Period 3 element phosphorus originates from oxidation of the white (but not red) phosphorus and should be called chemiluminescence. It is also the lightest element to easily produce stable exceptions to the octet rule. The vast majority of phosphorus compounds are consumed as fertilizers. Other applications include the role of organophosphorus compounds in detergents, pesticides and nerve agents, and matches. "Sulfur" (symbol S) is an abundant, multivalentnon-metal. Under normal conditions, sulfur atoms form cyclic octatomic molecules with chemical formula S. Elemental sulfur is a bright yellow crystalline solid when at room temperature. Chemically, sulfur can react as either an oxidant or reducing agent.
Red–black tree has at least: internal nodes. Using this lemma we can now show that the height of the tree is logarithmic. Since at least half of the nodes on any path from the root to a leaf are black (property 4 of a red–black tree), the black-height of the root is at least h(root)/2. By the lemma we get: Therefore, the height of the root is . In addition to the single-element insert, delete and lookup operations, several set operations have been defined on red-black trees: union, intersection and set difference. Then fast "bulk" operations on insertions or deletions can be