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The key factors in constructing an efficient algorithm are problem understanding, design strategy, time complexity, space complexity, and optimisation.

Understanding the problem is the first and foremost factor in constructing an efficient algorithm. It involves comprehending the problem statement, identifying the inputs and expected outputs, and understanding the constraints. This step is crucial as it lays the foundation for the rest of the algorithm design process. A clear understanding of the problem helps in choosing the right data structures and algorithms, which in turn leads to an efficient solution.

The design strategy is another important factor. There are several strategies for designing algorithms, such as divide and conquer, dynamic programming, greedy algorithms, and backtracking. The choice of strategy depends on the nature of the problem. For example, divide and conquer is a good strategy for problems that can be broken down into smaller sub-problems, while dynamic programming is suitable for problems with overlapping sub-problems.

Time complexity refers to the computational complexity that describes the amount of time an algorithm takes to run as a function of the size of the input to the program. It is a critical factor in determining the efficiency of an algorithm. An algorithm that can solve a problem in less time is considered more efficient. Therefore, it is important to analyse the time complexity of an algorithm during its design phase.

Space complexity is the amount of memory used by an algorithm (including the input values to the algorithm) to execute and produce the result. Space complexity becomes a concern when an algorithm uses more space than is available on a computer, causing the system to slow down or even crash. Therefore, an efficient algorithm should also aim to minimise space usage.

Lastly, optimisation is a key factor in constructing an efficient algorithm. This involves refining the algorithm to improve its performance by reducing the time it takes to run or the space it uses. Optimisation can be achieved through various techniques, such as loop unrolling, code restructuring, and using efficient data structures. It is an iterative process that requires a deep understanding of the algorithm and the problem it is trying to solve.

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