When we practice LeetCode questions, we always need to write a helper recursive function outside the main solution function. For example, to find the max value in a binary tree, we can have the following codes: (method-1)

class Solution {
// pre-order DFS
void helper(TreeNode *root, int &ret) {
if (!root)
return;
ret = std::max(ret, root->val);
helper(root->left);
helper(root->right);
}

public:
int findMax(TreeNode *root) {
int maxval = std::numeric_limits<int>::min();

helper(root, maxval);

return maxval;
}
};

Sometimes we don’t want to write the helper outside our working function, i.e. findMax in previous example. The reasons can be different. For me, I don’t want to add the reference type parameter ret. In fact, for questions in LeetCode, we always need to add many reference type parameters, such as problems related to backtracking. Since C++11, we can write lambda, further more, recursive lambda locally. This relies on the standard function type. (method-2)

class Solution {
public:
int findMax(TreeNode *root) {
int maxval = std::numeric_limits<int>::min();

// pre-order DFS
function<void(TreeNode*)> helper = [&](TreeNode *root) {
if (!root)
return;
maxval = std::max(ret, root->val);
helper(root->left);
helper(root->right);
};

helper(root);

return maxval;
}
};

In the code above, [&] indicates the helper lambda to capture the local variables (by references) before the statement. Actually, for the inside call of helper, it also references the name of itself. That’s why we cannot change function<void(TreeNode*)> to auto. If we use auto, the call to helper inside the function body will make it impossible for compiler to deduce the type of helper.

But we really do not want function<void(TreeNode*)>, because it is too long and it has the same content as (TreeNode *root) later. The reason we want to write lambda is to reduce length, but method-2 seems to make it longer (actually running time also becomes longer).

Luckily, since C++14, we have a better way to do it, that is the generic lambda. We still cannot use helper inside the lambda body for same reason. But taking advantages of generic parameter, here we have a more tricky way to do it. (method-3)

class Solution {
public:
int findMax(TreeNode *root) {
int maxval = std::numeric_limits<int>::min();

// pre-order DFS
auto helper = [&](auto &&self, auto root) {
if (!root)
return;
maxval = std::max(ret, root->val);
self(self, root->left);
self(self, root->right);
};

helper(helper, root);

return maxval;
}
};

This code can successfully compile and result in relatively same runtime efficiency as method-1. We avoid the call to helper inside the body. Instead, we introduce an r-value reference parameter called self. In this way, compiler can deduce out the type of helper when we call it later by helper(helper, root).

auto &&self can also be const auto &self to fit both l-value and r-value.

The reason why method-2 is slightly slower than method-1 and method-3 might be that capture by [&] has more overheads than directly pass the r-value reference argument. For more details, please refer to the reference links below.

Recursive lambda functions in C++14 - Stack Overflow

Recursive lambdas in C++(14) - Pedro Melendez