134 lines
4.0 KiB
Rust
134 lines
4.0 KiB
Rust
//! Helpers to generate a binary search tree stored in an array from a
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//! sorted array.
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//!
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//! Specifically, for any given sorted array 'input' permute the
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//! array so that the following rule holds:
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//!
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//! For each array item with index i, the item at 2i+1 is smaller and
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//! the item 2i+2 is larger.
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//!
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//! This structure permits efficient (meaning: O(log(n)) binary
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//! searches: start with item i=0 (i.e. the root of the BST), compare
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//! the value with the searched item, if smaller proceed at item
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//! 2i+1, if larger proceed at item 2i+2, and repeat, until either
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//! the item is found, or the indexes grow beyond the array size,
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//! which means the entry does not exist.
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//!
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//! Effectively this implements bisection, but instead of jumping
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//! around wildly in the array during a single search we only search
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//! with strictly monotonically increasing indexes.
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//!
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//! Algorithm is from casync (camakebst.c), simplified and optimized
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//! for rust. Permutation function originally by L. Bressel, 2017. We
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//! pass permutation info to user provided callback, which actually
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//! implements the data copy.
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//!
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//! The Wikipedia Artikel for [Binary
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//! Heap](https://en.wikipedia.org/wiki/Binary_heap) gives a short
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//! intro howto store binary trees using an array.
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fn copy_binary_search_tree_inner<F: FnMut(usize, usize)>(
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copy_func: &mut F,
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// we work on input array input[o..o+n]
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n: usize,
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o: usize,
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e: usize,
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i: usize,
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) {
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let p = 1 << e;
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let t = p + (p>>1) - 1;
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let m = if n > t {
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// |...........p.............t....n........(2p)|
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p - 1
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} else {
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// |...........p.....n.......t.............(2p)|
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p - 1 - (t-n)
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};
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(copy_func)(o+m, i);
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if m > 0 {
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copy_binary_search_tree_inner(copy_func, m, o, e-1, i*2+1);
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}
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if (m + 1) < n {
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copy_binary_search_tree_inner(copy_func, n-m-1, o+m+1, e-1, i*2+2);
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}
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}
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/// This function calls the provided `copy_func()` with the permutaion
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/// info.
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///
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/// ```
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/// # use proxmox_backup::catar::binary_search_tree::copy_binary_search_tree;
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/// copy_binary_search_tree(5, |src, dest| {
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/// println!("Copy {} to {}", src, dest);
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/// });
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/// ```
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///
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/// This will produce the folowing output:
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///
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/// ```no-compile
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/// Copy 3 to 0
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/// Copy 1 to 1
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/// Copy 0 to 3
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/// Copy 2 to 4
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/// Copy 4 to 2
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/// ```
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///
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/// So this generates the following permuation: `[3,1,4,0,2]`.
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pub fn copy_binary_search_tree<F: FnMut(usize, usize)>(
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n: usize,
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mut copy_func: F,
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) {
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if n == 0 { return };
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let e = (64 - n.leading_zeros() - 1) as usize; // fast log2(n)
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copy_binary_search_tree_inner(&mut copy_func, n, 0, e, 0);
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}
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#[test]
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fn test_binary_search_tree() {
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fn run_test(len: usize) -> Vec<usize> {
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const MARKER: usize = 0xfffffff;
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let mut output = vec![];
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for i in 0..len { output.push(MARKER); }
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copy_binary_search_tree(len, |s, d| {
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assert!(output[d] == MARKER);
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output[d] = s;
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});
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if len < 32 { println!("GOT:{}:{:?}", len, output); }
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for i in 0..len {
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assert!(output[i] != MARKER);
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}
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output
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}
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assert!(run_test(0).len() == 0);
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assert!(run_test(1) == [0]);
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assert!(run_test(2) == [1,0]);
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assert!(run_test(3) == [1,0,2]);
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assert!(run_test(4) == [2,1,3,0]);
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assert!(run_test(5) == [3,1,4,0,2]);
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assert!(run_test(6) == [3,1,5,0,2,4]);
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assert!(run_test(7) == [3,1,5,0,2,4,6]);
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assert!(run_test(8) == [4,2,6,1,3,5,7,0]);
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assert!(run_test(9) == [5,3,7,1,4,6,8,0,2]);
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assert!(run_test(10) == [6,3,8,1,5,7,9,0,2,4]);
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assert!(run_test(11) == [7,3,9,1,5,8,10,0,2,4,6]);
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assert!(run_test(12) == [7,3,10,1,5,9,11,0,2,4,6,8]);
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assert!(run_test(13) == [7,3,11,1,5,9,12,0,2,4,6,8,10]);
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assert!(run_test(14) == [7,3,11,1,5,9,13,0,2,4,6,8,10,12]);
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assert!(run_test(15) == [7,3,11,1,5,9,13,0,2,4,6,8,10,12,14]);
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assert!(run_test(16) == [8,4,12,2,6,10,14,1,3,5,7,9,11,13,15,0]);
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assert!(run_test(17) == [9,5,13,3,7,11,15,1,4,6,8,10,12,14,16,0,2]);
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for len in 18..1000 {
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run_test(len);
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}
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}
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