The field of study concerned with the theoretical and practical aspects of computing and computer technology is commonly referred to as Computer Science. The tree T is a left-child, right-sibling tree comprising n nodes, where each node contains a score represented by a positive real integer greater than zero. Determine a subset S from the set of all nodes that maximises the total sum of their respective scores, subject to the constraint that both a node and its child cannot be included in S. Compose a C++ function to resolve the maximum sum for nodes based on the given criteria. Evaluate the duration of programme execution.

The field of study concerned with the theoretical and practical aspects of computing and computer technology is commonly referred to as Computer Science. The tree T is a left-child, right-sibling tree comprising n nodes, where each node contains a score represented by a positive real integer greater than zero. Determine a subset S from the set of all nodes that maximises the total sum of their respective scores, subject to the constraint that both a node and its child cannot be included in S. Compose a C++ function to resolve the maximum sum for nodes based on the given criteria. Evaluate the duration of programme execution.