转自：http://blog.csdn.net/gigglesun/article/details/5570611
Data Structures with C++ using STL, 2nd Edition这本书有一个比较好的例子：
【The program compares the efficiency of the sequential and binary search by timing algorithm execution using the timer class.
Two integer arrays list1 and list2 of size ARRAY_SIZE are initialized with the same random integers in the range 0 to 999,999.
Initialize the array targetList having TARGET_SIZE elements to contain other random numbers in the same range.
Time the selection sort as it sorts list2 and output the result. using the elements in array targetList as target values for the sequential and binary searches,
time each algorithm and output the results. 】
即：这段示例代码自定义了timer类（使用clock()函数）、random类、heap 类，用于比较顺序查找和二分查找的效率。编写比较规范，适合模仿。
1.main.cpp
main.cpp
#include <iostream> #include "d_search.h" // generic sequential and binary searches #include "d_sort.h" // generic selection sort #include "d_random.h" // random number generation #include "d_timer.h" // time events using namespace std; int main() { const int ARRAY_SIZE = 100000, TARGET_SIZE = 50000; // arrays for the search int list1[ARRAY_SIZE], list2[ARRAY_SIZE], targetList[TARGET_SIZE]; int i; // t used for timing the search algorithms timer t; // random number object randomNumber rnd; // initialize the arrays with random numbers in the // range 0 to 999,999 for (i = 0; i < ARRAY_SIZE; i++) list1[i] = list2[i] = rnd.random(1000000); // initialize targetList with random numbers in the // same range 0 to 999,999 for (i=0;i < TARGET_SIZE; i++) targetList[i] = rnd.random(1000000); // sort list2 cout << "Timing the Selection Sort" << endl; t.start(); // start timer selectionSort(list2,ARRAY_SIZE); t.stop(); // stop timer cout << "Selection Sort takes " << t.time() << " seconds." << endl; cout << endl << "Timing the Sequential Search" << endl; t.start(); // start timer // perform sequential search with elements from list2 for (i = 0; i < TARGET_SIZE; i++) seqSearch(list1,0,ARRAY_SIZE,targetList[i]); t.stop(); // stop timer cout << "Sequential Search takes " << t.time() << " seconds." << endl; cout << endl << "Timing the Binary Search" << endl; t.start(); // start timer // perform binary search with elements from list1 for (i = 0; i < TARGET_SIZE; i++) binSearch(list2,0,ARRAY_SIZE,targetList[i]); t.stop(); // stop timer cout << "Binary Search takes " << t.time() << " seconds." << endl; return 0; }
2. d_sort.h
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#ifdef __BORLANDC__ // turn off Borland warning message about comparison of signed and // unsigned values #pragma warn -8012 #endif // __BORLANDC__ #ifndef SORTING_ALGORITHMS #define SORTING_ALGORITHMS #include <vector> #include <queue> #include "d_heap.h" // heap function library using namespace std; // sort an integer array using selection sort void selectionSort(int arr[], int n); // sort an array of type T using selection sort template <typename T> void selectionSort(T arr[], int n); // sort a vector of type T using selection sort template <typename T> void selectionSort(vector<T>& v); // sort a vector of type T using insertion sort template <typename T> void insertionSort(vector<T>& v); // sort the elements of a vector of type T in the range // [first, last) using insertion sort template <typename T> void insertionSort(vector<T>& v, int first, int last); // sort v using the radix sort. each integer has d digits void radixSort(vector<int>& v, int d); // sort a vector using heapsort template <typename T, typename Compare> void heapSort (vector<T>& v, Compare comp); // the elements in the ranges [first,mid) and [mid,last) are // ordered. the function merges the ordered sequences into // an ordered sequence in the range [first,last) template <typename T> void merge(vector<T>& v, int first, int mid, int last); // sorts v in the index range [first,last) by merging // ordered sublists template <typename T> void mergeSort(vector<T>& v, int first, int last); // using the value at the midpoint of [first,last) as the pivot, // locate the pivot in its final location so all elements // to its left are <= to its value and all elements to the // right are >= to its value. return the index of the pivot template <typename T> int pivotIndex(vector<T>& v, int first, int last); // sort a vector using quicksort template <typename T> void quicksort(vector<T>& v, int first, int last); // locate the kth largest element of v at index k template <typename T> void findK(vector<T>& v, int first, int last, int k); // IMPLEMENTATIONS void selectionSort(int arr[], int n) { int smallIndex; // index of smallest element in the sublist int pass, j; int temp; // pass has the range 0 to n-2 for (pass = 0; pass < n-1; pass++) { // scan the sublist starting at index pass smallIndex = pass; // j traverses the sublist arr[pass+1] to arr[n-1] for (j = pass+1; j < n; j++) // update if smaller element found if (arr[j] < arr[smallIndex]) smallIndex = j; // if smallIndex and pass are not the same location, // exchange the smallest item in the sublist with arr[pass] if (smallIndex != pass) { temp = arr[pass]; arr[pass] = arr[smallIndex]; arr[smallIndex] = temp; } } } template <typename T> void selectionSort(T arr[], int n) { int smallIndex; // index of smallest element in the sublist int pass, j; T temp; // pass has the range 0 to n-2 for (pass = 0; pass < n-1; pass++) { // scan the sublist starting at index pass smallIndex = pass; // j traverses the sublist arr[pass+1] to arr[n-1] for (j = pass+1; j < n; j++) // update if smaller element found if (arr[j] < arr[smallIndex]) smallIndex = j; // if smallIndex and pass are not the same location, // exchange the smallest item in the sublist with arr[pass] if (smallIndex != pass) { temp = arr[pass]; arr[pass] = arr[smallIndex]; arr[smallIndex] = temp; } } } template <typename T> void selectionSort(vector<T>& v) { // index of smallest item in each pass int smallIndex; // save the vector size in n int pass, j, n = v.size(); T temp; // sort v[0]..v[n-2], and arr[n-1] is in place for (pass = 0; pass < n-1; pass++) { // start the scan at index pass; set smallIndex to pass smallIndex = pass; // j scans the sublist v[pass+1]..v[n-1] for (j = pass+1; j < n; j++) // update smallIndex if smaller element is found if (v[j] < v[smallIndex]) smallIndex = j; // when finished, place smallest item in arr[pass] if (smallIndex != pass) { temp = v[pass]; v[pass] = v[smallIndex]; v[smallIndex] = temp; } } } template <typename T> void insertionSort(vector<T>& v) { int i, j, n = v.size(); T target; // place v[i] into the sublist // v[0] ... v[i-1], 1 <= i < n, // so it is in the correct position for (i = 1; i < n; i++) { // index j scans down list from v[i] looking for // correct position to locate target. assigns it to // v[j] j = i; target = v[i]; // locate insertion point by scanning downward as long // as target < v[j-1] and we have not encountered the // beginning of the list while (j > 0 && target < v[j-1]) { // shift elements up list to make room for insertion v[j] = v[j-1]; j--; } // the location is found; insert target v[j] = target; } } template <typename T> void insertionSort(vector<T>& v, int first, int last) { int i, j; T target; // place v[i] into the sublist // v[first] ... v[i-1], first <= i < last, // so it is in the correct position for (i = first+1; i < last; i++) { // index j scans down list from v[i] looking for // correct position to locate target. assigns it to // v[j] j = i; target = v[i]; // locate insertion point by scanning downward as long // as target < v[j-1] and we have not encountered the // beginning of the range while (j > first && target < v[j-1]) { // shift elements up list to make room for insertion v[j] = v[j-1]; j--; } // the location is found; insert target v[j] = target; } } // support function for radixSort() // distribute vector elements into one of 10 queues // using the digit corresponding to power // power = 1 ==> 1's digit // power = 10 ==> 10's digit // power = 100 ==> 100's digit // ... void distribute(const vector<int>& v, queue<int> digitQueue[], int power) { int i; // loop through the vector, inserting each element into // the queue (v[i] / power) % 10 for (i = 0; i < v.size(); i++) digitQueue[(v[i] / power) % 10].push(v[i]); } // support function for radixSort() // gather elements from the queues and copy back to the vector void collect(queue<int> digitQueue[], vector<int>& v) { int i = 0, digit; // scan the vector of queues using indices 0, 1, 2, etc. for (digit = 0; digit < 10; digit++) // collect items until queue empty and copy items back // to the vector while (!digitQueue[digit].empty()) { v[i] = digitQueue[digit].front(); digitQueue[digit].pop(); i++; } } void radixSort(vector<int>& v, int d) { int i; int power = 1; queue<int> digitQueue[10]; for (i=0;i < d;i++) { distribute(v, digitQueue, power); collect(digitQueue, v); power *= 10; } } template <typename T, typename Compare> void heapSort (vector<T>& v, Compare comp) { // "heapify" the vector v makeHeap(v, comp); int i, n = v.size(); // iteration that determines elements v[n-1] ... v[1] for(i = n; i > 1;i--) { // call popHeap() to move next largest to v[n-1] popHeap(v, i, comp); } } template <typename T> void merge(vector<T>& v, int first, int mid, int last) { // temporary vector to merge the sorted sublists vector<T> tempVector; int indexA, indexB, indexV; // set indexA to scan sublistA (index range [first,mid) // and indexB to scan sublistB (index range [mid, last) indexA = first; indexB = mid; // while both sublists are not exhausted, compare v[indexA] and // v[indexB]copy the smaller to vector temp using push_back() while (indexA < mid && indexB < last) if (v[indexA] < v[indexB]) { tempVector.push_back(v[indexA]); // copy element to temp indexA++; // increment indexA } else { tempVector.push_back(v[indexB]); // copy element to temp indexB++; // increment indexB } // copy the tail of the sublist that is not exhausted while (indexA < mid) { tempVector.push_back(v[indexA]); indexA++; } while (indexB < last) { tempVector.push_back(v[indexB]); indexB++; } // copy vector tempVector using indexV to vector v using indexA // which is initially set to first indexA = first; // copy elements from temporary vector to original list for (indexV = 0; indexV < tempVector.size(); indexV++) { v[indexA] = tempVector [indexV]; indexA++; } } // sorts v in the index range [first,last) by merging // ordered sublists template <typename T> void mergeSort(vector<T>& v, int first, int last) { // if the sublist has more than 1 element continue if (first + 1 < last) { // for sublists of size 2 or more, call mergeSort() // for the left and right sublists and then // merge the sorted sublists using merge() int midpt = (last + first) / 2; mergeSort(v, first, midpt); mergeSort(v, midpt, last); merge(v, first, midpt, last); } } template <typename T> int pivotIndex(vector<T>& v, int first, int last) { // index for the midpoint of [first,last) and the // indices that scan the index range in tandem int mid, scanUp, scanDown; // pivot value and object used for exchanges T pivot, temp; if (first == last) return last; else if (first == last-1) return first; else { mid = (last + first)/2; pivot = v[mid]; // exchange the pivot and the low end of the range // and initialize the indices scanUp and scanDown. v[mid] = v[first]; v[first] = pivot; scanUp = first + 1; scanDown = last - 1; // manage the indices to locate elements that are in // the wrong sublist; stop when scanDown <= scanUp for(;;) { // move up lower sublist; stop when scanUp enters // upper sublist or identifies an element >= pivot while (scanUp <= scanDown && v[scanUp] < pivot) scanUp++; // scan down upper sublist; stop when scanDown locates // an element <= pivot; we guarantee we stop at arr[first] while (pivot < v[scanDown]) scanDown--; // if indices are not in their sublists, partition complete if (scanUp >= scanDown) break; // indices are still in their sublists and identify // two elements in wrong sublists. exchange temp = v[scanUp]; v[scanUp] = v[scanDown]; v[scanDown] = temp; scanUp++; scanDown--; } // copy pivot to index (scanDown) that partitions sublists // and return scanDown v[first] = v[scanDown]; v[scanDown] = pivot; return scanDown; } } template <typename T> void quicksort(vector<T>& v, int first, int last) { // index of the pivot int pivotLoc; // temp used for an exchange when [first,last) has // two elements T temp; // if the range is not at least two elements, return if (last - first <= 1) return; // if sublist has two elements, compare v[first] and // v[last-1] and exchange if necessary else if (last - first == 2) { if (v[last-1] < v[first]) { temp = v[last-1]; v[last-1] = v[first]; v[first] = temp; } return; } else { pivotLoc = pivotIndex(v, first, last); // make the recursive call quicksort(v, first, pivotLoc); // make the recursive call quicksort(v, pivotLoc +1, last); } } template <typename T> void findK(vector<T>& v, int first, int last, int k) { int index; // partition range [first,last) in v about the // pivot v[index] index = pivotIndex(v, first, last); // if index == k, we are done. kth largest is v[k] if (index == k) return; else if(k < index) // search in lower sublist [first,index) findK(v, first, index, k); else // search in upper sublist [index+1,last) findK(v, index+1, last, k); } #endif // SORTING_ALGORITHMS
3. d_search.h
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#ifndef SEARCH_FUNCTIONS #define SEARCH_FUNCTIONS #include <vector> #include <list> using namespace std; // perform a sequential search of an integer array for a target // in the index range [first, last). return the index of a // match or last if the target is not in arr int seqSearch(const int arr[], int first, int last, int target); // perform asequential search for a target in the index range // [first, last). return the index of a match or last if the // target is not in arr template <typename T> int seqSearch(const T arr[], int first, int last, const T& target); // perform a binary search of an integer array for a target // in the index range [first, last). return the index of a // match or last if the target is not in arr int binSearch(const int arr[], int first, int last, int target); // perform a binary search of an array for a target // in the index range [first, last). return the index of a // match or last if the target is not in arr template <typename T> int binSearch(const T arr[], int first, int last, const T& target); // vector version of the sequential search template <typename T> int seqSearch(const vector<T>& v, int first, int last, const T& target); // vector version of the binary search template <typename T> int binSearch(const vector<T>& v, int first, int last, const T& target); // perform the sequential search for target in the list // iterator range [first, last). return an iterator pointing // at the target in the list or last if target is not found template <typename T> typename list<T>::iterator seqSearch(typename list<T>::iterator first, typename list<T>::iterator last, const T& target); // perform the sequential search for target in the container // iterator range [first, last). return an iterator pointing // at the target in the container or last if target is not // found template <typename Iterator, typename T> Iterator find(Iterator first, Iterator last, const T& target); // *********************************************************** // search function implementations // *********************************************************** int seqSearch(const int arr[], int first, int last, int target) { int i; // scan indices in the range first <= i < last for(i=first; i < last; i++) if (arr[i] == target) return i; // immediately return on a match return last; // return last if target not found } template <typename T> int seqSearch(const T arr[], int first, int last, const T& target) { int i; // scan indices in the range first <= i < last for(i=first; i < last; i++) if (arr[i] == target) // assume T has the "==" operator return i; // immediately return on a match return last; // return last if target not found } int binSearch(const int arr[], int first, int last, int target) { int mid; // index of the midpoint int midValue; // object that is assigned arr[mid] int origLast = last; // save original value of last while (first < last) // test for nonempty sublist { mid = (first+last)/2; midValue = arr[mid]; if (target == midValue) return mid; // have a match // determine which sublist to search else if (target < midValue) last = mid; // search lower sublist. reset last else first = mid+1; // search upper sublist. reset first } return origLast; // target not found } template <typename T> int binSearch(const T arr[], int first, int last, const T& target) { int mid; // index of the midpoint T midValue; // object that is assigned arr[mid] int origLast = last; // save original value of last while (first < last) // test for nonempty sublist { mid = (first+last)/2; midValue = arr[mid]; if (target == midValue) return mid; // have a match // determine which sublist to search else if (target < midValue) last = mid; // search lower sublist. reset last else first = mid+1; // search upper sublist. reset first } return origLast; // target not found } template <typename T> int seqSearch(const vector<T>& v, int first, int last, const T& target) { int i; // scan indices in the range first <= i < last for(i=first; i < last; i++) if (v[i] == target) // assume T has the "==" operator return i; // immediately return on a match return last; // otherwise return last } template <typename T> int binSearch(const vector<T>& v, int first, int last, const T& target) { int mid; // index of the midpoint T midvalue; // object that is assigned v[mid] int origLast = last; // save original value of last while (first < last) // test for nonempty sublist { mid = (first+last)/2; midvalue = v[mid]; if (target == midvalue) return mid; // have a match // determine which sublist to search else if (target < midvalue) last = mid; // search lower sublist. reset last else first = mid+1; // search upper sublist. reset first } return origLast; // target not found } template <typename T> typename list<T>::iterator seqSearch(typename list<T>::iterator first, typename list<T>::iterator last, const T& target) { // start at location first list<T>::iterator iter = first; // compare list elements with item until either // we arrive at last or locate item while(iter != last && !(*iter == target)) iter++; // iter either points at item or is last return iter; } template <typename Iterator, typename T> Iterator find(Iterator first, Iterator last, const T& target) { Iterator iter = first; // scan iterator range [first, last), stopping // if the loop locates target while (iter != last && *iter != target) iter++; // if target located, iter points at it; otherwise // is has value last return iter; } #endif // SEARCH_FUNCTIONS
4. d_random.h
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#include <iostream> #include <time.h> using namespace std; // generate random numbers class randomNumber { public: // initialize the random number generator randomNumber(long s = 0); // return a 32-bit random integer m, 1 <= m <= 2^31-2 long random(); // return a 32-bit random integer m, 0 <= m <= n-1, // where n <= 2^31-1 long random(long n); // return a real number x, 0 <= x < 1 double frandom(); private: static const long A; static const long M; static const long Q; static const long R; long seed; }; const long randomNumber::A = 48271; const long randomNumber::M = 2147483647; const long randomNumber::Q = M / A; const long randomNumber::R = M % A; randomNumber::randomNumber(long s) { if (s < 0) s = 0; if (s == 0) { // get time of day in seconds since 12:00 AM, // January 1, 1970 long t_time = time(NULL); // mix-up bits by squaring t_time *= t_time; // result can overflow. handle cases // > 0, < 0, = 0 if (t_time > 0) s = t_time ^ 0x5EECE66DL; else if (t_time < 0) s = (t_time & 0x7fffffff) ^ 0x5EECE66DL; else s = 0x5EECE66DL; } seed = s; } long randomNumber::random() { long tmpSeed = A * ( seed % Q ) - R * ( seed / Q ); if( tmpSeed >= 0 ) seed = tmpSeed; else seed = tmpSeed + M; return seed; } long randomNumber::random(long n) { double fraction = double(random())/double(M); return int(fraction * n); } double randomNumber::frandom() { return double(random())/double(M); }
5. d_timer.h
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#ifndef TIMER_CLASS #define TIMER_CLASS #include <time.h> // declares clock_t type, function clock(), // and constant CLOCKS_PER_SEC class timer { private: // starting and ending time measured in clock ticks clock_t startTime, endTime; public: timer(); // initialize the timer. // Postconditions: set the starting and ending event times to 0. // this creates an event whose time is 0.0 void start(); // start timing an event. // Postcondition: record the current time as the starting time void stop(); // stop timing an event. // Postconditon: record the current time as the ending time double time() const; // return the time the event took in seconds by computing // the difference between the ending and starting times. }; // *********************************************************** // timer class implementation // *********************************************************** // constructor. set starting and ending times to 0 timer::timer():startTime(0), endTime(0) {} // determine clock ticks at start void timer::start() { startTime = clock(); } // determine clock ticks at end void timer::stop() { endTime = clock(); } // return the elapsed time in seconds double timer::time() const { return (endTime-startTime)/double(CLOCKS_PER_SEC); } #endif // TIMER_CLASS
6. d_heap.h
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#ifndef HEAP_FUNCTIONS #define HEAP_FUNCTIONS #include <vector> #include <functional> using namespace std; // the vector elements in the range [0, last-1) are a heap. // insert the element v[last-1] into the heap so that the // range [0, last) is a heap. use the function object comp // to perform comparisons template <typename T, typename Compare> void pushHeap(vector<T>& v, int last, Compare comp); // filter the vector element v[first] down the heap with index // range [first, last) template <typename T, typename Compare> void adjustHeap(vector<T>& v, int first, int last, Compare comp); // the vector elements in the range [0, last) are a heap. // swap the first and last elements of the heap and then // make the elements in the index range [0, last-1) a heap. // use the function object comp to perform comparisons template <typename T, typename Compare> void popHeap(vector<T>& v, int last, Compare comp); // arrange the vector elements into a heap. use the function // object comp to perform comparisons template <typename T, typename Compare> void makeHeap(vector<T>& v, Compare comp); // implementations template <typename T, typename Compare> void pushHeap(vector<T>& v, int last, Compare comp) { // assume the new item is at location v[last-1] and that // the elements v[0] to v[last-2] are in heap order int currentPos, parentPos; T target; // currentPos is an index that traverses path of parents. // target is value hlist[i] and is repositioned in path currentPos = last-1; parentPos = (currentPos-1)/2; target = v[last-1]; // traverse path of parents up to the root while (currentPos != 0) { // compare target and parent value if (comp(target,v[parentPos])) { // move data from parent position to current // position. update current position to parent // position. compute next parent v[currentPos] = v[parentPos]; currentPos = parentPos; parentPos = (currentPos-1)/2; } else // if !comp(target, parentvalue), heap condition is ok. break break; } // the correct location has been discovered. assign target v[currentPos] = target; } template <typename T, typename Compare> void adjustHeap(vector<T>& v, int first, int last, Compare comp) { int currentPos, childPos; T target; // start at first and filter target down the heap currentPos = first; target = v[first]; // compute the left child index and begin a scan down // path of children, stopping at end of list (last) // or when we find a place for target childPos = 2 * currentPos + 1; while (childPos <= last-1) { // index of right child is childPos+1. compare the // two children. change childPos if // comp(v[childPos+1], v[childPos]) is true if ((childPos+1 <= last-1) && comp(v[childPos+1], v[childPos])) childPos = childPos + 1; // compare selected child to target if (comp(v[childPos],target)) { // comp(selected child, target) is true. // move selected child to the parent; // position of selected child is now vacated v[currentPos] = v[childPos]; // update indices to continue the scan currentPos = childPos; childPos = 2 * currentPos + 1; } else // target belongs at currentPos break; } v[currentPos] = target; } template <typename T, typename Compare> void popHeap(vector<T>& v, int last, Compare comp) { T temp; // exchange the first and last element in the heap temp = v[0]; v[0] = v[last-1]; v[last-1] = temp; // filter down the root over the range [0, last-1) adjustHeap(v, 0, last-1, comp); } template <typename T, typename Compare> void makeHeap(vector<T>& v, Compare comp) { int heapPos, lastPos; // compute the size of teh heap and the index // of the last parent lastPos = v.size(); heapPos = (lastPos - 2)/2; // filter down every parent in order from last parent // down to root while (heapPos >= 0) { adjustHeap(v,heapPos, lastPos, comp); heapPos--; } } #endif // HEAP_FUNCTIONS