101 lines
3.4 KiB
Markdown
101 lines
3.4 KiB
Markdown
# 二分查找（下）
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本节课讨论二分的各种变体。实际上在针对上一节的代码中，已经实现了两个变体。本次实现四个变体：
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* 第一个等于给定值的元素
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* 最后一个等于给定值的元素
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* 第一个不小于给定值的元素
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* 最后一个不大于给定值的元素
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```cpp
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/**
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* Created by Liam Huang (Liam0205) on 2018/10/26.
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*/
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#ifndef BSEARCH_BSEARCH_VARIENTS_HPP_
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#define BSEARCH_BSEARCH_VARIENTS_HPP_
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#include <iterator>
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#include <functional>
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enum class BsearchPolicy { UNSPECIFIED, FIRST, LAST, FIRST_NOT_LESS, LAST_NOT_GREATER };
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// Liam Huang: The algorithm works right with iterators that meet the ForwardIterator requirement,
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// but with a bad time complexity. For better performance, iterators should meet
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// the RandomAccessIterator requirement.
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template <typename IterT,
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typename ValueT = typename std::iterator_traits<IterT>::value_type,
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typename Compare>
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IterT bsearch(IterT first,
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IterT last,
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ValueT target,
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Compare comp,
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BsearchPolicy policy = BsearchPolicy::UNSPECIFIED) {
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IterT result = last;
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while (std::distance(first, last) > 0) {
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IterT mid = first + std::distance(first, last) / 2;
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if (policy == BsearchPolicy::FIRST_NOT_LESS) {
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if (!comp(*mid, target)) {
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if (mid == first or comp(*(mid - 1), target)) {
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result = mid;
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break;
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} else {
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last = mid;
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}
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} else {
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first = mid + 1;
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}
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} else if (policy == BsearchPolicy::LAST_NOT_GREATER) {
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if (comp(target, *mid)) {
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last = mid;
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} else {
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if (std::distance(mid, last) == 1 or comp(target, *(mid + 1))) {
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result = mid;
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break;
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} else {
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first = mid + 1;
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}
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}
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} else { // policy == UNSPECIFIED or FIRST or LAST
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if (comp(*mid, target)) {
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first = mid + 1;
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} else if (comp(target, *mid)) {
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last = mid;
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} else { // equal
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if (policy == BsearchPolicy::FIRST) {
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if (mid == first or comp(*(mid - 1), *mid)) {
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result = mid;
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break;
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} else {
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last = mid;
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}
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} else if (policy == BsearchPolicy::LAST) {
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if (std::distance(mid, last) == 1 or comp(*mid, *(mid + 1))) {
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result = mid;
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break;
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} else {
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first = mid + 1;
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}
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} else {
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result = mid;
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break;
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}
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}
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}
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}
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return result;
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}
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template <typename IterT,
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typename ValueT = typename std::iterator_traits<IterT>::value_type,
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typename Compare = std::less<ValueT>>
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IterT bsearch(IterT first,
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IterT last,
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ValueT target,
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BsearchPolicy policy = BsearchPolicy::UNSPECIFIED) {
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return bsearch(first, last, target, Compare(), policy);
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}
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#endif // BSEARCH_BSEARCH_VARIENTS_HPP_
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```
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