Builds a complete binary winner tree where each leaf holds an element's span index and each internal node holds the index of the smaller of its two children. Repeatedly reads the global minimum from the root, swaps it to its final sorted position, retires the leaf with a sentinel, and replays only the two affected leaf-to-root paths to restore the tree.
Each extraction costs exactly log₂(n) comparisons, one per internal node on a single path, making it one of the most comparison-efficient selection-based algorithms, at the cost of O(n) auxiliary memory for the winner tree array.