Contents
- 1 How do you find a decreasing sequence?
- 2 How do you find if an array is increasing or decreasing?
- 3 What is a strictly increasing sequence?
- 4 What is a subsequence math?
- 5 How do you work out if something is a term in a sequence?
- 6 How to find the longest subsequence of an array?
- 7 How to find the longest decreasing sequence in Java?
- 8 How to find the Count of strictly decreasing subarrays?
How do you find a decreasing sequence?
If an>an+1 a n > a n + 1 for all n, then the sequence is decreasing or strictly decreasing . If an≥an+1 a n ≥ a n + 1 then the sequence is non-increasing .
How do you find if an array is increasing or decreasing?
Increasing array: The first two and the last two elements must be in increasing order. Decreasing array: The first two and the last two elements must be in decreasing order. Increasing then decreasing array: The first two elements must be in increasing order and the last two elements must be in decreasing order.
How do you find the nth term of a decreasing sequence?
You can use the formula: nth term = a + (n-1)d. a is the first number in the sequence and d is the common difference of the sequence.
What is a strictly increasing sequence?
In words, a sequence is strictly increasing if each term in the sequence is larger than the preceding term and strictly decreasing if each term of the sequence is smaller than the preceding term. One way to determine if a sequence is strictly increasing is to show the n. th. term of the sequence.
What is a subsequence math?
In mathematics, a subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order of the remaining elements. For example, the sequence is a subsequence of obtained after removal of elements , , and. .
What is the nth term rule?
What is the nth term? The nth term is a formula that enables us to find any term in a sequence. The ‘n’ stands for the term number. We can make a sequence using the nth term by substituting different values for the term number(n).
How do you work out if something is a term in a sequence?
To find the number of terms in an arithmetic sequence, divide the common difference into the difference between the last and first terms, and then add 1.
How to find the longest subsequence of an array?
Given an array of N integers, find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in strictly decreasing order. Recommended: Please try your approach on {IDE} first, before moving on to the solution.
How to count descending sequences in an array?
The resulting array will have descending sequences: 2 3 8 4 3 2 4 12 12 6 and these need to be counted. The issue with it is that it exceeds the time limit in the last test given to it, but otherwise the answer is correct. Don’t use namespace std;, see for example Why is “using namespace std;” considered bad practice?.
How to find the longest decreasing sequence in Java?
It will help if you sketch out on paper first what you intend the algorithm to do for a given test input, and then run the algorithm while watching (printing) the Seq and Index values on each iteration. I think this could be a little bit simpler.
How to find the Count of strictly decreasing subarrays?
This can be improved by knowing the fact that if subarray arr [i:j] is not strictly decreasing, then subarrays arr [i:j+1], arr [i:j+2], .. arr [i:n-1] cannot be strictly decreasing. Efficient Approach: In the above solution, we count many subarrays twice.