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 <= 161 <= nums[i] <= 105
Solutions#
Solution 1#
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| 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
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| 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]);
}
}
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| 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]);
}
};
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| 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
}
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| 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;
}
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| 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#
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| 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
|
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| 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]);
}
}
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| 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);
}
};
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| 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
}
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| 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;
}
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Solution 3#
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| 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
|
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| 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;
}
}
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| 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;
}
};
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| 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
}
|
