## Decreasing-Increasing Array

### May 29, 2020

Given an array of integers, determine if it is in decreasing-increasing order, with some initial segment of the array in decreasing order and the remainder of the array in increasing order. If the array is in decreasing-increasing order, return the pivot element (the minimum element in the array); otherwise, return an indication the array is not in decreasing-increasing order. Array elements may be duplicated. For example, the array (10 10 10 8 8 6 4 4 3 12 13 22 31 40 59 68) is in decreasing-increasing order, with pivot element 3, but the array (1 2 4 8 12 32 64) is not in decreasing-increasing order.

The student who asked the question suggests a solution using binary search that takes O(log n) time, but can’t get it to work.

Your task is to write a program to determine if an array is in decreasing-increasing order as described above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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## Prime Power Triples

### May 22, 2020

Today’s exercise is Project Euler Problem 87:

The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is 28. In fact, there are exactly four numbers below fifty that can be expressed in such a way:

```28 = 22 + 23 + 24
33 = 32 + 23 + 24
49 = 52 + 23 + 24
47 = 22 + 33 + 24```

How many numbers below fifty million can be expressed as the sum of a prime square, prime cube, and prime fourth power?

Your task is to solve Project Euler 87; in the spirit of Project Euler, show only your code but not the solution. When you are finished, you are welcome to read
or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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## MinStack

### May 19, 2020

[ My apologies that this exercise is so long delayed. We have been rewriting all of our business practices in the light of the pandemic, and work has been madness. The biggest projects are now complete, and we have retreated to merely super-busy, so maybe I will have time to write some more exercises. I hope everyone is well; I am. ]

Today’s task is to implement a minstack data structure that provides the normal stack operations `push`, `pop` and `top` and also the operation `least` which returns the smallest item in the stack without altering the stack in any way. All four operations must operate in O(1) time and O(n) space, where n is the size of the stack.

Your task is to implement a minstack as described above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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