# 2022-05-27

## [231. Power of Two](https://leetcode.com/problems/power-of-two/)

### Description

Given an integer `n`, return *`true` if it is a power of two. Otherwise, return `false`*.

An integer `n` is a power of two, if there exists an integer `x` such that `n == 2x`.

**Example 1:**

```
Input: n = 1
Output: true
Explanation: 20 = 1
```

**Example 2:**

```
Input: n = 16
Output: true
Explanation: 24 = 16
```

**Example 3:**

```
Input: n = 3
Output: false
```

**Constraints:**

* `-2^31 <= n <= 2^31 - 1`&#x20;

**Follow up:** Could you solve it without loops/recursion?

### Solution

#### Approach #0

```go
func isPowerOfTwo(n int) bool {
    return n > 0 && n&(n-1) == 0
}
```

#### Approach #1

```go
func isPowerOfTwo(n int) bool {
    big := 1 << 30
    return n > 0 && big%n == 0
}
```

## [191. Number of 1 Bits](https://leetcode.com/problems/number-of-1-bits/)

### Description

Write a function that takes an unsigned integer and returns the number of '1' bits it has (also known as the [Hamming weight](http://en.wikipedia.org/wiki/Hamming_weight)).

**Note:**

* Note that in some languages, such as Java, there is no unsigned integer type. In this case, the input will be given as a signed integer type. It should not affect your implementation, as the integer's internal binary representation is the same, whether it is signed or unsigned.
* In Java, the compiler represents the signed integers using [2's complement notation](https://en.wikipedia.org/wiki/Two's_complement). Therefore, in **Example 3**, the input represents the signed integer. `-3`.

**Example 1:**

```
Input: n = 00000000000000000000000000001011
Output: 3
Explanation: The input binary string 00000000000000000000000000001011 has a total of three '1' bits.
```

**Example 2:**

```
Input: n = 00000000000000000000000010000000
Output: 1
Explanation: The input binary string 00000000000000000000000010000000 has a total of one '1' bit.
```

**Example 3:**

```
Input: n = 11111111111111111111111111111101
Output: 31
Explanation: The input binary string 11111111111111111111111111111101 has a total of thirty one '1' bits.
```

**Constraints:**

* The input must be a **binary string** of length `32`.

**Follow up:** If this function is called many times, how would you optimize it?

### Solution

#### Approach #0

```go
func hammingWeight(num uint32) int {
    count := 0
    for num > 0 {
        num = num & (num - 1)
        count++
    }
    return count
}
```

#### Approach #1

```go
func hammingWeight(num uint32) int {
    count := 0
    for i := 0; i < 32; i++ {
        if 1<<i&num > 0 {
            count++
        }
    }
    return count
}
```

## [223. Rectangle Area](https://leetcode.com/problems/rectangle-area/)

### Description

Given the coordinates of two **rectilinear** rectangles in a 2D plane, return *the total area covered by the two rectangles*.

The first rectangle is defined by its **bottom-left** corner `(ax1, ay1)` and its **top-right** corner `(ax2, ay2)`.

The second rectangle is defined by its **bottom-left** corner `(bx1, by1)` and its **top-right** corner `(bx2, by2)`.

**Example 1:**

![](https://img.content.cc/a/2022/05/27/11-17-28-606-300350bb515c93bfcecdfb2cfbc48194-2d1f1f.png)

```
Input: ax1 = -3, ay1 = 0, ax2 = 3, ay2 = 4, bx1 = 0, by1 = -1, bx2 = 9, by2 = 2
Output: 45
```

**Example 2:**

```
Input: ax1 = -2, ay1 = -2, ax2 = 2, ay2 = 2, bx1 = -2, by1 = -2, bx2 = 2, by2 = 2
Output: 16
```

**Constraints:**

* `-10^4 <= ax1, ay1, ax2, ay2, bx1, by1, bx2, by2 <= 10^4`

### Solution

#### Approach #0

```go
func computeArea(ax1 int, ay1 int, ax2 int, ay2 int, bx1 int, by1 int, bx2 int, by2 int) int {
    area1 := (ax2 - ax1) * (ay2 - ay1)
    area2 := (bx2 - bx1) * (by2 - by1)
    overlapWidth := min(ax2, bx2) - max(ax1, bx1)
    overlapHeight := min(ay2, by2) - max(ay1, by1)
    overlapArea := max(overlapWidth, 0) * max(overlapHeight, 0)
    return area1 + area2 - overlapArea
}

func max(a, b int) int {
    if a > b {
        return a
    }
    return b
}

func min(a, b int) int {
    if a < b {
        return a
    }
    return b
}
```