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Breaking the problem into smaller pieces

The idea behind the divide and conquer concept is breaking down a problem into smaller sub-problems, solving each sub-problem independently, and then combining the solutions to obtain the final solution to the original problem. The concept is based on the idea that if we can break down a problem into smaller pieces, it becomes easier to solve each sub-problem individually.

Divider and conquer algorithm

This technique is useful and powerful for solving problems that are too large or complex to solve using traditional brute-force methods. By dividing the problem into smaller sub-problems, we can reduce the amount of computation needed to solve the problem, making it more manageable.

So it's more efficient in comparison to brute-force methods and it's usually easier to understand and maintain. It can also be used to solve a wide variety of problems, from simple sorting problems to complex optimization problems. Some well-known algorithms are based on the divide and conquer approach, such as sorting algorithms and binary search.

The steps in a practical example

Let's say we want to sort an array of integers whose length can be a very large number. We can use a sorting algorithm to do that. Once this algorithm is based on the divide and conquer approach, the main steps would be:

1. Dividing the problem into smaller sub-problems: finding the base case, breaking the input into subarrays (sub-problems) instead of trying to sort a long array (original problem) at once. In other words, finding smaller instances of the same problem.

2. Conquering the sub-problems: sorting the subarrays recursively.

3. Combining the solutions to the sub-problems: merging the sorted subarrays in a sorting problem to get the final sorted array.

Conclusion

Divide and conquer approach is a powerful technique that can be used to solve complex problems efficiently.