Chapter 2-InsertionSort

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插入排序(Insertion Sort)的基本思想是：每次将一个待排序的元素，按其大小插入到前面已经排好序的子序列中的适当位置，直到全部元素插入完成为止。
设数组为a[0…n-1]。
1.初始时，a[0]自成1个有序区，无序区为a[1..n-1]。令i=1。
2.将a[i]并入当前的有序区a[0…i-1]中形成a[0…i]的有序区间。
3.i++并重复第二步直到i==n-1。排序完成。

Time Complexity: O(n2)
Space Complexity: O(1)
InsertionSort.cc

#include<iostream>
using namespace std;

template<typename T>
void InsertionSort(T sort_array[], int length);

int main()
{
    int test_array1[10] = {9, 8, 7, 6, 5, 4, 3, 2, 1, 0};
    int test_array2[9] = {5, 0, -99, 3, 56, 7, 8, -55, 56};
    int test_array3[10] = {-1, -8, 50, 4, 20, 0, 45, 9999, 520, 555555};
    InsertionSort(test_array1, 10);
    InsertionSort(test_array2, 9);
    InsertionSort(test_array3, 10);
    cout << "test_array1:\n";
    for(int index = 0; index < 10; index++)
    {
        cout << test_array1[index] << " ";
    }
    cout << "\ntest_array2:\n";
    for(int index = 0; index < 9; index++)
    {
        cout << test_array2[index] << " ";
    }
    cout << "\ntest_array3:\n";
    for(int index = 0; index < 10; index++)
    {
        cout << test_array3[index] << " ";
    }
    cout << endl;

    return 0;
}

template<typename T>
void InsertionSort(T sort_array[], int length)
{
    // sort_index is the index of element that we want to insert now
    // sort_array[0] is automatically sorted, so sort_index begins from 1
    for(int sort_index = 1; sort_index < length; sort_index++)
    {
        // store element in key
        T key = sort_array[sort_index];
        // compare from end to front only use 1 loop: move elements and
        // find proper position to insert key concurrently. Because when we can't move
        // elements, we find the proper position.
        // Otherwise compare from front to end use 2 loops: find the proper position
        // in one loop; and move elements in the other loop.
        int compare_index = sort_index - 1;  // compare from end to front
        while(compare_index >= 0 && sort_array[compare_index] > key)
        // if key is smaller than some elements in the front-sorted-array, then move
        {
            // we assume sort_array[compare_index + 1] = key before moving
            sort_array[compare_index + 1] = sort_array[compare_index];
            compare_index--;  // continue
        }
        // when we can't move elements, we find the proper position to insert key.
        sort_array[compare_index + 1] = key;
    }
}

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