Some jobs that begin with the letter T include:
#include<iostream> #include<vector> template<class T> void insertion_sort (std::vector<T>& v) { if (v.size()<2U) return; for (size_t index=1; index<v.size(); ++index) { T value = v[index]; size_t gap = index; size_t prev = index-1; while (gap && value<v[left] ) v[gap--]=v[left--]; v[gap] = value; } } int main() { std::vector<int> vect {42, 1, 27, 8, 15, 4}; for (auto v : vect) std::cout << v << '\t'; std::cout << std::endl; insertion_sort (vect); for (auto v : vect) std::cout << v << '\t'; std::cout << std::endl; }
Carbon steels are designated by 4 number referring to the manganese and carbon content (e.g. 1018, 4140, 1095) High speed steel use a letter and number configuration for their designation. The high speed steels designations begin with one of two letters either an M for Molybdenum type or T for Tungsten type high speed steels. ( e.g. M-2, M-4, M-48 or T-1, T-15)
Quicksort in any programming language is an algorithm for sorting data sequences. It is typically implemented as follows (example demonstrates a quicksort of an array of type int). Note that a half-open range, [begin:end), includes the one-past-the-end of the range and is the conventional means of defining a range of contiguous array values. When begin==end, the range is deemed empty. // forward declarations void qsort (int* unsigned); // this is the function you will actually invoke void qsort_rec (int*, int*); // recursive function int* partition (int*, int*); // utility functions... int* select_pivot (int*, int*); void swap (int*, int*); int count (int*, int*); // sort a data sequence of length size void qsort (int* data, unsigned size) { qsort_rec (data, data + size); } // recursively sort the half-open range [begin:end) void qsort_rec (int* begin, int* end) { if (count (begin, end) < 2) return; // end point of recursion int* pivot = partition (begin, end); qsort_rec (begin, pivot); qsort_rec (++pivot, end); } // divide the half-open range [begin:end) into two around a pivot value int* partition (int* begin, int* end) { if (count (begin, end) < 2) return begin; int* pivot = select_pivot (begin, end); swap (begin, pivot); --end; while (begin != end) { while (*(begin) <= *pivot && begin != end) ++begin; while (*pivot < *(end) && begin != end) --end; if (begin!=end) swap (begin, end); } assert (begin==end); // sanity check! swap (pivot, begin); return begin; } // select the median of three from a half-open range [begin:end) int* select_pivot (int* begin, int* end) { int* mid = begin + (count (begin, end) / 2); if (*end<*begin) swap (begin, end); if (*mid<*begin) swap (begin, mid); if (*end<*mid) swap (mid, end); return end; } // swap the values referred to by p and q void swap (int* p, int* q) { if (!p !q) return; // sanity check! int t = *p; *p = *q; *q = t; } // count the elements in the half-closed range [begin:end) int count (int* begin, int* end) { int cnt = 0; int add; if (begin>end) { // swap pointers if the range is reversed int* t = begin; begin = end; end = t; add = -1; // count will be negative } else { add = 1; // count will be positive } while (begin++!=end) cnt+=add; return cnt; }
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Using stacks won't remove recursion, they can only re-implement those recursions. In some cases we don't actually need a stack to implement a recursive algorithm, in which case an iterative implementation will typically perform better with little to no cost in additional memory. But if we require a stack in order to implement recursions iteratively, then we pay the cost in terms of additional memory consumption (the "built-in" call stack is fixed-size and exists whether we use it or not). In addition, there may be a performance cost if we cannot determine how much additional memory we need. As an example, consider the recursive quicksort algorithm: template<typename T>using iter = std::vector<T>::iterator; template<typename T>void quicksort (iter begin, iter end) { if (begin<end) { size_t pivot = partition (begin, end); quicksort (begin, pivot - 1); quicksort (pivot + 1, end); } // end if } Note that the partition algorithm is not shown for the sake of brevity. However, it is best implemented as a separate function as its local variables play no part in the recursion. Being a divide-and-conquer algorithm, this algorithm requires a stack for back-tracking. Here is the iterative equivalent using a stack: template<typename T>using iter = std::vector<T>::iterator; template<typename T>void quicksort (iter begin, iter end) { if (begin<end) { std::stack<std::pair<iter, iter>> s {}; s.push ({begin, end}); while (s.empty() == false) { begin = s.top().first(); end = s.top().second(); s.pop(); size_t pivot = partition (begin, end); if (pivot + 1<end) s.push ({pivot + 1, end}); if (begin<pivot - 1) s.push ({begin, pivot - 1}); } // end while } // end if } Note that the order we push the pairs on at the end of the while loop is the reverse order we wish them to be processed. The order doesn't actually matter, but it ensures both algorithms operate in a consistent manner, with depth-first traversal from left to right. This implementation is naive because each push allocates new memory for each pair object we push onto the stack, releasing the same memory with each pop. Allocating and releasing system memory on a per-element basis like this is highly inefficient, so it's highly unlikely that this version will perform any better than the recursive algorithm. However, the quicksort algorithm guarantees that there can never be more elements on the stack than there are elements in the initial range, so we can improve performance significantly by reserving sufficient memory in advance: template<typename T>using iter = std::vector<T>::iterator; template<typename T>void quicksort (iter begin, iter end) { if (begin<end) { std::vector<std::pair<iter, iter>> v {}; v.reserve (end - begin); v.emplace_back (begin, end); while (v.empty() == false) { begin = v.back().first(); end = v.back().second(); v.pop_back(); size_t pivot = partition (begin, end); if (begin < pivot - 1) v.emplace_back (begin, pivot - 1); if (pivot + 1 < end) v.emplace_back (pivot + 1, end); } // end while } // end if } Note that in this implementation we use a vector rather than a stack, however all pops and pushes (implemented as emplace_back operations) occur at the back of the vector where the unused elements are, and that's precisely how an efficient stack should be implemented. As a result, this version will perform significantly better than the previous version and should perform at least as well as the recursive implementation if not better. The only significant cost is the cost of reserving memory in the vector.
Some words that begin with the letter T and end with the letter K are:tacktalkteakthickticktooktracktrektricktrucktrunktuck
Some four-letter words that begin with "a" and end with "t" are "chat," "that," and "swat."
teapot
Some 5 letter words that begin with T:tabbytabletabletackytaffytainttakentalontapirtardytarrytastetaunttawnyteachteenyteethtempotenortensetepeetepidtersethanktheftthemetherethesethickthiefthinethingthinkthirdthongthornthreethrewthrobthrowthumbtidaltigertighttinkletitletoasttokentongstoothtopictorchtotaltouchtoughtracetracktradetrailtraintraittramptrashtreattrialtribetricktriketrouttrucktrunktrusttruthtuliptumortwist
Some prepositions that begin with the letter T are: through, towards, to, till, throughout, and toward.
Tetrodotoxin is a poison. It begins with the letter t.
tundra
tarragonthymetansy
turnovers
tabulatetalktastetangotelephonethinkthrowtickletranscribetranslatetransporttraveltugtutortype
Tiger.
typhoid