How to get rid of this global variable when using the recursion? - c++

Question

First of all, I don't want to use sort. This is just an illustration example. The main purpose of this question is that I want to:
find all possible combinations of m numbers out of n numbers and
process them, then return the unique processed result (since the
processed results of all possible combinations will be compared).
Question start at here
The following code get all possible combinations M numbers out of N numbers. Sum the M numbers and find the largest sum. In doing this I used a recursion function.
However, it seems that I must define a global variable to store the temporary largest sum. Is there any way to get rid of this global variable? For example, define the recursion function to return the largest sum... I don't want the global variable just become an argument &max_sum in the find_sum, since find_sum already have too many arguments.
#include <iostream>
#include <vector>
void find_sum(const std::vector<int>& ar, std::vector<int>& combine,
int index, int start);
int max_sum =0;
int main() {
int N = 10;
int M = 3;
std::vector<int> ar(N);
ar = {0,9,2,3,7,6,1,4,5,8};
int index = 0, start =0;
std::vector<int> combine(M);
find_sum(ar, combine, index, start);
std::cout << max_sum <<std::endl;
return 0;
}
void find_sum(const std::vector<int>& ar, std::vector<int>& combine,
int index, int start) {
if(index == combine.size()) {
int sum =0;
for(int i=0; i<index; ++i) {
sum += combine[i];
}
if(max_sum < sum) {
max_sum = sum;
}
return ;
}
for(int i = start;
i < ar.size() && ar.size()-i > combine.size()-index;
++i) {
combine[index] = ar[i];
find_sum(ar, combine, index+1, start+1);
}
}

Answer 1

An approach that scales well is to turn find_sum into a function object. The trick is to define a struct with an overloaded () operator that takes a certain set of parameters:
struct FindSum
{
void operator()(const std::vector<int>& ar, std::vector<int>& combine,
int index, int start){
/*ToDo - write the function here, a very explicit way of
/*engineering the recursion is to use this->operator()(...)*/
}
int max_sum; // I am now a member variable
};
Then instantiate FindSum find_sum;, set find_sum.max_sum if needed (perhaps even do that in a constructor), then call the overloaded () operator using find_sum(...).
This technique allows you to pass state into what essentially is a function.

Answer 2

From find_sum, return the so-far maximum sum (instead of void). That means that the recursion-terminating code would be:
if(index == combine.size()) {
int sum =0;
for(int i=0; i<index; ++i) {
sum += combine[i];
}
return sum;
}
and the recursive part would be
int max_sum = 0;
for(int i = start;
i < ar.size() && ar.size()-i > combine.size()-index;
++i) {
combine[index] = ar[i];
int thismaxsum = find_sum(ar, combine, index+1, start+1);
if(thismaxssum > max_sum)
max_sum = thismaxsum;
}
return max_sum;
So, the overall solution is:
#include <iostream>
#include <vector>
int find_sum(const std::vector<int>& ar, std::vector<int>& combine,
int index, int start);
int main() {
int N = 10;
int M = 3;
std::vector<int> ar(N);
ar = { 0,9,2,3,7,6,1,4,5,8 };
int index = 0, start = 0;
std::vector<int> combine(M);
int max_sum = find_sum(ar, combine, index, start);
std::cout << max_sum << std::endl;
return 0;
}
int find_sum(const std::vector<int>& ar, std::vector<int>& combine,
int index, int start)
{
if (index == combine.size())
{
int sum = 0;
for (int i = 0; i<index; ++i)
{
sum += combine[i];
}
return sum;
}
int max_sum = 0;
for (int i = start;
i < ar.size() && ar.size() - i > combine.size() - index;
++i)
{
combine[index] = ar[i];
int thismaxsum = find_sum(ar, combine, index + 1, start + 1);
if (thismaxsum > max_sum)
max_sum = thismaxsum;
}
return max_sum;
}

Answer 3

Global variables are much better then adding operands and variables to recursion functions because each operand and variable causes heap/stack trashing negatively impact performance and space usage risking stack overflow for higher recursions.
To avoid global variables (for code cosmetics and multi threading/instancing purposes) I usually use context or temp struct. For example like this:
// context type
struct f1_context
{
// here goes any former global variables and stuff you need
int n;
};
// recursive sub function
int f1_recursive(f1_context &ctx)
{
if (ctx.n==0) return 0;
if (ctx.n==1) return 1;
ctx.n--;
return (ctx.n+1)*f1_recursive(ctx.n);
}
// main API function call
int f1(int n)
{
// init context
f1_context ctx;
ctx.n=n;
// start recursion
return f1_recursion(ctx);
}
the f1(n) is factorial example. This way the operands are limited to single pointer to structure. Of coarse you can add any recursion tail operands after the context... the context is just for global and persistent stuff (even if I did use it for the recursion tail instead but that is not always possible).