//版本1 template <class InputIterator,class T> T accumulate(InputIterator first,InputIterator last,T init){for(;first != last; ++first){init += *first; //將每個元素數值累加到init身上}return init; }//版本2 template <class InputIterator,class T,class BinaryOperation> T accumulate(InputIterator first,InputIterator last,T init,BinaryOperation binary_op){for(;first!=last;++first){init = binary_op(init, *first);//對每一個元素執行二元操作}return init; }

• accumulate用于計算init和[first , last)內部所有元素的總和。需要提供一個init，表示當[first,last)為空的區間仍然可以獲取一個明確定義的數值，如果想獲得[first,last)內所有數值的總和，應將init設為0
• 二元操作符不必滿足交換律和結合律，是的accumulate的行為順序有著明確的定義：先將init初始化，然后針對[first,last)區間內的每一個迭代器i，依次執行init = init + *i(第一版本) 或者 init = binary_op(init, *i) (第二版本)

使用例子

#include <iostream> //std::cout #include <functional> //std::minuc #include <numeric> //std::accumulateint my_function(int x,int y){return x + 2*y;} struct my_class{int operator()(int x,int y){return x + 3*y;} }my_object;int main(){int init = 100;int numbers[] = {10,20,30}; // std::cout << << std::endl;std::cout << "using default accumulate" << std::endl;std::cout << std::accumulate(numbers,numbers+3,init) << std::endl;std::cout << "using functional's accumulate" << std::endl;std::cout << std::accumulate(numbers,numbers+3,init,std::minus<int>()) << std::endl;std::cout << "using custom function" << std::endl;std::cout << std::accumulate(numbers,numbers+3,init, my_function) << std::endl;std::cout << "using custom object" << std::endl;std::cout << std::accumulate(numbers,numbers+3,init, my_object) << std::endl;}

adjacent_difference

• 用于計算[first,last)中相鄰元素的差額
• 將*first 賦值給*result，并針對[first+1,last)內的每個迭代器i 將*i-*（i-1）的數值賦值給*（result+（i-first））
• 使用就地方式 也就是讓result 等于first 函數為質變算法
• 存儲第一元素的數值然后存儲后繼元素的差值，便可=可以重建輸入區間的原始內容
• adjacent_difference 和 partial_sum互為逆運算，如果對區間1 2 3 4 5 執行adjacent_difference結果為1 1 1 1 1，如果對這個結果執行partial_sum 便會得到原始的區間數值為1 2 3 4 5

#include <iostream> //std::cout #include <functional> //std::minuc #include <numeric> //std::adjacent_differencetemplate <class InputIterator,class OutputIterator> OutputIterator adjacent_difference(InputIterator first,InputIterator last,OutputIterator result){if(first != last){typename std::iterator_traits<InputIterator>::value_type val,prev;*result = prev = *first;while (++first != last){val = *first;*++result = val - prev; //*++result = binary_op(val,prev);prev = val;}++result;}return result; }template <class InputIterator,class OutputIterator,class BinaryOperation> OutputIterator adjacent_difference(InputIterator first,InputIterator last,OutputIterator result,BinaryOperation binary_op){if (first!=last){typename std::iterator_traits<InputIterator>::value_type val,prev;*result = prev = *first;while(++first != last){val = *first;*++result = binary_op(val,prev);prev = val;}}return result; }//int my_function(int x,int y){return x + 2*y;} //struct my_class{ // int operator()(int x,int y){ // return x + 3*y; // } //}my_object;int myop(int x,int y){return x+y; }int main(){int val[] = {4,2,3,5,9,11,12};int result[7];std::adjacent_difference(val,val+7,result);std::cout << "using default adjacent_difference" << std::endl;for (int i = 0; i < 7; ++i) {std::cout << result[i] << ' ';}std::cout << std::endl;std::adjacent_difference(val,val+7,result,std::multiplies<int>());std::cout << "using functional operation multiplies" << std::endl;for (int i = 0; i < 7; ++i) {std::cout << result[i] << ' ';}std::cout << std::endl;std::adjacent_difference(val,val+7,result, myop);std::cout << "using custom function" << std::endl;for (int i = 0; i < 7; ++i) {std::cout << result[i] << ' ';}std::cout << std::endl;// using default adjacent_difference // 4 -2 1 2 4 2 1 // using functional operation multiplies // 4 8 6 15 45 99 132 // using custom function // 4 6 5 8 14 20 23}

inner_product

• 執行兩個序列的一般內積
• 算法計算 [first1,last1) 和 [first2,first2 + （last1 - first1）)的一般內積
• 需要提供初始數值，用于區間為空的時候得到一個明確定義的結果

#include <iostream> //std::cout #include <functional> //std::minuc #include <numeric> //std::adjacent_differencetemplate <class InputIterator,class OutputIterator,class T> T inner_product(InputIterator first1,InputIterator last1,InputIterator first2,T init){while (first1 != last1){init =init + (*first1) * (*first2);++first1;++first2;}return init; }template <class InputIterator,class OutputIterator,class T,class BinaryOperation1,class BinaryOperation2> T inner_product(InputIterator first1,InputIterator last1,InputIterator first2,T init,BinaryOperation1 binary_op1,BinaryOperation2 binary_op2){//以第一序列的元素個數為依據，將兩個序列都遍歷一遍while (first1 != last1){init = binary_op1(init,binary_op2(*first1,*first2));++first1;++first2;}return init; }int myaccumulator(int x,int y){return x-y;} int myproduct(int x,int y){return x+y;}int main(){int init = 100;int series1[] = {10,20,30};int series2[] = {1,2,3};std::cout << "using default inner_product" << std::endl;std::cout << std::inner_product(series1,series1+3,series2,init); // for (int i = 0; i < 7; ++i) { // std::cout << result[i] << ' '; // }std::cout << std::endl;std::cout << "using functional operations" << std::endl;std::cout << std::inner_product(series1,series1+3,series2,init,std::minus<int>(),std::divides<int>()); // for (int i = 0; i < 7; ++i) { // std::cout << result[i] << ' '; // }std::cout << std::endl;std::cout << "using custom functions" << std::endl;std::cout << std::inner_product(series1,series1+3,series2,init, myaccumulator, myproduct); // for (int i = 0; i < 7; ++i) { // std::cout << result[i] << ' '; // }std::cout << std::endl; // using default inner_product // 240 = 100 + (10*1) + (20*2) + (30*3) // using functional operations // 70 = 100 - (10/1) - (20/2) - (30/3) // using custom functions // 34 = 100 - (10+1) - (20+2) - (30+3) }

partial_sum

• partial_sum用于計算局部總和，將*first賦值給*result，將*first和*（first+1）的數值的和賦值給*（result+1）
• 可以轉化為質變算法
• 函數返回 result + （last - first）
• 和先前介紹的adjacent_difference互為逆運算

?

#include <iostream> //std::cout #include <functional> //std::minuc #include <numeric> //std::adjacent_differencetemplate <class InputIterator,class OutputIterator> OutputIterator partial_sum(InputIterator first,InputIterator last,OutputIterator result){if (first != last){typename std::iterator_traits<InputIterator>::value_type val = *first;*result = val;while (++first!=last){val = val + *first;*++result = val;}++result;}return result; }template <class InputIterator,class OutputIterator,class BinaryOperation> OutputIterator partial_sum(InputIterator first,InputIterator last,BinaryOperation binary_op,OutputIterator result){if (first != last){typename std::iterator_traits<InputIterator>::value_type val = *first;*result = val;while (++first!=last){val = binary_op(val,*first);*++result = val;}++result;}return result; }//int myaccumulator(int x,int y){return x-y;} //int myproduct(int x,int y){return x+y;}int myop(int x,int y){return x+y+1;}int main(){ // int init = 100;int series1[] = {1,2,3,4,5};int result[5];std::cout << "using default partial_sum" << std::endl;std::partial_sum(series1,series1+5,result);for (int i = 0; i < 5; ++i) {std::cout << result[i] << ' ';}std::cout << std::endl;std::cout << "using functional operation multiplies" << std::endl;std::partial_sum(series1,series1+5,result,std::multiplies<int>());for (int i = 0; i < 5; ++i) {std::cout << result[i] << ' ';}std::cout << std::endl;std::cout << "using custom functions" << std::endl;std::partial_sum(series1,series1+5, result,myop);for (int i = 0; i < 5; ++i) {std::cout << result[i] << ' ';}std::cout << std::endl; // using default partial_sum // 1 3 6 10 15 // using functional operation multiplies // 1 2 6 24 120 // using custom functions // 1 4 8 13 19 }

Power

• ?計算某數的n冪次方 即自己對自己進行某種運算到達n次
• 運算類型可以由外界指定，如果指定為乘法那就是 乘冪
• 目前使用pow替代

//版本1 乘冪 template <class T,class Integer> inline T power(T x,Integer n){return power(x,n,std::multiplies<T>()); }//冪次方 指定為乘法運算，則當n >= 0 返回 x^n //需要滿足結合律 但是不需要滿足交換律 template <class T,class Integer,class MonoidOperation> T power(T x,Integer n,MonoidOperation op){if (n==0){return identity_element(op);} else{while((n&1)==0){n>>=1;x = op(x,x);}T result = x;n >> 1;while(n!=0){x = op(x,x);if ((n&1)!=0)result = op(result,x);n >>= 1;}return result;} }

itoa

• ?用于設定某個區間的內容，使其內的每一個元素從指定的value數值開始，呈現遞增的狀態
• 質變算法
• 在[first，last)區域內填入 value ，value+1,value+2

template <class ForwardIterator,class T> void iota(ForwardIterator first,ForwardIterator last,T value){while(first != last){*first++ = value++;} }

參考鏈接

• accumulate - C++ Reference
• adjacent_difference - C++ Reference
• inner_product - C++ Reference
• https://www.cplusplus.com/reference/numeric/partial_sum/?kw=partial_sum
• pow - C++ Reference

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