C ++ sorting series (1) Insert sorting-semi-insert sorting

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Binary insertion sort is an improvement in the insertion sorting algorithm. Because the Sorting Algorithm inserts elements into the sequence that has been sorted in sequence. Because the first half is divided into sorted columns, we do not need to look for insertion points in sequence. We can use the half-lookup method to speed up the search for insertion points.

When inserting a new element into an sorted array, when looking for the insertion point, set the first element of the area to a [low]. when the last element is set to a [High], the elements to be inserted during the round comparison will be compared with a [m], where M = (low + high)/2, if it is smaller than the reference element, select a [low] To M-1] as the new inserted area (that is, high = s-1 ), otherwise, select a [M + 1] to a [High] as the new insert area (that is, low = m + 1) Until low <= high is not true, after this position, all elements are moved one by one, and the new element is inserted into a [high + 1].

The semi-insertion sorting algorithm is a stable sorting algorithm, which significantly reduces the number of comparisons between keywords than the direct Insertion Algorithm. Therefore, the speed is faster than the direct insertion sorting algorithm, however, the number of records moving remains unchanged. Therefore, the time complexity of the semi-insertion sorting algorithm is O (n ^ 2), which is the same as that of the direct insertion sorting algorithm. Additional space O (1 ).

Implementation Code:

1 template <typename T> 2 void binary_insert_sort (t v [], const int sz) 3 {4 for (INT I = 1; I <SZ; ++ I) 5 {6 t tmp = V [I]; 7 int low = 0; 8 int high = I-1; 9 10 while (low <= high) 11 {12 int m = (low + high)/2; // half 13 if (TMP <V [m]) 14 {15 high = m-1; // insert point in low half Zone 16} 17 else18 {19 low = m + 1; // insert point in high half zone 20} 21} 22 23 for (Int J = I-1; j> = high + 1; -- j) 24 {25 V [J + 1] = V [J]; 26} 27 V [high + 1] = TMP; // insert 28} 29}