums);
  }
};

func countMaxOrSubsets(nums []int) int {
  n := len(nums)
  ans := 0
  mx := 0
  for mask := 1; mask < 1<<n; mask++ {
    t := 0
    for i, v := range nums {
      if ((mask >> i) & 1) == 1 {
        t |= v
      }
    }
    if mx < t {
      mx = t
      ans = 1
    } else if mx == t {
      ans++
    }
  }
  return ans
}

function countMaxOrSubsets(nums: number[]): number {
  const n = nums.length;
  let res = 0;
  let max = -Infinity;
  const dfs = (i: number, sum: number) => {
    for (let j = i; j < n; j++) {
      const num = sum | nums[j];
      if (num >= max) {
        if (num > max) {
          max = num;
          res = 0;
        }
        res++;
      }
      dfs(j + 1, num);
    }
  };
  dfs(0, 0);

  return res;
}

Solution 3

class Solution:
  def countMaxOrSubsets(self, nums: List[int]) -> int:
    n = len(nums)
    ans = 0
    mx = 0
    for mask in range(1 << n):
      t = 0
      for i, v in enumerate(nums):
        if (mask >> i) & 1:
          t |= v
      if mx < t:
        mx = t
        ans = 1
      elif mx == t:
        ans += 1
    return ans

class Solution {
  public int countMaxOrSubsets(int[] nums) {
    int n = nums.length;
    int ans = 0;
    int mx = 0;
    for (int mask = 1; mask < 1 << n; ++mask) {
      int t = 0;
      for (int i = 0; i < n; ++i) {
        if (((mask >> i) & 1) == 1) {
          t |= nums[i];
        }
      }
      if (mx < t) {
        mx = t;
        ans = 1;
      } else if (mx == t) {
        ++ans;
      }
    }
    return ans;
  }
}

class Solution {
public:
  int countMaxOrSubsets(vector<int>& nums) {
    int n = nums.size();
    int ans = 0;
    int mx = 0;
    for (int mask = 1; mask < 1 << n; ++mask) {
      int t = 0;
      for (int i = 0; i < n; ++i) {
        if ((mask >> i) & 1) {
          t |= nums[i];
        }
      }
      if (mx < t) {
        mx = t;
        ans = 1;
      } else if (mx == t)
        ++ans;
    }
    return ans;
  }
};

func countMaxOrSubsets(nums []int) int {
  mx, ans := 0, 0
  var dfs func(u, t int)
  dfs = func(u, t int) {
    if u == len(nums) {
      if t > mx {
        mx, ans = t, 1
      } else if t == mx {
        ans++
      }
      return
    }
    dfs(u+1, t)
    dfs(u+1, t|nums[u])
  }
  dfs(0, 0)
  return ans
}