PAT甲级 A1098

PAT甲级 A1098

题目详情

1098 Insertion or Heap Sort (25分)
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 resulting 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.

Sample Input 1:
10
3 1 2 8 7 5 9 4 6 0
1 2 3 7 8 5 9 4 6 0
Sample Output 1:
Insertion Sort
1 2 3 5 7 8 9 4 6 0
Sample Input 2:
10
3 1 2 8 7 5 9 4 6 0
6 4 5 1 0 3 2 7 8 9
Sample Output 2:
Heap Sort
5 4 3 1 0 2 6 7 8 9、

解题思路

这道题与前面一道题非常像，无非是用堆排序进行
堆排序的实现方法：一开始根据不同的子树建立大根堆，而后分别将堆顶堆低互换向下下沉，使得其变为从小到大的有序排序
以下为AC代码

#include <cstdio>
#include<algorithm>
#include<iostream>
#include<vector>
#include<cmath>
#include<iomanip>
#include<map>
#include<queue>;
using namespace std;
int N[200]; int K;
int ans[200];
bool issame(int a[200]) {
	for (int i = 0; i < K; i++) {
		if (ans[i] != a[i]) {
			return false;
		}
	}
	return true;
}
bool issame2(int a[200]) {
	for (int i = 0; i < K; i++) {
		if (ans[i] != a[i+1]) {
			return false;
		}
	}
	return true;
}
bool insertsort() {
	int temp[200];
	copy(N, N + K, temp);
	for (int i = 1; i < K; i++) {
		for (int j = i - 1; j >= 0; j--) {
			if (temp[j] > temp[j + 1]) {
				swap(temp[j], temp[j + 1]);
			}
			else {
				break;
			}
		}
		if (issame(temp)) {
			cout << "Insertion Sort" << '\n';
			i = i + 1;
			for (int j = i - 1; j >= 0; j--) {
				if (temp[j] > temp[j + 1]) {
					swap(temp[j], temp[j + 1]);
				}
				else {
					break;
				}
			}
			for (int t = 0; t < K; t++) {
				if (t != 0) {
					cout << " " << temp[t];
				}
				else {
					cout << temp[t];
				}
			}
			cout << '\n';
			return true;
		}

	}
	return false;
}
bool heapsort() {//需要建立一个大根堆
	int temp[200];
	int p = 0;
	copy(N, N + K, temp+1);
	int begin = K / 2;
	for (int i = begin; i > 0; i--) {//建立初始堆
		int pos = i;
		while (pos <= K) {
			if (2 * pos > K) {
				break;
			}
			if (2 * pos == K) {
				if (temp[2 * pos] > temp[pos]) {
					swap(temp[2 * pos], temp[pos]);
					pos = 2 * pos;
					break;
				}
				else {
					break;
				}
			}
			else if ((2 * pos + 1) <= K) {
				int num = max(temp[2 * pos], temp[2 * pos + 1]);
				if (num <= temp[pos]) {
					break;
				}
				else {
					if (num == temp[2 * pos]) {
						swap(temp[2 * pos], temp[pos]);
						pos = 2 * pos;
					}
					else {
						swap(temp[2 * pos + 1], temp[pos]);
						pos = 2 * pos + 1;
					}
				}
			}
		}
	}//建堆结束
	for (int i = K ; i > 0; i--) {
		if (i < K  && issame2(temp)) {
			p = 1;
		}
		swap(temp[i], temp[1]);
		//更换后重新开始下沉
		int pos = 1;
		while (pos <= i-1) {
			if (2 * pos > i-1) {
				break;
			}
			if (2 * pos == i-1) {
				if (temp[2 * pos] > temp[pos]) {
					swap(temp[2 * pos], temp[pos]);
					pos = 2 * pos;
					break;
				}
				else {
					break;
				}
			}
			else if ((2 * pos + 1) <= i-1) {
				int num = max(temp[2 * pos], temp[2 * pos + 1]);
				if (num <= temp[pos]) {
					break;
				}
				else {
					if (num == temp[2 * pos]) {
						swap(temp[2 * pos], temp[pos]);
						pos = 2 * pos;
					}
					else {
						swap(temp[2 * pos + 1], temp[pos]);
						pos = 2 * pos + 1;
					}
				}
			}
		}
		if (p == 1) {
			cout << "Heap sort" << '\n';
			for (int t = 1; t <= K; t++) {
				if (t != 1) {
					cout << " " << temp[t];
				}
				else {
					cout << temp[t];
				}
			}
			cout << '\n';
			return true;
		}
	}
	return false;
}
int main() {
	cin >> K;
	for (int i = 0; i < K; i++) {
		scanf_s("%d", &N[i]);
	}
	for (int i = 0; i < K; i++) {
		scanf_s("%d", &ans[i]);
	}
	if (!insertsort()) {
		heapsort();
	}
}