给定一个大小为N和D索引的数组arr[] ,任务是将数组旋转D索引。
左旋转:数组从左旋转 D 元素
例子:
Input:
arr[] = {1, 2, 3, 4, 5}
D = 2
Output:
3 4 5 1 2
Explanation: The initial array [1, 2, 3, 4, 5]
rotate by first index [2, 3, 4, 5, 1]
rotate by second index [3, 4, 5, 1, 2]
Input:
arr[] = {10, 34, 56, 23, 78, 12, 13, 65}
D = 7
Output:
65 10 34 56 23 78 12 13
1.使用临时数组
方法:在此方法中,只需创建一个临时数组并将数组 arr[] 的元素从 0 复制到第 D 个索引。在移动之后,数组 arr[] 的其余元素从索引 D 到 N。然后将临时数组元素移动到原始数组。
Input arr[] = [1, 2, 3, 4, 5], D = 2
1) Store the first d elements in a temp array: temp[] = [1, 2]
2) Shift rest of the arr[]: arr[] = [3, 4, 5]
3) Store back the D elements: arr[] = [3, 4, 5, 1, 2]
下面是上述方法的实现:
Java
// Java program to left rotate
// an array by D elements
class GFG {
// Function to left rotate arr[]
// of size N by D
void leftRotate(int arr[], int d, int n)
{
// create temp array of size d
int temp[] = new int[d];
// copy first d element in array temp
for (int i = 0; i < d; i++)
temp[i] = arr[i];
// move the rest element to index
// zero to N-d
for (int i = d; i < n; i++) {
arr[i - d] = arr[i];
}
// copy the temp array element
// in origninal array
for (int i = 0; i < d; i++) {
arr[i + n - d] = temp[i];
}
}
// utility function to print an array
void printArray(int arr[], int n)
{
for (int i = 0; i < n; i++)
System.out.print(arr[i] + " ");
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.leftRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
Java
// Java program to left rotate
// an array by d elements
class GFG {
// Function to left rotate arr[]
// of size n by d
void leftRotate(int arr[],
int d, int n)
{
for (int i = 0; i < d; i++)
leftRotatebyOne(arr, n);
}
void leftRotatebyOne(int arr[], int n)
{
int i, temp;
temp = arr[0];
for (i = 0; i < n - 1; i++)
arr[i] = arr[i + 1];
arr[i] = temp;
}
// utility function to print an array
void printArray(int arr[], int n)
{
for (int i = 0; i < n; i++)
System.out.print(arr[i] + " ");
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.leftRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
Java
// Java program to left rotate
// an array by d elements
class GFG {
// Function to left rotate arr[]
// of siz N by D
void leftRotate(int arr[], int d,
int n)
{
// To handle if d >= n
d = d % n;
int i, j, k, temp;
int g_c_d = gcd(d, n);
for (i = 0; i < g_c_d; i++) {
// move i-th values of blocks
temp = arr[i];
j = i;
while (true) {
k = j + d;
if (k >= n)
k = k - n;
if (k == i)
break;
arr[j] = arr[k];
j = k;
}
arr[j] = temp;
}
}
// function to print an array
void printArray(int arr[],
int size)
{
int i;
for (i = 0; i < size; i++)
System.out.print(arr[i] + " ");
}
// Function to get gcd of a and b
int gcd(int a, int b)
{
if (b == 0)
return a;
else
return gcd(b, a % b);
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.leftRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
Java
// Java program to rotate an array by
// D elements
class GFG {
// Function to right rotate arr[]
// of size N by D
void rightRotate(int arr[], int d, int n)
{
// if arr is rotated n times then
// you get the same array
while(d > n){
d = d - n;
}
// create temp array of size d
int temp[] = new int[n - d];
// copy first N-D element in array temp
for (int i = 0; i < n - d; i++)
temp[i] = arr[i];
// move the rest element to index
// zero to D
for (int i = n - d; i < n; i++) {
arr[i - d - 1] = arr[i];
}
// copy the temp array element
// in origninal array
for (int i = 0; i < n - d; i++) {
arr[i + d] = temp[i];
}
}
// utility function to print an array
void printArray(int arr[], int n)
{
for (int i = 0; i < n; i++)
System.out.print(arr[i] + " ");
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.rightRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
Java
// Java program to rotate an array by
// d elements
class GFG {
// Function to right rotate arr[]
// of size n by d
void rightRotate(int arr[],
int d, int n)
{
for (int i = n; i > d; i--)
rightRotatebyOne(arr, n);
}
void rightRotatebyOne(int arr[], int n)
{
int i, temp;
temp = arr[0];
for (i = 0; i < n - 1; i++)
arr[i] = arr[i + 1];
arr[i] = temp;
}
// utility function to print an array
void printArray(int arr[], int n)
{
for (int i = 0; i < n; i++)
System.out.print(arr[i] + " ");
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.rightRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
Java
// Java program to rotate an array by
// d elements
class GFG {
// Function to right rotate arr[]
// of siz N by D
void rightRotate(int arr[], int d, int n)
{
// to neglect n rotations if rtotations is greater
// than size of arr
while (d > n) {
d = d - n;
}
// to use as left rotation
d = n - d;
d = d % n;
int i, j, k, temp;
int g_c_d = gcd(d, n);
for (i = 0; i < g_c_d; i++) {
// move i-th values of blocks
temp = arr[i];
j = i;
while (true) {
k = j + d;
if (k >= n)
k = k - n;
if (k == i)
break;
arr[j] = arr[k];
j = k;
}
arr[j] = temp;
}
}
// UTILITY FUNCTIONS
// function to print an array
void printArray(int arr[], int size)
{
int i;
for (i = 0; i < size; i++)
System.out.print(arr[i] + " ");
}
// Function to get gcd of a and b
int gcd(int a, int b)
{
if (b == 0)
return a;
else
return gcd(b, a % b);
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.rightRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
3 4 5 1 2
时间复杂度: O(N)
辅助空间: O(D)
2.一一旋转:
方法:递归地将数组一个一个元素旋转——
Input arr[] = [1, 2, 3, 4, 5], D = 2
1) swap arr[0] to arr[1]
2) swap arr[1] to arr[2]
.
.
.
3) swap arr[N-1] to arr[N]
4) Repeat 1, 2, 3 to D times
要旋转一,将 arr[0] 存储在临时变量 temp 中,将 arr[1] 移动到 arr[0],将 arr[2] 移动到 arr[1] …最后将 temp 移动到 arr[n-1]
Let us take the same example arr[] = [1, 2, 3, 4, 5], d = 2
Rotate arr[] by one 2 times
We get [2, 3, 4, 5, 1] after first rotation and [ 3, 4, 5, 1, 2] after second rotation.
下面是上述方法的实现:
Java
// Java program to left rotate
// an array by d elements
class GFG {
// Function to left rotate arr[]
// of size n by d
void leftRotate(int arr[],
int d, int n)
{
for (int i = 0; i < d; i++)
leftRotatebyOne(arr, n);
}
void leftRotatebyOne(int arr[], int n)
{
int i, temp;
temp = arr[0];
for (i = 0; i < n - 1; i++)
arr[i] = arr[i + 1];
arr[i] = temp;
}
// utility function to print an array
void printArray(int arr[], int n)
{
for (int i = 0; i < n; i++)
System.out.print(arr[i] + " ");
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.leftRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
3 4 5 1 2
时间复杂度: O(N * D)
辅助空间: O(1)
3.杂耍算法:
方法:这是方法2的扩展,不是一个一个移动,而是将数组分成不同的集合,其中集合的数量等于n和d的GCD,并移动集合内的元素。
If GCD is 1 as-is for the above example array (n = 5 and d = 2), then elements will be moved within one set only, we just start with temp = arr[0] and keep moving arr[I+d] to arr[I] and finally store temp at the right place.
下面是上述方法的实现:
Java
// Java program to left rotate
// an array by d elements
class GFG {
// Function to left rotate arr[]
// of siz N by D
void leftRotate(int arr[], int d,
int n)
{
// To handle if d >= n
d = d % n;
int i, j, k, temp;
int g_c_d = gcd(d, n);
for (i = 0; i < g_c_d; i++) {
// move i-th values of blocks
temp = arr[i];
j = i;
while (true) {
k = j + d;
if (k >= n)
k = k - n;
if (k == i)
break;
arr[j] = arr[k];
j = k;
}
arr[j] = temp;
}
}
// function to print an array
void printArray(int arr[],
int size)
{
int i;
for (i = 0; i < size; i++)
System.out.print(arr[i] + " ");
}
// Function to get gcd of a and b
int gcd(int a, int b)
{
if (b == 0)
return a;
else
return gcd(b, a % b);
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.leftRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
3 4 5 1 2
时间复杂度: O(n)
辅助空间: O(1)
右旋转:数组从右旋转 D 元素
例子:
Input:
arr[] = {1, 2, 3, 4, 5}
D = 2
Output:
4 5 1 2 3
Explanation:
The initial array [1, 2, 3, 4, 5]
rotate first index [2, 3, 4, 5, 1]
rotate second index [3, 4, 5, 1, 2]
rotate third index [4, 5, 1, 2, 3]
Input:
arr[] = {10, 34, 56, 23, 78, 12, 13, 65}
D = 5
Output:
56 23 78 12 13 65 10 34
1.使用临时数组
方法:在这种方法中,只需创建一个临时数组,并将数组 arr[] 的元素从 0 复制到N – D索引。移动之后,数组 arr[] 的其余元素从索引 D 到 N。然后将临时数组元素移动到原始数组。
Input arr[] = [1, 2, 3, 4, 5], D = 2
1) Store the first d elements in a temp array
temp[] = [1, 2, 3]
2) Shift rest of the arr[]
arr[] = [4, 5]
3) Store back the D elements
arr[] = [4, 5, 1, 2, 3]
下面是上述方法的实现:
Java
// Java program to rotate an array by
// D elements
class GFG {
// Function to right rotate arr[]
// of size N by D
void rightRotate(int arr[], int d, int n)
{
// if arr is rotated n times then
// you get the same array
while(d > n){
d = d - n;
}
// create temp array of size d
int temp[] = new int[n - d];
// copy first N-D element in array temp
for (int i = 0; i < n - d; i++)
temp[i] = arr[i];
// move the rest element to index
// zero to D
for (int i = n - d; i < n; i++) {
arr[i - d - 1] = arr[i];
}
// copy the temp array element
// in origninal array
for (int i = 0; i < n - d; i++) {
arr[i + d] = temp[i];
}
}
// utility function to print an array
void printArray(int arr[], int n)
{
for (int i = 0; i < n; i++)
System.out.print(arr[i] + " ");
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.rightRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
4 5 1 2 3
时间复杂度: O(N)
辅助空间: O(D)
2.一一旋转:
方法:递归地将数组一个一个元素旋转——
Input arr[] = [1, 2, 3, 4, 5], D = 2
1) swap arr[N] to arr[N-1]
2) swap arr[N-1] to arr[N-2]
.
.
.
3) swap arr[2] to arr[1]
4) Repeat 1, 2, 3 to D times
要旋转 1,将 arr[N] 存储在临时变量 temp 中,将 arr[N-1] 移动到 arr[N],将 arr[N-2] 移动到 arr[N-1] …最后将 temp 移动到 arr[1] ]
Let us take the same example arr[] = [1, 2, 3, 4, 5], d = 2
Rotate arr[] by one 2 times
We get [5, 1, 2, 3, 4] after first rotation and [ 4, 5, 1, 2, 3] after second rotation.
下面是上述方法的实现:
Java
// Java program to rotate an array by
// d elements
class GFG {
// Function to right rotate arr[]
// of size n by d
void rightRotate(int arr[],
int d, int n)
{
for (int i = n; i > d; i--)
rightRotatebyOne(arr, n);
}
void rightRotatebyOne(int arr[], int n)
{
int i, temp;
temp = arr[0];
for (i = 0; i < n - 1; i++)
arr[i] = arr[i + 1];
arr[i] = temp;
}
// utility function to print an array
void printArray(int arr[], int n)
{
for (int i = 0; i < n; i++)
System.out.print(arr[i] + " ");
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.rightRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
4 5 1 2 3
时间复杂度: O(N * D)
辅助空间: O(1)
1.杂耍算法:
方法:这是方法2的扩展,不是一个一个移动,而是将数组分成不同的集合,其中集合的数量等于n和d的GCD,并移动集合内的元素。
If GCD is 1 as-is for the above example array (n = 5 and d =2), then elements will be moved within one set only, we just start with temp = arr[N] and keep moving arr[I+d] to arr[I] and finally store temp at the right place.
下面是上述方法的实现:
Java
// Java program to rotate an array by
// d elements
class GFG {
// Function to right rotate arr[]
// of siz N by D
void rightRotate(int arr[], int d, int n)
{
// to neglect n rotations if rtotations is greater
// than size of arr
while (d > n) {
d = d - n;
}
// to use as left rotation
d = n - d;
d = d % n;
int i, j, k, temp;
int g_c_d = gcd(d, n);
for (i = 0; i < g_c_d; i++) {
// move i-th values of blocks
temp = arr[i];
j = i;
while (true) {
k = j + d;
if (k >= n)
k = k - n;
if (k == i)
break;
arr[j] = arr[k];
j = k;
}
arr[j] = temp;
}
}
// UTILITY FUNCTIONS
// function to print an array
void printArray(int arr[], int size)
{
int i;
for (i = 0; i < size; i++)
System.out.print(arr[i] + " ");
}
// Function to get gcd of a and b
int gcd(int a, int b)
{
if (b == 0)
return a;
else
return gcd(b, a % b);
}
// Driver program to test above functions
public static void main(String[] args)
{
GFG rotate = new GFG();
int arr[] = { 1, 2, 3, 4, 5 };
rotate.rightRotate(arr, 2, arr.length);
rotate.printArray(arr, arr.length);
}
}
4 5 1 2 3
时间复杂度: O(n)
辅助空间: O(1)
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