Count_Inversion.cpp

Count_Inversion/Count_Inversion.cpp

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+// Count inversion using merge sort
+
+#include <iostream>
+using namespace std;
+
+//merge two sorted arrays such that resultant array is also sorted
+int merge(int array[], int aux[], int low, int mid, int high)
+{
+    int x = low, y = mid, z = low, count = 0;
+
+    // checking till left and right half of merge sort
+    while ((x <= mid-1) && (y <= high)) 
+    {
+        if (array[x] <= array[y]) 
+        {
+            aux[z++] = array[x++];
+        }
+        else
+        {
+            aux[z++] = array[y++];
+            count += mid-x;
+        }
+    }
+
+    // Copy remaining elements
+    while (x <= mid-1)
+    {
+        aux[z++] = array[x++];
+    }
+
+    while (y <= high) 
+    {
+        aux[z++] = array[y++];
+    }
+
+    // Sorting the original array with the help of aux array
+    for (int i = low; i <= high; i++)
+    {
+        array[i] = aux[i];
+    }
+    return count;
+}
+
+//merge sort to find inversion count
+int mergeSort(int array[], int aux[], int low, int high) 
+{
+    int count = 0;
+    if (high > low)
+    {
+        int mid = (low + high) / 2;
+
+        // merge sort on Left half of the array
+        count = mergeSort(array, aux, low, mid);
+        // merge sort on Right half of the array
+        count += mergeSort(array, aux, mid + 1, high);
+        // Merge the two half
+        count += merge(array, aux, low, mid + 1, high);
+    }
+    return count;
+}
+
+//wrapper function that returns number of inversions
+int inversions_count(int array[], int n) 
+{
+    int aux[n];
+    return mergeSort(array, aux, 0, n-1);
+}
+
+int main ()
+{       
+    int n;
+    cin >> n;
+    int arr[n];
+    for(int i=0; i<n; i++)
+    cin >> arr[i];
+    cout << (inversions_count(arr, n))<<endl;
+    return 0;
+}
+
+/* Sample input 
+5
+1 20 6 4 5
+
+Sample Output
+5 */