Adding code to count the number of inversions.

1 files changed, 27 insertions, 0 deletions

diff --git a/math/inversions.cpp b/math/inversions.cpp
new file mode 100644
index 0000000..0720407
--- /dev/null
+++ b/math/inversions.cpp
@@ -0,0 +1,27 @@
+// Laufzeit: O(n*log(n))
+ll merge(vector<ll> &v, vector<ll> &left, vector<ll> &right) {
+  int a = 0, b = 0, i = 0;
+  ll inv = 0;
+  while (a < (int)left.size() && b < (int)right.size()) {
+    if (left[a] < right[b]) v[i++] = left[a++];
+    else {
+      inv += left.size() - a;
+      v[i++] = right[b++];
+    }
+  }
+  while (a < (int)left.size()) v[i++] = left[a++];
+  while (b < (int)right.size()) v[i++] = right[b++];
+  return inv;
+}
+
+ll mergeSort(vector<ll> &v) { // Sortiert v und gibt Inversionszahl zurück.
+  int n = v.size();
+  vector<ll> left(n / 2), right((n + 1) / 2);
+  for (int i = 0; i < n / 2; i++) left[i] = v[i];
+  for (int i = n / 2; i < n; i++) right[i - n / 2] = v[i];
+
+  ll result = 0;
+  if (left.size() > 1) result += mergeSort(left);
+  if (right.size() > 1) result += mergeSort(right);
+  return result + merge(v, left, right);
+}