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This video explains how to perform insertion sort and merge sort, two algorithms that can be used to sort a list of numbers. The author also explains how to use a skew heap to efficiently merge two lists of numbers.

**00:00:00**In this lecture, the lecturer discusses a new heap type, the skew heap, and how merging works for this heap type. He also discusses an important operation for leftist merging.**00:05:00**Chapter seven of the textbook covers sorting algorithms. The first sorting algorithm discussed is insertion sort, which uses a pass number to keep track of which elements have been sorted. In insertion sort, the elements are sorted in a reverse order from the pass number. The second sorting algorithm discussed is merge sort, which uses a pass number and a list of elements to keep track of the order of the elements.**00:10:00**In this video, the author describes how to perform a set of five passes through a list to find the correct position for a given number. The first pass moves the element at position one to the position zero. The second pass compares the element at position one with the element at position one minus one, and if the former is less, swaps them. The third pass compares the element at position two with the element at position one minus one, and if the former is less, swaps them. The fourth pass compares the element at position three with the element at position one minus one, and if the former is less, swaps them. The fifth pass compares the element at position four with the element at position one minus one, and if the former is less, swaps them.**00:15:00**In this video, the author explains how to perform the three position moves needed in the insertion sort. These moves are 64 to the position 5, 51 to the position 4, and 34 to the position 3.**00:20:00**The algorithm for inserting sorted items into a container can be run in linear time if the number of inversion iterations is known in advance.

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