## What Is the Knapsack Problem?

An article in the Smithsonian Magazine poses this (hopefully) fictional dilemma:

Imagine you’re a thief robbing a museum exhibit of tantalizing jewelry, geodes, and rare gems. You’re new at this, so you only brought a single backpack. Your goal should be to get away with the most valuable objects without overloading your bag until it breaks or becomes too heavy to carry. How do you choose among the objects to maximize your loot? You could list all the artifacts and their weights to work out the answer by hand. But the more objects there are, the more taxing this calculation becomes for a person—or a computer.

This scenario helps to understand the knapsack problem, which, according to Wikipedia, is “a problem in combinatorial optimization.” No worries if you don’t know what that is. I don’t either. What I do know is that the knapsack problem involves taking a given set of items, each with a weight and value, and determining how much of each item you can include in a collection so the total weight doesn’t exceed a given limit and the total value is as large as possible.

The purpose of this fictional problem is to determine the best way to allocate resources given a fixed budget and time constraint. Computer programmers deal with this problem all the time, so do investors and warehouse managers.

You’ve dealt with it in some way at some point, too, though maybe you didn’t realize it had a name at the time. After all, who can’t relate to the problem of packing the most valuable or useful items without overloading our luggage and having to pay an extra fee to the airlines? That’s the knapsack problem in action.

We also find this principle in the Bible, and we can apply it both in a general sense as well as to our own journeys toward perfection. There are two passages in the Bible that immediately come to mind as applicable to the Knapsack Problem.

### Martha and Mary

“As they traveled along, Jesus entered a village where a woman named Martha welcomed him into her home. She had a sister named Mary, who sat at the Lord’s feet listening to His message. But Martha was distracted by all the preparations to be made. She came to Jesus and said, ‘Lord, do you not care that my sister has left me to serve alone? Tell her to help me!’ ‘Martha, Martha,” the Lord replied, ‘you are worried and upset about many things. But only one thing is necessary. Mary has chosen the good portion, and it will not be taken away from her.’” (Luke 10:38-42)

Martha and Mary packed their knapsacks very differently, didn’t they? We can all related to this struggle between all that we think needs accomplished and spending time with the Lord as well as to comparing what we have in our knapsack to what we think is in, or should be in, other people’s knapsacks.

### The Race of Faith

“Therefore, since we are surrounded by such a great cloud of witnesses, let us throw off everything that hinders and the sin that so easily entangles. And let us run with perseverance the race marked out for us, fixing our eyes on Jesus, the pioneer and perfector of faith. For the joy set before him he endured the cross, scorning its shame, and sat down at the right had of the throne of God. Consider him who endured such opposition from sinners, so that you will not grow wear and lose heart.” (Hebrews 12:1-2)

Figuring out what hinders and entangles us is, essentially, deciding what to put in our knapsacks (i.e., our lives) and what to leave out of them. Having too much to carry certainly lessens perseverance, doesn’t it? It also affects joy and peace and impacts our focus by overwhelming us.