# Posts published in “Algorithms”

Given a matrix A, return the transpose of A.

The transpose of a matrix is the matrix flipped over it’s main diagonal, switching the row and column indices of the matrix.

Example 1:

Input: [[1,2,3],[4,5,6],[7,8,9]]
Output: [[1,4,7],[2,5,8],[3,6,9]]


Example 2:

Input: [[1,2,3],[4,5,6]]
Output: [[1,4],[2,5],[3,6]]


Note:

1. 1 <= A.length <= 1000
2. 1 <= A[0].length <= 1000

# Solution: Brute Force

Time complexity: O(mn)

Space complexity: O(mn)

# Problem

Given an array which consists of non-negative integers and an integer m, you can split the array into m non-empty continuous subarrays. Write an algorithm to minimize the largest sum among these m subarrays.

Note:
If n is the length of array, assume the following constraints are satisfied:

• 1 ≤ n ≤ 1000
• 1 ≤ m ≤ min(50, n)

Examples:

Input:
nums = [7,2,5,10,8]
m = 2

Output:
18

Explanation:
There are four ways to split nums into two subarrays.
The best way is to split it into [7,2,5] and [10,8],
where the largest sum among the two subarrays is only 18.


# Solution: DP

Time complexity: O(n^2*m)

Space complexity: O(n*m)

C++ / Recursion + Memorization

C++ / DP

# Solution: Binary Search

Time complexity: O(log(sum(nums))*n)

Space complexity: O(1)

# Problem

Suppose you have a long flowerbed in which some of the plots are planted and some are not. However, flowers cannot be planted in adjacent plots – they would compete for water and both would die.

Given a flowerbed (represented as an array containing 0 and 1, where 0 means empty and 1 means not empty), and a number n, return if n new flowers can be planted in it without violating the no-adjacent-flowers rule.

Example 1:

Input: flowerbed = [1,0,0,0,1], n = 1
Output: True


Example 2:

Input: flowerbed = [1,0,0,0,1], n = 2
Output: False


Note:

1. The input array won’t violate no-adjacent-flowers rule.
2. The input array size is in the range of [1, 20000].
3. n is a non-negative integer which won’t exceed the input array size.

# Solution: Greedy

Time complexity: O(n)

Space complexity: O(1)

C++

# Problem

Given a sorted integer array without duplicates, return the summary of its ranges.

Example 1:

Input:  [0,1,2,4,5,7]
Output: ["0->2","4->5","7"]
Explanation: 0,1,2 form a continuous range; 4,5 form a continuous range.


Example 2:

Input:  [0,2,3,4,6,8,9]
Output: ["0","2->4","6","8->9"]
Explanation: 2,3,4 form a continuous range; 8,9 form a continuous range.

# Solution

Time complexity: O(n)

Space complexity: O(k)

C++

# Problem

Let’s call an array A a mountain if the following properties hold:

• A.length >= 3
• There exists some 0 < i < A.length - 1 such that A[0] < A[1] < ... A[i-1] < A[i] > A[i+1] > ... > A[A.length - 1]

Given an array that is definitely a mountain, return any i such that A[0] < A[1] < ... A[i-1] < A[i] > A[i+1] > ... > A[A.length - 1].

Example 1:

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


Example 2:

Input: [0,2,1,0]
Output: 1

Note:

1. 3 <= A.length <= 10000
2. 0 <= A[i] <= 10^6
3. A is a mountain, as defined above.

# Solution1: Liner Scan

Time complexity: O(n)

Space complexity: O(1)

# Solution 2: Binary Search

Find the smallest l such that A[l] > A[l + 1].

Time complexity: O(logn)

Space complexity: O(1)

## Python3

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