714515. Count Total Setbits
Count Total Setbits
Slug: count-total-setbits
Difficulty: Medium
Id: 714515
Topic Tags: Bit Magic, Data Structures, Algorithms
Company Tags: None
Summary
This problem requires you to write a function that counts the total number of set bits in all numbers from 1 to N. A set bit is a bit that has a value of 1. For example, the binary representation of 9 (which is 1001) has two set bits.
Detailed Explanation
To solve this problem, we can use a simple approach by iterating over each number from 1 to N and counting the set bits for each number. We can do this using bitwise operations. Specifically, we can use the expression n & (n - 1) to count the number of set bits in n. This works because the leftmost set bit will be shifted to the right when we subtract 1 from n, and all other bits will remain unchanged.
Here's a step-by-step breakdown of the solution:
- Initialize a variable
setbitsto 0, which will store the total number of set bits. - Iterate over each number
ifrom 1 to N. - For each number
i, count the number of set bits using the expressioni & (i - 1). This gives us the number of set bits ini. - Add this count to the total setbits variable.
- Return the total setbits variable.
Here's a time complexity analysis: O(N), where N is the input size. We need to iterate over each number from 1 to N, so the time complexity is linear.
Here's a space complexity analysis: O(1). We only need a constant amount of space to store the total setbits variable, so the space complexity is constant.
Optimized Solutions
Java
public int countTotalSetBits(int n) {
int setbits = 0;
for (int i = 1; i <= n; i++) {
setbits += Integer.bitCount(i);
}
return setbits;
}