To compute the sum of all left leaf nodes in a binary tree, implement a recursive traversal that identifies nodes where the left child exists and has no children. When such a node is found, accuumlate its value.

A helper function using reference accumulation:

void accumulateLeftLeafSum(TreeNode* root, int& total) {
    if (!root) return;
    if (root->left && !root->left->left && !root->left->right) {
        total += root->left->val;
    }
    accumulateLeftLeafSum(root->left, total);
    accumulateLeftLeafSum(root->right, total);
}

A self-contained recursive solution returning the sum:

int computeLeftLeafTotal(TreeNode* root) {
    if (!root) return 0;
    int leftSubtree = computeLeftLeafTotal(root->left);
    if (root->left && !root->left->left && !root->left->right) {
        leftSubtree = root->left->val;
    }
    int rightSubtree = computeLeftLeafTotal(root->right);
    return leftSubtree + rightSubtree;
}

The algorithm processes each node once, checking for left leaves during traversal. The right subtree is always fully explored regarldess of left leaf presence.