Migrate time_complexity java implementation to kotlin to for en docs

en/codes/kotlin/chapter_computational_complexity/time_complexity.kt

@@ -0,0 +1,160 @@
+/**
+ * File: time_complexity.kt
+ * Created Time: 2024-07-14
+ * Author: eyedol
+ */
+package chapter_computational_complexity.time_complexity
+
+/* Constant complexity */
+fun constant(n: Int): Int {
+    var count = 0
+    val size = 100000
+    for (i in 0 until size) count++
+    return count
+}
+
+/* Linear complexity */
+fun linear(n: Int): Int {
+    var count = 0
+    for (i in 0 until n) count++
+    return count
+}
+
+/* Linear complexity (traversing an array) */
+fun arrayTraversal(nums: IntArray): Int {
+    var count = 0
+    // Loop count is proportional to the length of the array
+    for (num in nums) {
+        count++
+    }
+    return count
+}
+
+/* Quadratic complexity */
+fun quadratic(n: Int): Int {
+    var count = 0
+    // Loop count is squared in relation to the data size n
+    for (i in 0 until n) {
+        for (j in 0 until n) {
+            count++
+        }
+    }
+    return count
+}
+
+/* Quadratic complexity (bubble sort) */
+fun bubbleSort(nums: IntArray): Int {
+    var count = 0 // Counter
+    // Outer loop: unsorted range is [0, i]
+    for (i in nums.size - 1 downTo 1) {
+        // Inner loop: swap the largest element in the unsorted range [0, i] to the right end of the range
+        for (j in 0 until i) {
+            if (nums[j] > nums[j + 1]) {
+                // Swap nums[j] and nums[j + 1]
+                val tmp = nums[j]
+                nums[j] = nums[j + 1]
+                nums[j + 1] = tmp
+                count += 3 // Element swap includes 3 individual operations
+            }
+        }
+    }
+    return count
+}
+
+/* Exponential complexity (loop implementation) */
+fun exponential(n: Int): Int {
+    var count = 0
+    var base = 1
+    // Cells split into two every round, forming the sequence 1, 2, 4, 8, ..., 2^(n-1)
+    for (i in 0 until n) {
+        for (j in 0 until base) {
+            count++
+        }
+        base *= 2
+    }
+    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
+    return count
+}
+
+/* Exponential complexity (recursive implementation) */
+fun expRecur(n: Int): Int {
+    if (n == 1) return 1
+    return expRecur(n - 1) + expRecur(n - 1) + 1
+}
+
+/* Logarithmic complexity (loop implementation) */
+fun logarithmic(n: Int): Int {
+    var n1 = n
+    var count = 0
+    while (n1 > 1) {
+        n1 /= 2
+        count++
+    }
+    return count
+}
+
+/* Logarithmic complexity (recursive implementation) */
+fun logRecur(n: Int): Int {
+    if (n <= 1) return 0
+    return logRecur(n / 2) + 1
+}
+
+/* Linear logarithmic complexity */
+fun linearLogRecur(n: Int): Int {
+    if (n <= 1) return 1
+    var count = linearLogRecur(n / 2) + linearLogRecur(n / 2)
+    for (i in 0 until n) {
+        count++
+    }
+    return count
+}
+
+/* Factorial complexity (recursive implementation) */
+fun factorialRecur(n: Int): Int {
+    if (n == 0) return 1
+    var count = 0
+    // From 1 split into n
+    for (i in 0 until n) {
+        count += factorialRecur(n - 1)
+    }
+    return count
+}
+
+/* Driver Code */
+fun main() {
+    // Can modify n to experience the trend of operation count changes under various complexities
+    val n = 8
+    println("Input data size n = $n")
+
+    var count = constant(n)
+    println("Number of constant complexity operations = $count")
+
+    count = linear(n)
+    println("Number of linear complexity operations = $count")
+    count = arrayTraversal(IntArray(n))
+    println("Number of linear complexity operations (traversing the array) = $count")
+
+    count = quadratic(n)
+    println("Number of quadratic order operations = $count")
+    val nums = IntArray(n)
+    for (i in 0 until n) nums[i] = n - i // [n,n-1,...,2,1]
+
+    count = bubbleSort(nums)
+    println("Number of quadratic order operations (bubble sort) = $count")
+
+    count = exponential(n)
+    println("Number of exponential complexity operations (implemented by loop) = $count")
+    count = expRecur(n)
+    println("Number of exponential complexity operations (implemented by recursion) = $count")
+
+    count = logarithmic(n)
+    println("Number of logarithmic complexity operations (implemented by loop) = $count")
+    count = logRecur(n)
+    println("Number of logarithmic complexity operations (implemented by recursion) = $count")
+
+    count = linearLogRecur(n)
+    println("Number of linear logarithmic complexity operations (implemented by recursion) = $count")
+
+    count = factorialRecur(n)
+    println("Number of factorial complexity operations (implemented by recursion) = $count")
+}