Insertion or Heap Sort PAT甲级真题（堆排序）

来源：http://blog.csdn.net/liuchuo/article/details/52252172

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.

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

题目大意：给出n和n个数的序列a和b，a为原始序列，b为排序其中的一个步骤，问b是a经过了堆排序还是插入排序的，并且输出它的下一步~~
分析：插入排序的特点是：b数组前面的顺序是从小到大的，后面的顺序不一定，但是一定和原序列的后面的顺序相同~~所以只要遍历一下前面几位，遇到不是从小到大的时候，开始看b和a是不是对应位置的值相等，相等就说明是插入排序，否则就是堆排序啦~~~
插入排序的下一步就是把第一个不符合从小到大的顺序的那个元素插入到前面已排序的里面的合适的位置，那么只要对前几个已排序的+后面一位 这个序列sort排序即可~~~

堆排序的特点是后面是从小到大的，前面的顺序不一定，那么就可以到第一个不是前面所有序列最大值的那个数字i，把它和第一个数字交换，然后把1~i-1进行一次向下调整~~~向下调整，low和high是需要调整的区间，因为是大顶堆，就是不断比较当前结点和自己的孩子结点哪个大，如果孩子大就把孩子结点和自己交换，然后再不断调整直到到达区间的最大值不能再继续了为止~~~~

[cpp] view plain copy

 print?

1. #include <cstdio>  
2. #include <vector>  
3. #include <algorithm>  
4. using namespace std;  
5. vector<int> a, b;  
6. void downAdjust(int low, int high) {  
7.     int i = 1, j = i * 2;  
8.     while(j <= high) {  
9.         if(j + 1 <= high && b[j] < b[j + 1])  
10.             j = j + 1;  
11.         if(b[i] < b[j]) {  
12.             swap(b[i], b[j]);  
13.             i = j; j = i * 2;  
14.         } else {  
15.             break;  
16.         }  
17.     }  
18. }  
19. int main() {  
20.     int n, p = 2;  
21.     scanf("%d", &n);  
22.     a.resize(n + 1), b.resize(n + 1);  
23.     for(int i = 1; i <= n; i++)  
24.         scanf("%d", &a[i]);  
25.     for(int i = 1; i <= n; i++)  
26.         scanf("%d", &b[i]);  
27.     while(p <= n && b[p - 1] <= b[p]) p++;  
28.     int index = p;  
29.     while(p <= n && a[p] == b[p]) p++;  
30.     if(p == n + 1) {  
31.         printf("Insertion Sort\n");  
32.         sort(b.begin() + 1, b.begin() + index + 1);  
33.         printf("%d", b[1]);  
34.         for(int i = 2; i <= n; i++)  
35.             printf(" %d", b[i]);  
36.     } else {  
37.         printf("Heap Sort\n");  
38.         p = n;  
39.         while(p >= 2 && b[p] >= b[p - 1]) p--;  
40.         swap(b[1], b[p]);  
41.         downAdjust(1, p - 1);  
42.         printf("%d", b[1]);  
43.         for(int i = 2; i <= n; i++)  
44.             printf(" %d", b[i]);  
45.     }  
46.     return 0;  
47. }  

我写了个糟糕的代码，不知道为什么有个点没过，过程是用暴力的：

#include <stdio.h>#define maxn  110#define INF 0x7fffffint flag1,flag2;int isout1,isout2;int cmp(int a[],int b[],int N){for(int i=1;i<=N;i++){if(a[i]!=b[i]) return 0;}return 1;}void output(int a[],int N){int flag =1;for(int i=1;i<=N;i++){if(flag) flag=0;else printf(" ");printf("%d",a[i] );}printf("\n");}void exch(int a[],int t1,int t2){int temp = a[t1];a[t1] = a[t2];a[t2] = temp;}void sink(int a[],int u,int N){while(u*2<=N){int j=2*u;if(j+1<=N && a[j+1]>a[j]) j++;if(a[j] < a[u]) break;exch(a,j,u);u=j;}}void swim(int a[],int u){while(u/2 && a[u] > a[u/2]  ){exch(a,u,u/2);u/=2;}}void Insertion(int a[],int b[],int N){int ready=0;for(int i=2;i<=N;i++){if(flag1) ready = 1;for(int j=i;j>1;j--){if(a[j] < a[j-1]){exch(a,j,j-1);if(cmp(a,b,N)){flag1 = 1;}}}if(ready){printf("Insertion Sort\n");output(a,N);isout1=1;return ;}}}void HeapSort(int a[],int b[],int N){int tempsize = N;for(int i=N/2;i>=1;i--){sink(a,i,N);}while(tempsize){exch(a,1,tempsize--);sink(a,1,tempsize);if(flag2){printf("Heap Sort\n");output(a,N);isout2=1;return ;}if(cmp(a,b,N)){flag2 = 1;}}}int main(int argc, char const *argv[]){int N;int a[maxn],b[maxn],c[maxn];scanf("%d",&N);for(int i=1;i<=N;i++){scanf("%d",(a+i));c[i]=a[i];}for(int i=1;i<=N;i++)scanf("%d",(b+i));Insertion(a,b,N);if(!flag1){HeapSort(c,b,N);}if(flag1 && !isout1){printf("Insertion Sort\n");output(a,N);isout1=1;}if(flag2 && !isout2){printf("Heap Sort\n");output(c,N);isout2=1;}return 0;}