When it comes to algorithm design, there are many techniques that can be used to solve complex problems. In this post, we’ll explore some of the most common algorithm design techniques: Divide & Conquer, Recursivity, Greedy Algorithms, and Dynamic Programming. We’ll explain each technique and provide some examples to help illustrate the concepts.

Divide & Conquer

The Divide & Conquer algorithm design technique involves breaking a problem down into smaller, more manageable sub-problems, solving each sub-problem independently, and then combining the solutions to form a final solution to the original problem.

A classic example of Divide & Conquer is the Merge Sort algorithm, which sorts an array of elements by dividing the array in half, sorting each half, and then merging the sorted halves.

fun mergeSort(array: Array<Int>): Array<Int> {
    if (array.size <= 1) {
        return array
    }
    val middle = array.size / 2
    val left = array.sliceArray(0 until middle)
    val right = array.sliceArray(middle until array.size)
    return merge(mergeSort(left), mergeSort(right))
}

fun merge(left: Array<Int>, right: Array<Int>): Array<Int> {
    var i = 0
    var j = 0
    val result = mutableListOf<Int>()
    while (i < left.size && j < right.size) {
        if (left[i] < right[j]) {
            result.add(left[i])
            i++
        } else {
            result.add(right[j])
            j++
        }
    }
    while (i < left.size) {
        result.add(left[i])
        i++
    }
    while (j < right.size) {
        result.add(right[j])
        j++
    }
    return result.toTypedArray()
}

Recursivity

Recursivity is a technique that involves solving a problem by breaking it down into smaller instances of the same problem. In other words, a function calls itself to solve a problem.

A classic example of Recursivity is the Fibonacci sequence, which generates the sequence by summing the two previous numbers in the sequence.

fun fibonacci(n: Int): Int {
    if (n == 0) {
        return 0
    }
    if (n == 1) {
        return 1
    }
    return fibonacci(n-1) + fibonacci(n-2)
}

Greedy Algorithms

Greedy Algorithms are a technique that involves making the locally optimal choice at each step of a problem to eventually arrive at a globally optimal solution.

A classic example of Greedy Algorithms is the Knapsack problem, which involves filling a knapsack with items of different values and weights to maximize the value of the knapsack.

kotlinCopy codefun knapsack(items: List<Item>, capacity: Int): List<Item> {
    val sortedItems = items.sortedByDescending { it.value / it.weight.toDouble() }
    var remainingCapacity = capacity
    val selectedItems = mutableListOf<Item>()
    for (item in sortedItems) {
        if (item.weight <= remainingCapacity) {
            remainingCapacity -= item.weight
            selectedItems.add(item)
        }
    }
    return selectedItems
}

Dynamic Programming

Dynamic Programming is a technique that involves breaking a problem down into smaller, overlapping sub-problems, and storing the solutions to these sub-problems to avoid redundant computations.

A classic example of Dynamic Programming is the Longest Common Subsequence problem, which involves finding the longest subsequence that is present in two given sequences.

fun lcs(s1: String, s2: String): String {
    val m = s1.length
    val n = s2.length
    val table = Array(m+1) { IntArray(n+1) }
    for (i in 0..m) {
        for (j in 0..n) {
            if (i == 0 || j == 0) {
                table[i][j] = 0
            } else if (s1[i-1] == s2[j-1]) {
                table[i][j] = table[i-1][j-1] + 1
            } else {
                table[i][j] = max(table[i-1][j], table[i][j-1])
            }
        }
    }
    var i = m
    var j = n
    val result = StringBuilder()
    while (i > 0 && j > 0) {
        if (s1[i-1] == s2[j-1]) {
            result.append(s1[i-1])
            i--
            j--
        } else if (table[i-1][j] > table[i][j-1]) {
            i--
        } else {
            j--
        }
    }
    return result.reverse().toString()
}

Conclusion

These are just a few of the many algorithm design techniques that can be used to solve complex problems. By understanding these techniques and their applications, you can become a more skilled and efficient programmer. Remember that the choice of technique depends on the problem at hand, and that some problems may require a combination of techniques. With practice and experience, you can master these techniques and develop your own problem-solving skills.