|
| 1 | +# Python 3 program to count inversions in an array |
| 2 | + |
| 3 | +# Function to Use Inversion Count |
| 4 | +def mergeSort(arr, n): |
| 5 | + # A temp_arr is created to store |
| 6 | + # sorted array in merge function |
| 7 | + temp_arr = [0] * n |
| 8 | + return _mergeSort(arr, temp_arr, 0, n - 1) |
| 9 | + |
| 10 | + |
| 11 | +# This Function will use MergeSort to count inversions |
| 12 | + |
| 13 | +def _mergeSort(arr, temp_arr, left, right): |
| 14 | + # A variable inv_count is used to store |
| 15 | + # inversion counts in each recursive call |
| 16 | + |
| 17 | + inv_count = 0 |
| 18 | + |
| 19 | + # We will make a recursive call if and only if |
| 20 | + # we have more than one elements |
| 21 | + |
| 22 | + if left < right: |
| 23 | + # mid is calculated to divide the array into two subarrays |
| 24 | + # Floor division is must in case of python |
| 25 | + |
| 26 | + mid = (left + right) // 2 |
| 27 | + |
| 28 | + # It will calculate inversion counts in the left subarray |
| 29 | + |
| 30 | + inv_count += _mergeSort(arr, temp_arr, left, mid) |
| 31 | + |
| 32 | + # It will calculate inversion counts in right subarray |
| 33 | + |
| 34 | + inv_count += _mergeSort(arr, temp_arr, mid + 1, right) |
| 35 | + |
| 36 | + # It will merge two subarrays in a sorted subarray |
| 37 | + |
| 38 | + inv_count += merge(arr, temp_arr, left, mid, right) |
| 39 | + return inv_count |
| 40 | + |
| 41 | + |
| 42 | +# This function will merge two subarrays in a single sorted subarray |
| 43 | +def merge(arr, temp_arr, left, mid, right): |
| 44 | + i = left # Starting index of left subarray |
| 45 | + j = mid + 1 # Starting index of right subarray |
| 46 | + k = left # Starting index of to be sorted subarray |
| 47 | + inv_count = 0 |
| 48 | + |
| 49 | + # Conditions are checked to make sure that i and j don't exceed their |
| 50 | + # subarray limits. |
| 51 | + |
| 52 | + while i <= mid and j <= right: |
| 53 | + |
| 54 | + # There will be no inversion if arr[i] <= arr[j] |
| 55 | + |
| 56 | + if arr[i] <= arr[j]: |
| 57 | + temp_arr[k] = arr[i] |
| 58 | + k += 1 |
| 59 | + i += 1 |
| 60 | + else: |
| 61 | + # Inversion will occur. |
| 62 | + temp_arr[k] = arr[j] |
| 63 | + inv_count += (mid - i + 1) |
| 64 | + k += 1 |
| 65 | + j += 1 |
| 66 | + |
| 67 | + # Copy the remaining elements of left subarray into temporary array |
| 68 | + while i <= mid: |
| 69 | + temp_arr[k] = arr[i] |
| 70 | + k += 1 |
| 71 | + i += 1 |
| 72 | + |
| 73 | + # Copy the remaining elements of right subarray into temporary array |
| 74 | + while j <= right: |
| 75 | + temp_arr[k] = arr[j] |
| 76 | + k += 1 |
| 77 | + j += 1 |
| 78 | + |
| 79 | + # Copy the sorted subarray into Original array |
| 80 | + for loop_var in range(left, right + 1): |
| 81 | + arr[loop_var] = temp_arr[loop_var] |
| 82 | + |
| 83 | + return inv_count |
| 84 | + |
| 85 | + |
| 86 | +# Driver Code |
| 87 | +# Given array is |
| 88 | +arr = [1, 20, 6, 4, 5] |
| 89 | +n = len(arr) |
| 90 | +result = mergeSort(arr, n) |
| 91 | +print("Number of inversions are", result) |
0 commit comments