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Change fenwick tree to accept uint32 to avoid extra copy
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BSD 2-Clause License | ||
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Copyright (c) 2017, Stefan Nilsson | ||
All rights reserved. | ||
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Redistribution and use in source and binary forms, with or without | ||
modification, are permitted provided that the following conditions are met: | ||
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* Redistributions of source code must retain the above copyright notice, this | ||
list of conditions and the following disclaimer. | ||
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* Redistributions in binary form must reproduce the above copyright notice, | ||
this list of conditions and the following disclaimer in the documentation | ||
and/or other materials provided with the distribution. | ||
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" | ||
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | ||
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE | ||
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE | ||
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | ||
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR | ||
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER | ||
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, | ||
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | ||
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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This is https://github.com/yourbasic/fenwick with int64 replaced with uint32 to avoid constructing temporary []int64 slice just for the lib. |
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// Package fenwick provides a list data structure supporting prefix sums. | ||
// | ||
// A Fenwick tree, or binary indexed tree, is a space-efficient list | ||
// data structure that can efficiently update elements and calculate | ||
// prefix sums in a list of numbers. | ||
// | ||
// Compared to a common array, a Fenwick tree achieves better balance | ||
// between element update and prefix sum calculation – both operations | ||
// run in O(log n) time – while using the same amount of memory. | ||
// This is achieved by representing the list as an implicit tree, | ||
// where the value of each node is the sum of the numbers in that | ||
// subtree. | ||
// | ||
package fenwick | ||
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// List represents a list of numbers with support for efficient | ||
// prefix sum computation. The zero value is an empty list. | ||
type List struct { | ||
// The tree slice stores range sums of an underlying array t. | ||
// To compute the prefix sum t[0] + t[1] + t[k-1], add elements | ||
// which correspond to each 1 bit in the binary expansion of k. | ||
// | ||
// For example, this is how the sum of the 13 first elements | ||
// in t is computed: 13 is 1101₂ in binary, so the elements | ||
// at indices 1101₂ - 1, 1100₂ - 1, and 1000₂ - 1 are added; | ||
// they contain the range sums t[12], t[8] + … t[11], and | ||
// t[0] + … + t[7], respectively. | ||
// | ||
tree []uint32 | ||
} | ||
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// New creates a new list with the given elements. | ||
func New(n ...uint32) *List { | ||
len := len(n) | ||
t := make([]uint32, len) | ||
copy(t, n) | ||
for i := range t { | ||
if j := i | (i + 1); j < len { | ||
t[j] += t[i] | ||
} | ||
} | ||
return &List{ | ||
tree: t, | ||
} | ||
} | ||
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// Len returns the number of elements in the list. | ||
func (l *List) Len() int { | ||
return len(l.tree) | ||
} | ||
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// Get returns the element at index i. | ||
func (l *List) Get(i int) uint32 { | ||
sum := l.tree[i] | ||
j := i + 1 | ||
j -= j & -j | ||
for i > j { | ||
sum -= l.tree[i-1] | ||
i -= i & -i | ||
} | ||
return sum | ||
} | ||
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// Set sets the element at index i to n. | ||
func (l *List) Set(i int, n uint32) { | ||
n -= l.Get(i) | ||
for len := len(l.tree); i < len; i |= i + 1 { | ||
l.tree[i] += n | ||
} | ||
} | ||
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// Add adds n to the element at index i. | ||
func (l *List) Add(i int, n uint32) { | ||
for len := len(l.tree); i < len; i |= i + 1 { | ||
l.tree[i] += n | ||
} | ||
} | ||
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// Sum returns the sum of the elements from index 0 to index i-1. | ||
func (l *List) Sum(i int) uint32 { | ||
var sum uint32 | ||
for i > 0 { | ||
sum += l.tree[i-1] | ||
i -= i & -i | ||
} | ||
return sum | ||
} | ||
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// SumRange returns the sum of the elements from index i to index j-1. | ||
func (l *List) SumRange(i, j int) uint32 { | ||
var sum uint32 | ||
for j > i { | ||
sum += l.tree[j-1] | ||
j -= j & -j | ||
} | ||
for i > j { | ||
sum -= l.tree[i-1] | ||
i -= i & -i | ||
} | ||
return sum | ||
} | ||
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// Append appends a new element to the end of the list. | ||
func (l *List) Append(n uint32) { | ||
i := len(l.tree) | ||
l.tree = append(l.tree, 0) | ||
l.tree[i] = n - l.Get(i) | ||
} |
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