231,338,326,Power of Two(Three,Four)Counting Bits 类似的技巧题
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231. Power of Two
Given an integer, write a function to determine if it is a power of two.
题意:
一个数是否 2的n次方的判断
思想:
把该数n转换为2进制,与该数n-1进行&操作 可以判断出是否为2^n
C++ AC代码:Time O(1) Space O(1)
class Solution {public: bool isPowerOfTwo(int n) { if(n<=0) return false; return !(n&(n-1)); }};
338. Counting Bits
该题为231的一个引申题
Given a non negative integer number num. For every numbers i in the range 0 ≤ i ≤ num calculate the number of 1's in their binary representation and return them as an array.
Example:
For num = 5
you should return [0,1,1,2,1,2]
.
Follow up:
- It is very easy to come up with a solution with run time O(n*sizeof(integer)). But can you do it in linear time O(n) /possibly in a single pass?
- Space complexity should be O(n).
- Can you do it like a boss? Do it without using any builtin function like __builtin_popcount in c++ or in any other language.
题意:
给出一个数num 求0-num中每个数转化为2进制数 1的个数。
思想:
可以这样想,假设一个数A 它会是数 B=A&A-1的2进制1的个数加1 如3 2进制(11) 会是2 2进制(10)中2进制个数加1
C++ AC代码: Time O(n) Space(n)
class Solution {public: vector<int> countBits(int num) { vector<int> res(num+1,0); for(int i=1;i<=num;i++){ res[i] =res[i&(i-1)] + 1; } return res; }};
326. Power of Three
Given an integer, write a function to determine if it is a power of three.
题意:
一个数是否 3的n次方的判断
思想:
方法一:
假设这个数最大为int型范围内2^31-1 那么先求3的^n能到达这个int型范围内的最大值 3^19 max
直接判断n>0&&max%n==0
方法二:
fmod(log10(num)/log10(3),1)==0;fmod c++判断模运算
C++ AC代码:Time O(1) Space O(1)
public class Solution { public boolean isPowerOfThree(int n) { return n > 0 && 1162261467 % n == 0; //3^19 = 1162261467 }}
342. Power of Four
Given an integer (signed 32 bits), write a function to check whether it is a power of 4.
题意:
一个数是否 4的n次方的判断
思想:
方法一:
fmod(log10(num)/log10(4),1)==0
方法二:先判断是否是2^n 在判断该数a-1是否整除3
return num>0&&(num&(num-1))==0&&((num-1)%3==0);
C++ AC代码: Time O(1) Space(1)
class Solution {public: bool isPowerOfFour(int num) { return num>0&&(num&(num-1))==0&&((num-1)%3==0); }};
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