Please help with #6 'rove: Given a sequence of n2 +1 distinct integers, either there is...
Please help with #6 'rove: Given a sequence of n2 +1 distinct integers, either there is an increasing subsequence of n+1 terms or a decreasing subsequence of n +1 terms. 'rove: Given a sequence of n2 +1 distinct integers, either there is an increasing subsequence of n+1 terms or a decreasing subsequence of n +1 terms.
Let S be a sequence of n distinct integers stored in an array as array elements S[1], S[2], · · · , S[n]. Use the technique of dynamic programming to find the length of a longest ascending subsequence of entries in S. For example, if the entries of S are 11, 17, 5, 8, 6, 4, 7, 12, 3, then one longest ascending subsequence is 5, 6, 7, 12. Specifically: (a) define a proper function and find the recurrence for...
4. Consider the sequence {z,.) such that z1-0, z2-1 and æn-telths,Yn (i) Show that (n) is convergent by showing that the subsequence of odd-indexed terms is monotonic increasing and subsequence of even-indexed terms is monotonic decreasing (ii) Find the limit of {%) (Hint: Consider x,-h-i) 4. Consider the sequence {z,.) such that z1-0, z2-1 and æn-telths,Yn (i) Show that (n) is convergent by showing that the subsequence of odd-indexed terms is monotonic increasing and subsequence of even-indexed terms is monotonic...
(20 points) You are given an array A of distinct integers of size n. The sequence A[1], A[2], ..., A[n] is unimodal if for some index k between 1 and n the values increase up to position k and then decrease the reminder of the way until position n. (example 1, 4, 5, 7, 9, 10, 13, 14, 8, 6, 4, 3, 2 where the values increase until 14 and then decrease until 1). (a) Propose a recursive algorithm to...
ALGORITHM PROBLEM: A) Significant Inversions: We are given a sequence of n arbitrary but distinct real numbers <a1 , a2 ,..., an>. We define a significant inversion to be a pair i < j such that ai > 2 aj . Design and analyze an O(n log n) time algorithm to count the number of significant inversions in the given sequence. [Hint: Use divide-&-conquer. Do the “combine” step carefully] B) The Maximum-Sum Monotone Sub-Array Problem: Input: An array A[1..n] of...
Let the sequence X be defined recursively by x1 = 1 and Xn+1 = Xn + (-1)-1 for n 2 1. Then X n is a decreasing sequence. an increasing sequence. a Cauchy sequence either increasing or decreasing. QUESTION 12 Check if the following statement is true or false: COS n The sequence is divergent. True False
C++ Given a sequence of integers, check to see if the sequence constitutes a heap Input: the first line is an integer n(0 < n < 10000), The second line is n integers Output: If the sequence is a very small heap, that is, the top of the heap is the smallest element, then output "min heap". If the sequence is a very large heap, the top of the heap is the largest element The output includes one line with...
A sequence of n distinct values A[O..n – 1] is said to be downup if there is an index p with 0 < p < n such that the values of A decrease up to Aſp) and then increase for the remainder of the sequence. The index p of value Aſp) is the valley of the sequence. For example sequence 50, 10, 5, 2, 1, 20, 30 is downup with valley 4, since A[5] = 60 and the sequence decreases...
write the solution of the program by python 3 language : I need the program using list : You are given a non-decreasing sequence of n positive integers a1,a2,…,an. Print the number of distinct values in the sequence. For example, if the sequence is 1,2,2,2,3,4,4,5,7,10, the answer is 6 since distinct values are 1,2,3,4,5,7,10. Input The first line contains a positive integer n (1≤n≤1000) — the length of the sequence. The second line contains n space-separated positive integers a1,a2,…,an (1≤ai≤1000)...
1. (16 pts.) Sorted Array Given a sorted array A of n (possibly negative) distinct integers, you want to find out whether there is an index i for which Al = i. Give a divide-and-conquer algorithm that runs in time O(log n). Provide only the main idea and the runtime analysis.