Final answer:
The global and local invariants of red-black trees ensure that the length of the longest path from the root to a leaf can be no more than twice the length of the shortest path. This maintains a balanced tree structure by limiting the height of the tree.
Step-by-step explanation:
The question is about the properties of red-black trees, a type of self-balancing binary search tree, about the length of the longest path from the root to a leaf. Red-black trees have certain global and local invariants that guarantee the tree remains balanced after insertions and deletions.
One of the global properties is that every path from a node to its descendant NULL nodes has the same number of black nodes, known as the black-height. A local property, on the other hand, is that a red node cannot have a red child (red violation). These properties imply that the longest path from the root to a leaf, which is the path with the largest number of black nodes followed by a red node, can be no more than twice the length of the shortest path - the one with only black nodes. In other words, the tree's height is limited in such a way that it's at most twice the black-height.