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merge-sort-tree.py
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merge-sort-tree.py
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from bisect import bisect_left as lower_bound
def build_tree(tree, arr, idx, l, r):
if l == r:
tree[idx].append(arr[l])
else:
mid = (l + r) // 2
build_tree(tree, arr, 2 * idx + 1, l, mid)
build_tree(tree, arr, 2 * idx + 2, mid + 1, r)
tree[idx] = merge(tree[2 * idx + 1], tree[2 * idx + 2])
def merge(left, right):
myList = []
i = 0
j = 0
while i < len(left) and j < len(right):
if left[i] < right[j]:
myList.append(left[i])
i += 1
else:
myList.append(right[j])
j += 1
while i < len(left):
myList.append(left[i])
i += 1
while j < len(right):
myList.append(right[j])
j += 1
return myList
def query(Tree, index, s, e, l, r, k):
if r < s or l > e:
return 0
if s >= l and e <= r:
return len(Tree[index]) - lower_bound(Tree[index], k)
mid = (s + e) // 2
return query(Tree, 2 * index + 1, s, mid, l, r, k) + query(
Tree, 2 * index + 2, mid + 1, e, l, r, k
)
if __name__ == "__main__":
n = 4
arr = [1, 2, 3, 4]
tree = [[] for i in range(2 * n - 1)]
build_tree(tree, arr, 0, 0, n - 1)
print(tree)
for i in range(n):
print(query(tree, 1, 0, n - 1, i, n - 1, arr[i]))