# 2022-05-26

## ​70. Climbing Stairs​

### Description

You are climbing a staircase. It takes `n` steps to reach the top.
Each time you can either climb `1` or `2` steps. In how many distinct ways can you climb to the top?
Example 1:
Input: n = 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps
Example 2:
Input: n = 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step
Constraints:
• `1 <= n <= 45`

### Solution

#### Approach #0

func climbStairs(n int) int {
p, q, r := 0, 0, 1
for i := 0; i < n; i++ {
p = q
q = r
r = p + q
}
return r
}

## ​198. House Robber​

### Description

You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed, the only constraint stopping you from robbing each of them is that adjacent houses have security systems connected and it will automatically contact the police if two adjacent houses were broken into on the same night.
Given an integer array `nums` representing the amount of money of each house, return the maximum amount of money you can rob tonight without alerting the police.
Example 1:
Input: nums = [1,2,3,1]
Output: 4
Explanation: Rob house 1 (money = 1) and then rob house 3 (money = 3).
Total amount you can rob = 1 + 3 = 4.
Example 2:
Input: nums = [2,7,9,3,1]
Output: 12
Explanation: Rob house 1 (money = 2), rob house 3 (money = 9) and rob house 5 (money = 1).
Total amount you can rob = 2 + 9 + 1 = 12.
Constraints:
• `1 <= nums.length <= 100`
• `0 <= nums[i] <= 400`

### Solution

#### Approach #0

func rob(nums []int) int {
if len(nums) == 0 {
return 0
}
r0, r1 := 0, nums
for i := 1; i < len(nums); i++ {
r0, r1 = r1, max(r1, r0+nums[i])
}
return r1
}
func max(a, b int) int {
if a > b {
return a
}
return b
}

## ​120. Triangle​

### Description

Given a `triangle` array, return the minimum path sum from top to bottom.
For each step, you may move to an adjacent number of the row below. More formally, if you are on index `i` on the current row, you may move to either index `i` or index `i + 1` on the next row.
Example 1:
Input: triangle = [,[3,4],[6,5,7],[4,1,8,3]]
Output: 11
Explanation: The triangle looks like:
2
3 4
6 5 7
4 1 8 3
The minimum path sum from top to bottom is 2 + 3 + 5 + 1 = 11 (underlined above).
Example 2:
Input: triangle = [[-10]]
Output: -10
Constraints:
• `1 <= triangle.length <= 200`
• `triangle.length == 1`
• `triangle[i].length == triangle[i - 1].length + 1`
• `-104 <= triangle[i][j] <= 104`
Follow up: Could you do this using only `O(n)` extra space, where `n` is the total number of rows in the triangle?

### Solution

#### Approach #0: Better than the official solution

func minimumTotal(triangle [][]int) int {
if len(triangle) == 1 {
return triangle
}
for i := 1; i < len(triangle); i++ {
size := len(triangle[i])
triangle[i] = triangle[i-1] + triangle[i]
for j := 1; j < size-1; j++ {
triangle[i][j] = min(triangle[i-1][j], triangle[i-1][j-1]) + triangle[i][j]
}
triangle[i][size-1] = triangle[i-1][size-2] + triangle[i][size-1]
}
r := triangle[len(triangle)-1]
for _, item := range triangle[len(triangle)-1] {
r = min(r, item)
}
return r
}
func min(a, b int) int {
if a < b {
return a
}
return b
}

## ​699. Falling Squares​

### Description

There are several squares being dropped onto the X-axis of a 2D plane.
You are given a 2D integer array `positions` where `positions[i] = [lefti, sideLengthi]` represents the `ith` square with a side length of `sideLengthi` that is dropped with its left edge aligned with X-coordinate `lefti`.
Each square is dropped one at a time from a height above any landed squares. It then falls downward (negative Y direction) until it either lands on the top side of another square or on the X-axis. A square brushing the left/right side of another square does not count as landing on it. Once it lands, it freezes in place and cannot be moved.
After each square is dropped, you must record the height of the current tallest stack of squares.
Return an integer array `ans` where `ans[i]` represents the height described above after dropping the `ith` square.
Example 1: Input: positions = [[1,2],[2,3],[6,1]]
Output: [2,5,5]
Explanation:
After the first drop, the tallest stack is square 1 with a height of 2.
After the second drop, the tallest stack is squares 1 and 2 with a height of 5.
After the third drop, the tallest stack is still squares 1 and 2 with a height of 5.
Thus, we return an answer of [2, 5, 5].
Example 2:
Input: positions = [[100,100],[200,100]]
Output: [100,100]
Explanation:
After the first drop, the tallest stack is square 1 with a height of 100.
After the second drop, the tallest stack is either square 1 or square 2, both with heights of 100.
Thus, we return an answer of [100, 100].
Note that square 2 only brushes the right side of square 1, which does not count as landing on it.
Constraints:
• `1 <= positions.length <= 1000`
• `1 <= lefti <= 10^8`
• `1 <= sideLengthi <= 10^6`

### Solution

#### Approach #0

func fallingSquares(positions [][]int) []int {
n := len(positions)
heights := make([]int, n)
for i, p := range positions {
left1, right1 := p, p+p-1
heights[i] = p
for j, q := range positions[:i] {
left2, right2 := q, q+q-1
if left1 <= right2 && right1 >= left2 {
heights[i] = max(heights[i], heights[j]+p)
}
}
}
for i := 1; i < n; i++ {
heights[i] = max(heights[i], heights[i-1])
}
return heights
}
func max(a, b int) int {
if a > b {
return a
}
return b
}

## ​27. Remove Element​

### Description

Given an integer array `nums` and an integer `val`, remove all occurrences of `val` in `nums` in-place. The relative order of the elements may be changed.
Since it is impossible to change the length of the array in some languages, you must instead have the result be placed in the first part of the array `nums`. More formally, if there are `k` elements after removing the duplicates, then the first `k` elements of `nums` should hold the final result. It does not matter what you leave beyond the first `k` elements.
Return `k` after placing the final result in the first `k` slots of `nums`.
Do not allocate extra space for another array. You must do this by modifying the input array in-place with O(1) extra memory.
Custom Judge:
The judge will test your solution with the following code:
int[] nums = [...]; // Input array
int val = ...; // Value to remove
int[] expectedNums = [...]; // The expected answer with correct length.
// It is sorted with no values equaling val.
int k = removeElement(nums, val); // Calls your implementation
assert k == expectedNums.length;
sort(nums, 0, k); // Sort the first k elements of nums
for (int i = 0; i < actualLength; i++) {
assert nums[i] == expectedNums[i];
}
If all assertions pass, then your solution will be accepted.
Example 1:
Input: nums = [3,2,2,3], val = 3
Output: 2, nums = [2,2,_,_]
Explanation: Your function should return k = 2, with the first two elements of nums being 2.
It does not matter what you leave beyond the returned k (hence they are underscores).
Example 2:
Input: nums = [0,1,2,2,3,0,4,2], val = 2
Output: 5, nums = [0,1,4,0,3,_,_,_]
Explanation: Your function should return k = 5, with the first five elements of nums containing 0, 0, 1, 3, and 4.
Note that the five elements can be returned in any order.
It does not matter what you leave beyond the returned k (hence they are underscores).
Constraints:
• `0 <= nums.length <= 100`
• `0 <= nums[i] <= 50`
• `0 <= val <= 100`

### Solution

#### Approach #0

func removeElement(nums []int, val int) int {
i := 0
for j := 0; j < len(nums); j++ {
if nums[j] != val {
nums[i], nums[j] = nums[j], nums[i]
i++
}
}
return i
}

#### Approach #1

func removeElement(nums []int, val int) int {
i, j := 0, len(nums)
for i < j {
if nums[i] != val {
i++
} else {
nums[i] = nums[j-1]
j--
}
}
return i
}