1098 Insertion or Heap Sort

According to Wikipedia:

Insertion sort iterates, consuming one input element each repetition, and growing a sorted output list. Each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list, and inserts it there. It repeats until no input elements remain.

Heap sort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element and moving that to the sorted region. it involves the use of a heap data structure rather than a linear-time search to find the maximum.

Now given the initial sequence of integers, together with a sequence which is a result of several iterations of some sorting method, can you tell which sorting method we are using?

Input Specification:
Each input file contains one test case. For each case, the first line gives a positive integer N (≤100). Then in the next line, N integers are given as the initial sequence. The last line contains the partially sorted sequence of the N numbers. It is assumed that the target sequence is always ascending. All the numbers in a line are separated by a space.

Output Specification:
For each test case, print in the first line either “Insertion Sort” or “Heap Sort” to indicate the method used to obtain the partial result. Then run this method for one more iteration and output in the second line the resuling sequence. It is guaranteed that the answer is unique for each test case. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.
分析：
给定初始序列a和进行部分排序的序列b，问这是哪种排序方式，并且再用该规则进行一次排序，然后输出排序后的序列。
先判断是否是插入排序。因为若为插入排序的话，那么b中前部分是有序的，而后一部分则与a相对应的位置元素相同。
如果是堆排序的话，则从后往前找，找到未排序的那段的最后一个元素，然后与第一个元素（未排序中最大的值）进行交换。接着进行堆的调整。重点是进行堆的调整。
参考代码：（代码参考了别人的）

#include<iostream>
#include<algorithm>
#include<vector>

using namespace std;
int main()
{
    int n;
    scanf_s("%d", &n);
    vector<int>a(n + 1), b(n + 1);
    for (int i = 1; i <= n; i++) {
        scanf_s("%d", &a[i]);
    }
    for (int i = 1; i <= n; i++) {
        scanf_s("%d", &b[i]);
    }
    int i = 1;
    while (b[i] <= b[i + 1])i++;
    int j = i + 1;
    while (j <= n && a[j] == b[j])j++;
    if (j == n + 1) {
        cout << "Insertion Sort" << endl;
        sort(b.begin() + 1, b.begin() + i + 2);
    }
    else {
        cout << "Heap Sort" << endl;
        for (i = n; i >= 2; i--) {
            if (b[i] < b[i - 1])break;
        }
        swap(b[1], b[i]);
        int high = i - 1; i = 1; j = 2 * i;
        while (j <= high)
        {
            if (j + 1 <= high && b[j] < b[j + 1])
                j = j + 1;
            if (b[j] > b[i]) {
                swap(b[i], b[j]);
                i = j;
                j = 2 * i;
            }
            else { break; }
        }
    }
    int flag = 0;
    for (int i = 1; i <= n; i++) {
        if (flag)
            cout << " ";
        else flag = 1;
        cout << b[i];
    }

    return 0;
}

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