1.5.3.9 Math

• An example about partial_sum
  std::vector<int>v(10, 2);  ______________________________// new initialize method 
  std::partial_sum(v.begin(), v.end(), 
            std::ostream_iterator<int>(std::cout, "␣")); 
      //2 4 6 8 10 12 
   
  std::partial_sum(v.begin(), v.end(), v.begin(), 
                              std::multiplies<int>()); 
  std::cout << "The␣first␣10␣powers␣of␣2␣are:␣"; 
   for (auto n : v) { 
        //2 4 8 16 32 
      }
• An example about accumulate
  std::vector<int> v{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; 
  int sum = std::accumulate(v.begin(), v.end(), 0); 
  int product = std::accumulate(v.begin(), v.end(), 1, 
                                             multiplies<int>()); 
   
  std::string s = std::accumulate(v.begin(), v.end(), 
                                          std::string{}, 
                               [](const std::string& a, int b) { 
                 return a.empty() ? to_string(b) 
                                 : a + ’-’ + to_string(b); }); 
                           _____________________________________________ to_string is in C++11
• An example about adjacency_difference
   v = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}; 
      std::adjacent_difference(v.begin(), v.end() - 1, 
                           v.begin() + 1, std::plus<int>()); 
            //fibonacci
• difference some algorithms
  1. For accumulate, input a init, –>calculate(init, element)–>return it to init.
  2. For adjacent_difference: first -> dfirst, f(first+1, first)–>dfirst+1; Pay attention, for first element, assign it directly.
  3. For partial_sum function, you can think it as accumulate, accumulate just return one value, but partial_sum return many value, and write them back to target iterators one by one.
  4. accumulate and inner_product return one value, partial_sum and adjacent_difference return a list of value.