recursion.groovy

recursion.groovy

@@ -0,0 +1,69 @@
+// http://en.wikipedia.org/wiki/Counting_sort
+
+def countingSort(list) {
+    min = list.min(); max = list.max()
+    range = max - min
+    counts = new int[range+1]
+    list.each { counts[it-min]++ }
+    (1..counts.size()-1).each { counts[it] += counts[it-1] }
+
+    result = new int[list.size()]
+    (list.size()-1..0).each {
+        index = list[it]
+        result[counts[index-min]-- -1] = index
+    }
+    result
+}
+
+assert [3,4,4,5,6,7] == countingSort([7,3,6,4,5,4])
+
+
+def swap(list, p, q) {
+    lp = list[p]; list[p] = list[q]; list[q] = lp
+}
+
+list = [1,2,3,4,5,6]
+swap(list, 0, 3)
+assert [4,2,3,1,5,6] == list
+
+
+// http://en.wikipedia.org/wiki/Selection_algorithm
+
+def partition(list, left, right, pivotIndex) {
+    pivot = list[pivotIndex]
+    swap(list, pivotIndex, right) // Move pivot to end
+    storeIndex = left
+    (left..right-1).each {
+        if (list[it] < pivot) swap(list, storeIndex++, it)
+    }
+    swap(list, right, storeIndex) // Move pivot to its final place
+    storeIndex
+}
+
+list = [6,1,5,3,4,2]
+assert 3 == partition(list, 0, list.size()-1, 4)
+assert [1,3,2,4,5,6] == list
+
+
+def select(list, p, q, i) {
+    if (p == q) return list[p]
+    pivotIndex = p + new Random().nextInt(q-p+1) // randomized partition to get O(n)
+    r = partition(list, p, q, pivotIndex)
+    k = r - p + 1
+    if (i == k) return list[r]
+    if (i < k) return select(list, p, r-1, i)
+    select(list, r+1, q, i-k)
+}
+
+
+list = [6,1,5,3,8,7,4,2]
+assert 4 == select(list, 0, list.size()-1, 4)
+
+list = [6,1,5,3,8,7,4,2]
+assert 1 == select(list, 0, list.size()-1, 1) // min
+
+list = [6,1,5,3,8,7,4,2]
+assert 8 == select(list, 0, list.size()-1, list.size()) // max
+
+list = [6,1,2,3,8,4,4,2]
+assert 4 == select(list, 0, list.size()-1, 5)