Tag: Computing

Dynamic Programming: An Approach to Solving Computing Problems

Laurent

Sometimes in computer science, you will run into problems. You can divide these into subproblems, which can, in turn, be divided into smaller subproblems. If the smaller subproblems overlap, then you can save the result in memory for future reference. This way, you don’t need to compute the same result multiple times, thus increasing the efficiency of the program substantially. This way of solving these problems is referred to as dynamic programming.

Dynamic Programming – Learn to Solve Algorithmic Problems & Coding Challenges. | Video: freeCodeCamp.org

In this article, you will learn what dynamic programming is. I will also show how to compute Fibonacci numbers, which is a simple problem that dynamic programming can solve. I will compare the dynamic programming solutions to the naive solution that uses recursion. These examples are written in Python syntax. Finally, I’ll also give some general pointers to keep in mind when attempting to solve problems using dynamic programming

Dynamic programming

Dynamic programming is an efficient method for solving computing problems by saving solutions in memory for future reference. When you have overlapping subproblems, you can apply dynamic programming to save time and increase program efficiency. 

More From Artturi Jalli: Python Cheat Sheet: A Handy Guide to Python

 

What Types of Problems Can Dynamic Programming Solve?

Dynamic programming is typically a way to optimize solutions to certain problems that use recursion. If a recursive solution to a problem has to compute solutions for subproblems with the same inputs repeatedly, then you can optimize it through dynamic programming. As mentioned earlier, in this case, you would simply save the result of the computation for use later if and when it’s needed. This optimization can reduce the time complexity of an algorithm from exponential time to polynomial time. This means that the number of computations n scales like a polynomial expression instead of scaling like an exponential expression as n increases. In general, polynomial expressions grow much slower than exponential expressions.

There are two conditions that need to be satisfied to use dynamic programming:

  1. Overlapping subproblems
  2. Optimal substructure property

 

What Are Overlapping Subproblems?

I alluded to

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A new language for quantum computing | MIT Information

Laurent

Time crystals. Microwaves. Diamonds. What do these three disparate points have in widespread? 

Quantum computing. Unlike conventional computers that use bits, quantum computer systems use qubits to encode info as zeros or types, or each at the exact time. Coupled with a cocktail of forces from quantum physics, these fridge-sized machines can course of action a whole great deal of facts — but they’re considerably from flawless. Just like our normal personal computers, we will need to have the correct programming languages to appropriately compute on quantum desktops. 

Programming quantum desktops demands recognition of anything named “entanglement,” a computational multiplier for qubits of kinds, which interprets to a good deal of power. When two qubits are entangled, actions on 1 qubit can improve the worth of the other, even when they are bodily separated, supplying increase to Einstein’s characterization of “spooky action at a length.” But that potency is equivalent components a supply of weak point. When programming, discarding 1 qubit without getting mindful of its entanglement with an additional qubit can demolish the details stored in the other, jeopardizing the correctness of the system. 

Scientists from MIT’s Personal computer Science and Synthetic Intelligence (CSAIL) aimed to do some unraveling by making their individual programming language for quantum computing referred to as Twist. Twist can explain and verify which items of facts are entangled in a quantum software, via a language a classical programmer can comprehend. The language makes use of a notion called purity, which enforces the absence of entanglement and final results in far more intuitive plans, with ideally fewer bugs. For case in point, a programmer can use Twist to say that the short term details generated as garbage by a application is not entangled with the program’s solution, earning it protected to throw away.

Although the nascent discipline can sense a very little flashy and futuristic, with photos of mammoth wiry gold devices coming to head, quantum personal computers have prospective for computational breakthroughs in classically unsolvable duties, like cryptographic and interaction protocols, search, and computational physics and chemistry. One particular of the critical troubles in

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MIT’s New Programming Language for Quantum Computing

Laurent

Time crystals. Microwaves. Diamonds. What do these three disparate factors have in common?

Quantum computing. Contrary to standard desktops that use bits, quantum pcs use qubits to encode facts as zeros or kinds, or the two at the identical time. Coupled with a cocktail of forces from quantum physics, these refrigerator-sized machines can system a whole whole lot of data — but they’re much from flawless. Just like our typical personal computers, we have to have to have the suitable programming languages to correctly compute on quantum personal computers.

Programming quantum personal computers needs consciousness of something referred to as “entanglement,” a computational multiplier for qubits of kinds, which interprets to a great deal of power. When two qubits are entangled, actions on 1 qubit can transform the price of the other, even when they are bodily divided, supplying rise to Einstein’s characterization of “spooky action at a length.” But that potency is equivalent areas a resource of weakness. When programming, discarding one qubit with no being mindful of its entanglement with another qubit can demolish the details stored in the other, jeopardizing the correctness of the plan.

Experts from quantum computing called Twist. Twist can describe and verify which pieces of data are entangled in a quantum program, through a language a classical programmer can understand. The language uses a concept called purity, which enforces the absence of entanglement and results in more intuitive programs, with ideally fewer bugs. For example, a programmer can use Twist to say that the temporary data generated as garbage by a program is not entangled with the program’s answer, making it safe to throw away.

IBM Quantum Computer Close

While

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