AOJ/初等排序习题集

ALDS1_1_D-MaximumProfit.

Codes:

//#define LOCAL
#include <cstdio>
#include <algorithm>
using namespace std;
#define maxSize 200010
int a[maxSize];
int main()
{
	#ifdef LOCAL
		freopen("E:\\Temp\\input.txt", "r", stdin);
		freopen("E:\\Temp\\output.txt", "w", stdout);
	#endif
	int n;
	scanf("%d", &n);
	for(int i=0; i<n; ++i) scanf("%d", &a[i]);
	int maxv = -1e9, minv = a[0];
	for(int i=1; i<n; ++i) {
		maxv = max(maxv, a[i]-minv);
		minv = min(minv, a[i]);
	}
	printf("%d\n", maxv);
	return 0;
}

ALDS1_1_A-InsertionSort.

Description:

Write a program of the Insertion Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode:

for i = 1 to A.length-1

key = A[i]

/* insert A[i] into the sorted sequence A[0,...,j-1] */

j = i - 1

while j >= 0 and A[j] > key

A[j+1] = A[j]

j--

A[j+1] = key

Note that, indices for array elements are based on 0-origin.

To illustrate the algorithms, your program should trace intermediate result for each step.

Input:

The first line of the input includes an integer N, the number of elements in the sequence.

In the second line, N elements of the sequence are given separated by a single space.

Output:

The output consists of N lines. Please output the intermediate sequence in a line for each step. Elements of the sequence should be separated by single space.

Constraints:

1 ≤ N ≤ 100

Sample Input 1:

6

5 2 4 6 1 3

Sample Output 1:

5 2 4 6 1 3

2 5 4 6 1 3

2 4 5 6 1 3

2 4 5 6 1 3

1 2 4 5 6 3

1 2 3 4 5 6

Sample Input 2:

3

1 2 3

Sample Output 2:

1 2 3

1 2 3

1 2 3

Codes:

/*#define LOCAL*/
#include <cstdio>
void trace(int a[], int n) {
	for(int i=0; i<n; ++i) {
		if(i) printf(" ");
		printf("%d", a[i]);
	}
	printf("\n");
}
void insertionSort(int a[], int n) {
	for(int i=1; i<n; ++i) {
		int j = i-1, v = a[i];
		while(j>=0 && a[j]>v) {
			a[j+1] = a[j];
			--j;
		}
		a[j+1] = v;
		trace(a, n);
	}
}
int main()
{
	#ifdef LOCAL
		freopen("E:\\Temp\\input.txt", "r", stdin);
		freopen("E:\\Temp\\output.txt", "w", stdout);
	#endif
	int n, a[110];
	scanf("%d", &n);
	for(int i=0; i<n; ++i) scanf("%d", &a[i]);
	trace(a, n);
	insertionSort(a, n);
	return 0;
}

ALDS1_2_A-BubbleSort.

Description:

Write a program of the Bubble Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode:

BubbleSort(A)

1 for i = 0 to A.length-1

2 for j = A.length-1 downto i+1

3 if A[j] < A[j-1]

4 swap A[j] and A[j-1]

Note that, indices for array elements are based on 0-origin.

Your program should also print the number of swap operations defined in line 4 of the pseudocode.

Input:

The first line of the input includes an integer N, the number of elements in the sequence.

In the second line, N elements of the sequence are given separated by spaces characters.

Output:

The output consists of 2 lines.

In the first line, please print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.

In the second line, please print the number of swap operations.

Constraints:

1 ≤ N ≤ 100

Sample Input 1:

5

5 3 2 4 1

Sample Output 1:

1 2 3 4 5

8

Sample Input 2:

6

5 2 4 6 1 3

Sample Output 2:

1 2 3 4 5 6

9

Codes:

//#define LOCAL
#include <cstdio>
int bubbleSort(int a[], int n) {
	int counter = 0;
	bool flag = 1;
	for(int i=0; flag; ++i) {
		flag = 0;
		for(int j=n-1; j>i; --j) {
			if(a[j] < a[j-1]) {
				int temp = a[j]; a[j] = a[j-1]; a[j-1] = temp;
				flag = 1; ++counter;
			}
		}
	}
	return counter;
}
int main()
{
	#ifdef LOCAL
		freopen("E:\\Temp\\input.txt", "r", stdin);
		freopen("E:\\Temp\\output.txt", "w", stdout);
	#endif
	int n, counter, a[110];
	scanf("%d", &n);
	for(int i=0; i<n; ++i) scanf("%d", &a[i]);
	counter = bubbleSort(a, n);
	for(int i=0; i<n; ++i) {
		if(i) printf(" ");
		printf("%d", a[i]);
	}
	printf("\n%d\n", counter);
	return 0;
}

ALDS1_2_B-SelectionSort.

Description:

Write a program of the Selection Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode:

SelectionSort(A)

1 for i = 0 to A.length-1

2 mini = i

3 for j = i to A.length-1

4 if A[j] < A[mini]

5 mini = j

6 swap A[i] and A[mini]

Note that, indices for array elements are based on 0-origin.

Your program should also print the number of swap operations defined in line 6 of the pseudocode in the case where i ≠ mini.

Input:

The first line of the input includes an integer N, the number of elements in the sequence.

In the second line, N elements of the sequence are given separated by space characters.

Output:

he output consists of 2 lines.

In the first line, please print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.

In the second line, please print the number of swap operations.

Constraints:

1 ≤ N ≤ 100

Sample Input 1:

6

5 6 4 2 1 3

Sample Output 1:

1 2 3 4 5 6

4

Sample Input 2:

6

5 2 4 6 1 3

Sample Output 2:

1 2 3 4 5 6

3

Codes:

//#define LOCAL
#include <cstdio>
int selectionSort(int a[], int n) {
	int minv, counter = 0;
	for(int i=0; i<n-1; ++i) {
		minv = i;
		for(int j=i+1; j<n; ++j)
			if(a[j] < a[minv]) minv = j;
		if(i != minv) {
			int t = a[minv]; a[minv] = a[i];
			a[i] = t; ++counter;
		}
	}
	return counter;
}
int main()
{
	#ifdef LOCAL
		freopen("E:\\Temp\\input.txt", "r", stdin);
		freopen("E:\\Temp\\output.txt", "w", stdout);
	#endif
	int n, counter, a[110];
	scanf("%d", &n);
	for(int i=0; i<n; ++i) scanf("%d", &a[i]);
	counter = selectionSort(a, n);
	for(int i=0; i<n; ++i) {
		if(i) printf(" ");
		printf("%d", a[i]);
	}
	printf("\n%d\n", counter);
	return 0;
}

ALDS1_2_C-StableSort.

Description:

Let's arrange a deck of cards. There are totally 36 cards of 4 suits(S, H, C, D) and 9 values (1, 2, ... 9). For example, 'eight of heart' is represented by H8 and 'one of diamonds' is represented by D1.

Your task is to write a program which sorts a given set of cards in ascending order by their values using the Bubble Sort algorithms and the Selection Sort algorithm respectively. These algorithms should be based on the following pseudocode:

BubbleSort(C)

1 for i = 0 to C.length-1

2 for j = C.length-1 downto i+1

3 if C[j].value < C[j-1].value

4 swap C[j] and C[j-1]

SelectionSort(C)

1 for i = 0 to C.length-1

2 mini = i

3 for j = i to C.length-1

4 if C[j].value < C[mini].value

5 mini = j

6 swap C[i] and C[mini]

Note that, indices for array elements are based on 0-origin.

Input:

The first line contains an integer N, the number of cards.

N cards are given in the following line. Each card is represented by two characters. Two consecutive cards are separated by a space character.

Output:

In the first line, print the arranged cards provided by the Bubble Sort algorithm. Two consecutive cards should be separated by a space character.

In the second line, print the stability ("Stable" or "Not stable") of this output.

In the third line, print the arranged cards provided by the Selection Sort algorithm. Two consecutive cards should be separated by a space character.

In the fourth line, print the stability ("Stable" or "Not stable") of this output.

Constraints:

1 ≤ N ≤ 36

Sample Input 1:

5

H4 C9 S4 D2 C3

Sample Output 1:

D2 C3 H4 S4 C9

Stable

D2 C3 S4 H4 C9

Not stable

Sample Input 2:

2

S1 H1

Sample Output 2:

S1 H1

Stable

S1 H1

Stable

Codes:

//#define LOCAL
#include <cstdio>
struct Card {char suit, value;};
void bubble(struct Card a[], int n) {
	for(int i=0; i<n; ++i) {
		for(int j=n-1; j>=i+1; --j)
			if(a[j].value < a[j-1].value) {
				Card t = a[j]; a[j] = a[j-1]; a[j-1] = t;
			}
	}
}
void selection(struct Card a[], int n) {
	for(int i=0; i<n; ++i) {
		int minv = i;
		for(int j=i+1; j<n; ++j)
			if(a[j].value < a[minv].value) minv = j;
		Card t = a[minv]; a[minv] = a[i]; a[i] = t;
	}
}
void print(struct Card a[], int n) {
	for(int i=0; i<n; ++i) {
		if(i) printf(" ");
		printf("%c%c", a[i].suit, a[i].value);
	}
	printf("\n");
} 
bool isStable(struct Card C1[], struct Card C2[], int n) {
	for(int i=0; i<n; ++i)
		if(C1[i].suit != C2[i].suit) return false;
	return true;
}
int main()
{
	#ifdef LOCAL
		freopen("E:\\Temp\\input.txt", "r", stdin);
		freopen("E:\\Temp\\output.txt", "w", stdout);
	#endif
	char str[5];
	int n, j = 0;
	Card C1[100], C2[100];
	scanf("%d", &n);
	for(int i=0; i<n; ++i) {
		scanf("%s", str);
		C1[i].suit = C2[i].suit = str[0];
		C1[i].value = C2[i].value = str[1];
	}
	bubble(C1, n);
	selection(C2, n);
	print(C1, n); printf("Stable\n");
	print(C2, n);
	if(isStable(C1, C2, n)) printf("Stable\n");
	else printf("Not stable\n");
	return 0;
}

ALDS1_2_D-ShellSort.

Codes:

//#define LOCAL
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <vector>
using namespace std;
int l, n, A[1000000];
long long cnt;
vector<int> G;
void insertionSort(int A[], int n, int g) {
	for(int i=g; i<n; ++i) {
		int v = A[i], j = i-g;
		while(j>=0 && A[j]>v) {
			A[j+g] = A[j];
			j -= g; ++cnt;
		}
		A[j+g] = v;
	}
}
void shellSort(int A[], int n) {
	for(int h=1;;) {
		if(h > n) break;
		G.push_back(h);
		h = 3*h+1;
	}
	for(int i=G.size()-1; i>=0; --i) {
		insertionSort(A, n, G[i]);
	}
}
int main()
{
	#ifdef LOCAL
			freopen("E:\\Temp\\input.txt", "r", stdin);
			freopen("E:\\Temp\\output.txt", "w", stdout);
	#endif
	scanf("%d", &n);
	for(int i=0; i<n; ++i) scanf("%d", &A[i]);
	cnt = 0;
	shellSort(A, n);
	printf("%d\n", G.size());
	for(int i=G.size()-1; i>=0; --i) {
		printf("%d", G[i]);
		if(i) printf(" ");
	}
	printf("\n%d\n", cnt);
	for(int i=0; i<n; ++i) printf("%d\n", A[i]);
	return 0;
}