14 minute read

整理自：Thinking in C++, Volume 2

基本都是来自 <algorithm>。

缩写

Abbr. Original
InI InputIterator
OutI OutputIterator
ForwI ForwardIterator
BiI BidirectionalIterator
RAI RandomAccessIterator
SWO StrictWeakOrdering
BinPred BinaryPredicate
UnaFunc UnaryFunction
BinFunc BinaryFunction

1. Filling and generating

  • void fill(ForwI first, ForwI last, const T& value):
    • assigns value to every element in the range [first, last)
  • void fill_n(OutI first, Size n, const T& value):
    • assigns value to n elements starting at first.
  • void generate(ForwI first, ForwI last, Generator gen):
    • makes a call to gen() for each element in the range [first, last)
  • void generate_n(OutI first, Size n, Generator gen):
    • calls gen() n times and assigns each result to n elements starting at first.

2. Counting

  • count(InI first, InI last, const EqualityComparable& value):
    • returns the number of elements in [first, last) that are equivalent to value (when tested using operator==).
  • count_if(InI first, InI last, Predicate pred):
    • returns the number of elements in [first, last) that each cause pred` to return true.

3. Manipulating sequences

  • OutI copy(InI first, InI last, OutI destination)
  • BiI2 copy_backward(BiI1 first, BiI1 last, BiI2 destinationEnd)
  • void reverse(BiI first, BiI last)
  • OutI reverse_copy(BiI first, BiI last, OutI destination)
  • ForwI2 swap_ranges(ForwI1 first1, ForwI1 last1, ForwI2 first2)
    • Exchanges the contents of this two ranges of equal size by swapping corresponding elements.
  • void rotate(ForwI first, ForwI middle, ForwI last)
    • Moves the contents of [first, middle) to the end of the sequence, and the contents of [middle, last) to the beginning.
  • OutI rotate_copy(ForwI first, ForwI middle, ForwI last, OutI destination)
    • The original range is untouched, and the rotated version is copied into destination, returning the past-the-end iterator of the resulting range.
    • Note that while swap_ranges() requires that the two ranges be exactly the same size, the “rotate” functions do not.
  • bool next_permutation(BiI first, BiI last)
  • bool next_permutation(BiI first, BiI last, SWO binary_pred)
  • bool prev_permutation(BiI first, BiI last)
  • bool prev_permutation(BiI first, BiI last, SWO binary_pred)
    • A permutation is one unique ordering of a set of elements. If you have n unique elements, there are n! (n factorial) distinct possible combinations of those elements. All these combinations can be conceptually sorted into a sequence using a lexicographical (dictionary-like) ordering and thus produce a concept of a “next” and “previous” permutation. So whatever the current ordering of elements in the range, there is a distinct “next” and “previous” permutation in the sequence of permutations.
    • The next_permutation() and prev_permutation() functions rearrange the elements into their next or previous permutation and, if successful, return true.
      • If there are no more “next” permutations, the elements are in sorted order so next_permutation() returns false.
      • If there are no more “previous” permutations, the elements are in descending sorted order so previous_permutation() returns false.
    • The versions of the functions that have a SWO argument perform the comparisons using binary_pred instead of operator<.
  • void random_shuffle(RAI first, RAI last)
  • void random_shuffle(RAI first, RAI last, RandomNumberGenerator& rand)
    • Randomly rearranges the elements in the range.
    • The first form uses an internal random number generator,
    • and the second uses a user-supplied random-number generator.
      • The generator must return a value in the range [0, n) for some positive n
  • BiI partition(BiI first, BiI last, Predicate pred)
  • BiI stable_partition(BiI first, BiI last, Predicate pred)
    • The “partition” functions move elements that satisfy pred to the beginning of the sequence.
    • An iterator pointing one past the last of those elements is returned,
      • which is, in effect, an “end iterator” for the initial subsequence of elements that satisfy pred.
      • This location is often called the “partition point.”

4. Searching and replacing

  • InI find(InI first, InI last, const EqualityComparable& value)
  • InI find_if(InI first, InI last, Predicate pred)
    • 见名知意
  • ForwI adjacent_find(ForwI first, ForwI last)
  • ForwI adjacent_find(ForwI first, ForwI last, BinPred binary_pred)
    • The first version searches for two adjacent elements that are equivalent (via operator==).
    • The second version searches for two adjacent elements that, when passed together to binary_pred, produce a true result.
  • ForwI1 find_first_of(ForwI1 first1, ForwI1 last1, ForwI2 first2, ForwI2 last2)
  • ForwI1 find_first_of(ForwI1 first1, ForwI1 last1, ForwI2 first2, ForwI2 last2, BinPred binary_pred)
    • Search for the first element in the second range that’s equivalent to one in the first
      • 注意这是 range 2 的元素逐个与 range 1 的元素比较，是一个双重循环。可以想象成两个集合取交集时的比较。并不是 string 里找 substring 的逻辑
    • The first version uses operator==.
    • The second version searches for two elements that, when passed together to binary_pred, produce a true result.
  • ForwI1 search(ForwI1 first1, ForwI1 last1, ForwI2 first2, ForwI2 last2)
  • ForwI1 search(ForwI1 first1, ForwI1 last1, ForwI2 first2, ForwI2 last2 BinPred binary_pred)
    • Checks to see if the second range occurs (in the exact order of the second range) within the first range, and if so returns an iterator pointing to the place in the first range where the second range begins.
    • 这才是 string 里找 substring 的逻辑
  • ForwI1 find_end(ForwI1 first1, ForwI1 last1, ForwI2 first2, ForwI2 last2)
  • ForwI1 find_end(ForwI1 first1, ForwI1 last1, ForwI2 first2, ForwI2 last2, BinPred binary_pred)
    • search 的逆向版本。search 是找第一个 substring，find_end 是找最后一个 substring
  • ForwI search_n(ForwI first, ForwI last, Size count, const T& value)
  • ForwI search_n(ForwI first, ForwI last, Size count, const T& value, BinPred binary_pred)
    • Looks for a group of count consecutive values in [first, last) that are all equal to value (in the first form) or that all cause a return value of true when passed into binary_pred (in the second form).
    • Returns last if such a group cannot be found.
  • ForwI min_element(ForwI first, ForwI last)
  • ForwI min_element(ForwI first, ForwI last, BinPred binary_pred)
    • Returns an iterator pointing to the first occurrence of the “smallest” value in the range
    • Returns last if the range is empty.
    • The first version performs comparisons with operator<, and the value r returned is such that *e < *r is false for every element e in the range [first, r)
    • The second version compares using binary_pred, and the value r returned is such that binary_pred(*e, *r) is false for every element e in the range [first, r)
  • ForwI max_element(ForwI first, ForwI last)
  • ForwI max_element(ForwI first, ForwI last, BinPred binary_pred)
    • Returns an iterator pointing to the first occurrence of the largest value in the range.
    • Returns last if the range is empty.
    • The first version performs comparisons with operator<, and the value r returned is such that *r < *e is false for every element e in the range [first, r).
    • The second version compares using binary_pred, and the value r returned is such that binary_pred(*r, *e) is false for every element e in the range [first, r).
  • void replace(ForwI first, ForwI last, const T& old_value, const T& new_value)
  • void replace_if(ForwI first, ForwI last, Predicate pred, const T& new_value)
  • OutI replace_copy(InI first, InI last, OutI result, const T& old_value, const T& new_value)
  • OutI replace_copy_if(InI first, InI last, OutI result, Predicate pred, const T& new_value)

5. Comparing ranges

  • bool equal(InI first1, InI last1, InI first2)
  • bool equal(InI first1, InI last1, InI first2, BinPred binary_pred)
    • Returns true if both ranges are exactly the same.
    • In the first case, the operator== performs the comparison,
    • and in the second case binary_pred decides if two elements are the same.
  • bool lexicographical_compare(InI1 first1, InI1 last1, InI2 first2, InI2 last2)
  • bool lexicographical_compare(InI1 first1, InI1 last1, InI2 first2, InI2 last2, BinPred binary_pred)
    • Lexicographical comparison, or “dictionary” comparison, means that the comparison is done in the same way that we establish the order of strings in a dictionary.
    • 其实就是 java 的 String compare 的逻辑，但是要注意 returnType 是 bool。这里的逻辑是 return range1 < range2;
    • In the first version of the function, operator< performs the comparisons,
    • and in the second version, binary_pred is used.
  • pair<InI1, InI2> mismatch(InI1 first1, InI1 last1, InI2 first2)
  • pair<InI1, InI2> mismatch(InI1 first1, InI1 last1, InI2 first2, BinPred binary_pred)
    • Returns
      • (1) the element in the first range where the mismatch occurred and
      • (2) the element in the second range where the mismatch occurred
    • If no mismatch occurs, the return value is last1 combined with the past-the-end iterator of the second range.
    • The pair template class is a struct with two members defined in the <utility> header.
    • The first function tests for equality using operator== while the second one uses binary_pred.

6. Removing elements

首先要说下 remove 操作。remove 的时候，STL 的想法是维持 [first, last) 这个 range，不直接干掉元素而是把要删除的元素挪到了容器末尾，同时 remove 会 return 一个 new_last，这样 [first, new_last) 就成了新的 range，[new_last, last) is the sequence of removed elements，而 iterators in [new_last, last) are dereferenceable, and the element values are unspecified.

如果要强制删除，可以用 c.erase(remove(c.begin(), c.end(), value), c.end()); 或者 remove 后紧接一个 resize。

  • ForwI remove(ForwI first, ForwI last, const T& value)
  • ForwI remove_if(ForwI first, ForwI last, Predicate pred)
  • OutI remove_copy(InI first, InI last, OutI result, const T& value)
  • OutI remove_copy_if(InI first, InI last, OutI result, Predicate pred)
    • The “if” versions pass each element to pred(). If pred() returns true, the element is removed.
    • The “copy” versions do not modify the original sequence, but instead copy the remained values into a new range beginning at result and return an iterator indicating the past-the-end value of this new range.
  • ForwI unique(ForwI first, ForwI last)
  • ForwI unique(ForwI first, ForwI last, BinPred binary_pred)
  • OutI unique_copy(InI first, InI last, OutI result)
  • OutI unique_copy(InI first, InI last, OutI result, BinPred binary_pred)
    • 如果有连续的重复元素，则只保留一个，比如 aaaabbcd 会变成 abcd。但是这个操作和 remove 一样，要维持 [first, last) 这个 range；同时也是一样返回一个 new_last。
    • 用 binary_pred 的版本，如果 binary_pred(*i, *(i-1)) 返回 true，我们则认为这两个相邻的元素是重复的。

7. Sorting and operations on sorted ranges

7.1 Sorting

  • void sort(RAI first, RAI last)
    • Use operator< to sort the range into ascending order.
  • void sort(RAI first, RAI last, SWO binary_pred)
  • void stable_sort(RAI first, RAI last)
  • void stable_sort(RAI first, RAI last, SWO binary_pred)
    • sort() 是 unstable 的。unstable 是指相等的元素没有稳定的排序结果，有可能这次是 “A1 < A2 < B” 下次就是 “A2 < A1 < B”
  • void partial_sort(RAI first, RAI middle, RAI last)
  • void partial_sort(RAI first, RAI middle, RAI last, SWO binary_pred)
    • Elements before middle are the smallest ones in the entire range and are sorted in ascending order, while the remaining elements are left without any specific order.
  • RAI partial_sort_copy(InI first, InI last, RAI result_first, RAI result_last)
  • RAI partial_sort_copy(InI first, InI last, RAI result_first, RAI result_last, SWO binary_pred)
    • 假设 range1 [first, last) 有 n 个元素，range2 [result_first, result_last) 有 m 个元素，一般会假设 m <= n。把 range1 排序，结果截取 m 个元素 copy 到 range2
    • 如果 m > n，也只能把 range1 的 n 个全部 copy 过去
    • range1 的实际顺序并没有改变
  • void nth_element(RAI first, RAI nth, RAI last)
  • void nth_element(RAI first, RAI nth, RAI last, SWO binary_pred)
    • 书上的解释我实在是看不懂，以下参考 What’s the practical difference between std::nth_element and std::sort?
    • 假设 [first, last) 有 m 个元素，m > n。nth_element 执行的是一个排序，排序过后，[first, nth) 内的元素都比 *nth 小（前 n-1 名），(nth, last) 内的元素都比 *nth 大（后 m-n-1 名）；而 *nth 一定是第 n 小的元素（第 n 名）
      • [first, nth) 和 (nth, last) 这两个范围内并没有严格排序
    • If you want to answer “which element is the 4^th-smallest?” or “which elements are the 4 smallest ones?”, use nth_element(first, first+3, last)
    • If you want to get the 4 smallest elements in order, you may want to consider using partial_sort(first, first+3, last)

7.2 Locating elements in sorted ranges

  • bool binary_search(ForwI first, ForwI last, const T& value)
  • bool binary_search(ForwI first, ForwI last, const T& value, SWO binary_pred)
    • Tells you whether value appears in the sorted range [first, last).
  • ForwI lower_bound(ForwI first, ForwI last, const T& value)
  • ForwI lower_bound(ForwI first, ForwI last, const T& value, SWO binary_pred)
    • Returns an iterator indicating the first occurrence of value in the SORTED range [first, last).
    • If value is not present, an iterator to where it would fit in the sequence is returned.
  • ForwI upper_bound(ForwI first, ForwI last, const T& value)
  • ForwI upper_bound(ForwI first, ForwI last, const T& value, SWO binary_pred)
    • Returns an iterator indicating one past the last occurrence of value in the SORTED range [first, last).
    • If value is not present, an iterator to where it would fit in the sequence is returned.
  • pair<ForwI, ForwI> equal_range(ForwI first, ForwI last, const T& value)
  • pair<ForwI, ForwI> equal_range(ForwI first, ForwI last, const T& value, SWO binary_pred)
    • Essentially returns lower_bound() and upper_bound() results in a pair

7.3 Merging sorted ranges

  • OutI merge(InI1 first1, InI1 last1, InI2 first2, InI2 last2, OutI result)
  • OutI merge(InI1 first1, InI1 last1, InI2 first2, InI2 last2, OutI result, SWO binary_pred)
    • 假定 range1 和 range2 都已经排好序，合并 range1 和 range2 到 result 并再次排序
  • void inplace_merge(BiI first, BiI middle, BiI last)
  • void inplace_merge(BiI first, BiI middle, BiI last, SWO binary_pred)
    • Assumes that [first, middle) and [middle, last) are both sorted ranges in the same sequence. Merge these two sub-ranges in sorted order.

7.4 Set operations on sorted ranges

  • bool includes(InI1 first1, InI1 last1, InI2 first2, InI2 last2)
  • bool includes(InI1 first1, InI1 last1, InI2 first2, InI2 last2, SWO binary_pred)
    • 你可以理解为 “如果 range2 是 range1 的子集，则返回 true”
    • 但实际并不是严格意义上的判断子集，因为 range1 和 range2 都不算是 set，是可以有重复元素的
  • OutI set_union(InI1 first1, InI1 last1, InI2 first2, InI2 last2, OutI result)
  • OutI set_union(InI1 first1, InI1 last1, InI2 first2, InI2 last2, OutI result, SWO binary_pred)
    • 同理，并不是严格意义上的取并集
    • 返回 result 的 last
  • OutI set_intersection(InI1 first1, InI1 last1, InI2 first2, InI2 last2, OutI result)
  • OutI set_intersection(InI1 first1, InI1 last1, InI2 first2, InI2 last2, OutI result, SWO binary_pred)
    • 同理，并不是严格意义上的取交集
    • 返回 result 的 last
  • OutI set_difference(InI1 first1, InI1 last1, InI2 first2, InI2 last2, OutI result)
  • OutI set_difference(InI1 first1, InI1 last1, InI2 first2, InI2 last2, OutI result, SWO binary_pred)
    • 同理，并不是严格意义上的取交集
    • All the elements that are in [first1, last1) but not in [first2, last2) are placed in the result set.
    • 返回 result 的 last
  • OutI set_symmetric_difference(InI1 first1, InI1 last1, InI2 first2, InI2 last2, OutI result)
  • OutI set_symmetric_difference(InI1 first1, InI1 last1, InI2 first2, InI2 last2, OutI result, SWO binary_pred)
    • 所谓 symmetric difference 就是 A-B 并上 B-A，等价于 A、B 的并集减去 A、B 的交集
    • 返回 result 的 last

8. Heap operations

这里 heap 并不是内存的那个 heap，单指 heap 这种数据结构。

A heap is a way to organize the elements of a range that allows for fast retrieval of the element with the highest value at any moment (with pop_heap()), even repeatedly, while allowing for fast insertion of new elements (with push_heap()).

The element with the highest value is always pointed by first. The order of the other elements depends on the particular implementation, but it is consistent throughout all heap-related functions of this header.

  • void make_heap(RAI first, RAI last)
  • void make_heap(RAI first, RAI last, SWO binary_pred)
    • Turns an arbitrary range into a heap.
  • void push_heap(RAI first, RAI last)
  • void push_heap(RAI first, RAI last, SWO binary_pred)
    • Adds the element *(last-1) to the heap determined by the range [first, last-1)
  • void pop_heap(RAI first, RAI last)
  • void pop_heap(RAI first, RAI last, SWO binary_pred)
    • Places the largest element, i.e. *first, into the position (last-1) and reorganizes the remaining range so that it’s still in heap order.
    • If you simply fetch *first, the next element would not be the next-largest element.
  • void sort_heap(RAI first, RAI last)
  • void sort_heap(RAI first, RAI last, SWO binary_pred)
    • This could be thought of as the complement to make_heap(). It takes a range that is in heap order and turns it into ordinary sorted order, so it is no longer a heap.
    • That means that if you call sort_heap(), push_heap() or pop_heap() no longer make any sense.

9. Applying an operation to each element in a range

  • UnaFunc for_each(InI first, InI last, UnaFunc f)
    • Applies the function object f to each element in [first, last)
    • Returns f
  • OutI transform(InI first, InI last, OutI result, UnaFunc f)
  • OutI transform(InI1 first, InI1 last, InI2 first2, OutI result, BinFunc f)
    • Applies the function object f to each element in the range1 [first, last), or along with each element in range2 in the second version.
    • Copies the return value (using operator=) into *result, incrementing result after each copy

10. Numeric algorithms

From <numeric>.

  • T accumulate(InI first, InI last, T init)
  • T accumulate(InI first, InI last, T init, BinFunc f)
    • for(i in range) { init += f(init, i); } return init;
  • T inner_product(InI1 first1, InI1 last1, InI2 first2, T init)
  • T inner_product(InI1 first1, InI1 last1, InI2 first2, T init, BinFunc1 op1, BinFunc2 op2)
    • 假定 range1 = {1, 1, 2, 2} and range2 = {1, 2, 3, 4}
    • version 1 的计算方法就是 (11) + (12) + (23) + (24)，最后加上 init 的值
    • version 2 的计算方法是：
      1. init = op1(init, op2(1,1));
      2. init = op1(init, op2(1,2));
      3. init = op1(init, op2(2,3));
      4. init = op1(init, op2(2,4));
  • OutI partial_sum(InI first, InI last, OutI result)
  • OutI partial_sum(InI first, InI last, OutI result, BinFunc op)
    • 计算 accumulative sum 序列
    • 比如假定 range1 = {1, 1, 2, 2, 3}, the generated sequence is {1, 1 + 1, 1 + 1 + 2, 1 + 1 + 2 + 2, 1 + 1 + 2 + 2 + 3}, that is, {1, 2, 4, 6, 9}.
    • version 2 是用 op 替代了 version 1 的 operator+。比如我们给 op 传一个 multiplies<int>()，那么得到的序列就是 {1, 1 x 1, 1 x 1 x 2, 1 x 1 x 2 x 2, 1 x 1 x 2 x 2 x 3}, that is, {1, 1, 2, 4, 12}.
    • 返回 result 的 last
  • OutI adjacent_difference(InI first, InI last, OutI result)
  • OutI adjacent_difference(InI first, InI last, OutI result, BinFunc op)
    • 假定 range1 = {1, 1, 2, 2, 3}, the resulting sequence is {1, 1 – 1, 2 – 1, 2 – 2, 3 – 2}, that is: {1, 0, 1, 0, 1}.
    • version 2 是用 op 替代了 version 1 的 operator-
    • 返回 result 的 last

11. General utilities

  • const LessThanComparable& min(const LessThanComparable& a, const LessThanComparable& b)
  • const T& min(const T& a, const T& b, BinPred binary_pred)
  • const LessThanComparable& max(const LessThanComparable& a, const LessThanComparable& b)
  • const T& max(const T& a, const T& b, BinPred binary_pred)
  • void swap(Assignable& a, Assignable& b)
    • When this function is applied to two containers of the same type, it uses container’s member function swap() to achieve fast performance.
    • Consequently, if you apply the sort() algorithm to a container of containers, you will find that the performance is very fast—it turns out that fast sorting of a container of containers was a design goal of the STL.
  • void iter_swap(ForwI1 a, ForwI2 b)

From <utility>.

  • template<class T1, class T2> struct pair
  • template<class T1, class T2> pair<T1, T2> make_pair(const T1&, const T2&)

From <iterator>.

  • difference_type distance(InI first, InI last)
    • Tells you the number of elements between first and last.
    • More precisely, it returns an integral value that tells you the number of times first must be incremented before it is equal to last.
  • void advance(InI& i, Distance n)
    • Moves the iterator i forward by the value of n.
    • It can also be moved backward for negative values of n if the iterator is bidirectional.
  • back_insert_iterator **back_inserter**(Container& x)
  • front_insert_iterator **front_inserter**(Container& x)
  • insert_iterator **inserter**(Container& x, Iterator i)

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