Posts tagged as “bit”

花花酱 LeetCode 78. Subsets

By zxi on December 22, 2018

Given a set of distinct integers, nums, return all possible subsets (the power set).

Note: The solution set must not contain duplicate subsets.

Example:

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

Solution: Combination

Time complexity: O(2^n)
Space complexity: O(n)

Implemention 1: DFS

C++

// Author: Huahua, running time: 4 ms

class Solution {

public:

vector<vector<int>> subsets(vector<int>& nums) {

vector<vector<int>> ans;

vector<int> cur;

for (int i = 0; i <= nums.size(); ++i)

dfs(nums, i, 0, cur, ans);

return ans;

}

private:

void dfs(const vector<int>& nums, int n, int s,

vector<int>& cur, vector<vector<int>>& ans) {

if (n == cur.size()) {

ans.push_back(cur);

return;

}

for (int i = s; i < nums.size(); ++i) {

cur.push_back(nums[i]);

dfs(nums, n, i + 1, cur, ans);

cur.pop_back();

}

};

Python3

# Author: Huahua, running time: 60 ms

class Solution:

def subsets(self, nums):

ans = []

def dfs(n, s, cur):

if n == len(cur):

ans.append(cur.copy())

return

for i in range(s, len(nums)):

cur.append(nums[i])

dfs(n, i + 1, cur)

cur.pop()

for i in range(len(nums) + 1):

dfs(i, 0, [])

return ans

Implementation 2: Binary

C++

// Author: Huahua, running time: 4 ms

class Solution {

public:

vector<vector<int>> subsets(vector<int>& nums) {

const int n = nums.size();

vector<vector<int>> ans;

for (int s = 0; s < 1 << n; ++s) {

vector<int> cur;

for (int i = 0; i < n; ++i)

if (s & (1 << i)) cur.push_back(nums[i]);

ans.push_back(cur);

}

return ans;

}

};

Python3

# Author: Huahua, 40 ms

class Solution:

def subsets(self, nums):

n = len(nums)

return [[nums[i] for i in range(n) if s & 1 << i > 0] for s in range(1 << n)]

花花酱 LeetCode 927. Three Equal Parts

By zxi on October 20, 2018

Problem

Given an array A of 0s and 1s, divide the array into 3 non-empty parts such that all of these parts represent the same binary value.

If it is possible, return any [i, j] with i+1 < j, such that:

A[0], A[1], ..., A[i] is the first part;
A[i+1], A[i+2], ..., A[j-1] is the second part, and
A[j], A[j+1], ..., A[A.length - 1] is the third part.
All three parts have equal binary value.

If it is not possible, return [-1, -1].

Note that the entire part is used when considering what binary value it represents. For example, [1,1,0] represents 6 in decimal, not 3. Also, leading zeros are allowed, so [0,1,1] and [1,1] represent the same value.

Example 1:

Input: [1,0,1,0,1]
Output: [0,3]

Example 2:

Input: [1,1,0,1,1]
Output: [-1,-1]

Note:

3 <= A.length <= 30000
A[i] == 0 or A[i] == 1

Solution:

each part should have the same number of 1 s.

Find the suffix (without leading os) of the last part which should have 1/3 of the total ones.

Time complexity: O(n^2) in theory but close to O(n) in practice

Space complexity: O(n)

C++

// Author: Huahua, 44 ms

class Solution {

public:

vector<int> threeEqualParts(vector<int>& A) {

string s(begin(A), end(A));

int ones = accumulate(begin(A), end(A), 0);

if (ones % 3 != 0) return {-1, -1};

if (ones == 0) return {0, A.size() - 1};

ones /= 3;

int right = A.size() - 1;

while (ones) if (A[right--]) --ones;

string suffix(begin(s) + right + 1, end(s));

size_t l = suffix.length();

size_t left = s.find(suffix);

if (left == std::string::npos) return {-1, -1};

size_t mid = s.find(suffix, left + l);

if (mid == std::string::npos

|| mid + 2 * l > s.length()) return {-1, -1};

return {left + l - 1, mid + l};

}

};

花花酱 LeetCode 898. Bitwise ORs of Subarrays

By zxi on September 1, 2018

Problem

We have an array A of non-negative integers.

For every (contiguous) subarray B = [A[i], A[i+1], ..., A[j]] (with i <= j), we take the bitwise OR of all the elements in B, obtaining a result A[i] | A[i+1] | ... | A[j].

Return the number of possible results. (Results that occur more than once are only counted once in the final answer.)

Example 1:

Input: [0]
Output: 1
Explanation: 
There is only one possible result: 0.

Example 2:

Input: [1,1,2]
Output: 3
Explanation: 
The possible subarrays are [1], [1], [2], [1, 1], [1, 2], [1, 1, 2].
These yield the results 1, 1, 2, 1, 3, 3.
There are 3 unique values, so the answer is 3.

Example 3:

Input: [1,2,4]
Output: 6
Explanation: 
The possible results are 1, 2, 3, 4, 6, and 7.

Note:

1 <= A.length <= 50000
0 <= A[i] <= 10^9

Solution 1: DP (TLE)

dp[i][j] := A[i] | A[i + 1] | … | A[j]

dp[i][j] = dp[i][j – 1] | A[j]

ans = len(set(dp))

Time complexity: O(n^2)

Space complexity: O(n^2) -> O(n)

C++ SC O(n^2)

// Author: Huahua

// Running time: TLE (73/83 passed).

class Solution {

public:

int subarrayBitwiseORs(vector<int>& A) {

int n = A.size();

vector<vector<int>> dp(n, vector<int>(n));

unordered_set<int> ans(begin(A), end(A));

for (int l = 1; l <= n; ++l)

for (int i = 0; i <= n - l; ++i) {

int j = i + l - 1;

if (l == 1) {

dp[i][j] = A[i];

continue;

}

dp[i][j] = dp[i][j - 1] | A[j];

ans.insert(dp[i][j]);

}

return ans.size();

}

};

C++ SC O(n)

// Author: Huahua

// Running time: TLE (75/83 passed)

class Solution {

public:

int subarrayBitwiseORs(vector<int>& A) {

int n = A.size();

vector<int> dp(A);

unordered_set<int> ans(begin(A), end(A));

for (int l = 2; l <= n; ++l)

for (int i = 0; i <= n - l; ++i)

ans.insert(dp[i] |= A[i + l - 1]);

return ans.size();

}

};

Solution 2: DP opted

dp[i] := {A[i], A[i] | A[i – 1], A[i] | A[i – 1] | A[i – 2], … , A[i] | A[i – 1] | … | A[0]}, bitwise ors of all subarrays end with A[i].

|dp[i]| <= 32

Proof: all the elements (in the order of above sequence) in dp[i] are monotonically increasing by flipping 0 bits to 1 from A[i].

There are at most 32 0s in A[i]. Thus the size of the set is <= 32.

证明： dp[i] = {A[i], A[i] | A[i – 1], A[i] | A[i – 1] | A[i – 2], … , A[i] | A[i – 1] | … | A[0]}，这个序列单调递增，通过把A[i]中的0变成1。A[i]最多有32个0。所以这个集合的大小 <= 32。

e.g. 举例：Worst Case 最坏情况 A = [8, 4, 2, 1, 0] A[i] = 2^(n-i)。

A[5] = 0，dp[5] = {0, 0 | 1, 0 | 1 | 2, 0 | 1 | 2 | 4, 0 | 1 | 2 | 4 | 8} = {0, 1, 3, 7, 15}.

Time complexity: O(n*log(max(A))) < O(32n)

Space complexity: O(n*log(max(A)) < O(32n)

C++

// Author: Huahua

// Running time: 456 ms

class Solution {

public:

int subarrayBitwiseORs(vector<int>& A) {

unordered_set<int> ans;

unordered_set<int> cur;

unordered_set<int> nxt;

for (int a : A) {

nxt.clear();

nxt.insert({a});

for (int b : cur) {

nxt.insert(a | b);

}

cur.swap(nxt);

ans.insert(begin(cur), end(cur));

}

return ans.size();

}

};

Java

// Author: Huahua

// Running time: 434 ms

class Solution {

public int subarrayBitwiseORs(int[] A) {

Set<Integer> ans = new HashSet<>();

Set<Integer> cur = new HashSet<>();

for (int a : A) {

Set<Integer> nxt = new HashSet<>();

nxt.add(a);

for (int b : cur)

nxt.add(a | b);

ans.addAll(nxt);

cur = nxt;

}

return ans.size();

}

Python3

# Author: Huahua

# Running time: 812 ms

class Solution:

def subarrayBitwiseORs(self, A):

cur = set()

ans = set()

for a in A:

cur = {a | b for b in cur} | {a}

ans |= cur

return len(ans)

花花酱 LeetCode 869. Reordered Power of 2

By zxi on July 14, 2018

Problem

Starting with a positive integer N, we reorder the digits in any order (including the original order) such that the leading digit is not zero.

Return true if and only if we can do this in a way such that the resulting number is a power of 2.

Example 1:

Input: 1
Output: true

Example 2:

Input: 10
Output: false

Example 3:

Input: 16
Output: true

Example 4:

Input: 24
Output: false

Example 5:

1 2	<strong>Input: </strong><span id="example-input-5-1">46</span> <strong>Output: </strong><span id="example-output-5">true</span>

Note:

1 <= N <= 10^9

Solution: HashTable

Compare the counter of digit string with that of all power of 2s.

e.g. 64 -> {4: 1, 6: 1} == 46 {4:1, 6: 1}

Time complexity: O(1)

Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

bool reorderedPowerOf2(int N) {

auto m = countMap(N);

for (int i = 0; i < 31; ++i)

if (m == countMap(1 << i)) return true;

return false;

}

private:

map<int, int> countMap(int n) {

map<int, int> m;

while (n) {

++m[n % 10];

n /= 10;

}

return m;

}

};

花花酱 LeetCode 868. Binary Gap

By zxi on July 14, 2018

Problem

Given a positive integer N, find and return the longest distance between two consecutive 1’s in the binary representation of N.

If there aren’t two consecutive 1’s, return 0.

Example 1:

Input: 22
Output: 2
Explanation: 
22 in binary is 0b10110.
In the binary representation of 22, there are three ones, and two consecutive pairs of 1's.
The first consecutive pair of 1's have distance 2.
The second consecutive pair of 1's have distance 1.
The answer is the largest of these two distances, which is 2.

Example 2:

Input: 5
Output: 2
Explanation: 
5 in binary is 0b101.

Example 3:

Input: 6
Output: 1
Explanation: 
6 in binary is 0b110.

Example 4:

Input: 8
Output: 0
Explanation: 
8 in binary is 0b1000.
There aren't any consecutive pairs of 1's in the binary representation of 8, so we return 0.\

Note:

1 <= N <= 10^9

Solution: Bit

Time complexity: O(logN)

Space complexity: O(1)

C++

// Author: Huahua

// Running time: 4 ms

class Solution {

public:

int binaryGap(int N) {

int l = -1;

int ans = 0;

for (int i = 0; i < 31; ++i)

if (N & (1 << i)) {

if (l >= 0)

ans = max(ans, i - l);

l = i;

}

return ans;

}

};