divide and conquer applications

python/38_divide_and_conquer/merge_sort_counting.py

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+#!/usr/bin/python
+# -*- coding: UTF-8 -*-
+
+inversion_num = 0
+
+
+def merge_sort_counting(nums, start, end):
+    if start >= end:
+        return
+
+    mid = (start + end)//2
+    merge_sort_counting(nums, start, mid)
+    merge_sort_counting(nums, mid+1, end)
+    merge(nums, start, mid, end)
+
+
+def merge(nums, start, mid, end):
+    global inversion_num
+    i = start
+    j = mid+1
+    tmp = []
+    while i <= mid and j <= end:
+        if nums[i] <= nums[j]:
+            inversion_num += j - mid - 1
+            tmp.append(nums[i])
+            i += 1
+        else:
+            tmp.append(nums[j])
+            j += 1
+
+    while i <= mid:
+        # 这时nums[i]的逆序数是整个nums[mid+1: end+1]的长度
+        inversion_num += end - mid
+        tmp.append(nums[i])
+        i += 1
+
+    while j <= end:
+        tmp.append(nums[j])
+        j += 1
+
+    nums[start: end+1] = tmp
+
+
+if __name__ == '__main__':
+    print('--- count inversion number using merge sort ---')
+    # nums = [5, 0, 4, 2, 3, 1, 6, 8, 7]
+    nums = [5, 0, 4, 2, 3, 1, 3, 3, 3, 6, 8, 7]
+    print('nums  : {}'.format(nums))
+    merge_sort_counting(nums, 0, len(nums)-1)
+    print('sorted: {}'.format(nums))
+    print('inversion number: {}'.format(inversion_num))