I have the following problem to test:
Rotate an array of n elements to the right by k steps.
For instance, with n = 7 and k = 3, the array [1,2,3,4,5,6,7] is rotated to
[5,6,7,1,2,3,4]. How many different ways do you know to solve this problem?
My solution in intermediate array:
With Space is O(n) and time is O(n), I can create a new array and then copy elements to the new array. Then change the original array by using System.arraycopy().
public void rotate(int[] nums, int k) {
if (k > nums.length)
k = k % nums.length;
int[] result = new int[nums.length];
for (int i = 0; i < k; i++) {
result[i] = nums[nums.length - k + i];
}
int j = 0;
for (int i = k; i < nums.length; i++) {
result[i] = nums[j];
j++;
}
System.arraycopy(result, 0, nums, 0, nums.length);
}
But is there a better way we can do it with bubble rotate (like bubble sort) in O(1) space?
Method 1 - The Reversal Algorithm(Good One):
Algorithm:
rotate(arr[], d, n)
reverse(arr[], l, n);
reverse(arr[], 1, n-d) ;
reverse(arr[], n - d + 1, n);
Let AB are the two parts of the input array where A = arr[0..n-d-1] and B = arr[n-d..n-1]. The idea of the algorithm is:
Reverse all to get (AB) r = BrAr.
Reverse A to get BrA. /* Ar is reverse of A */
Reverse B to get BA. /* Br is reverse of B */
For arr[] = [1, 2, 3, 4, 5, 6, 7], d =2 and n = 7
A = [1, 2, 3, 4, 5] and B = [ 6, 7]
Reverse all, we get BrAr = [7, 6, 5, 4, 3, 2, 1]
Reverse A, we get ArB = [7, 6, 1, 2, 3, 4, 5]
Reverse B, we get ArBr = [6, 7, 5, 4, 3, 1, 2]
Here is the Code Snippet:
void righttRotate(int arr[], int d, int n)
{
reverseArray(arr, 0, n-1);
reverseArray(arr, 0, n-d-1);
reverseArray(arr, n-d, n-1);
}
void reverseArray(int arr[], int start, int end)
{
int i;
int temp;
while(start < end)
{
temp = arr[start];
arr[start] = arr[end];
arr[end] = temp;
start++;
end--;
}
}
Method 2 - A Juggling Algorithm
Divide the array in different sets where number of sets is equal to GCD of n and d and move the elements within sets.
If GCD is 1, 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.
Here is an example for n =12 and d = 3. GCD is 3 and
Let arr[] be {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
Elements are first moved in first set
arr[] after this step --> {4 2 3 7 5 6 10 8 9 1 11 12}
Then in second set.
arr[] after this step --> {4 5 3 7 8 6 10 11 9 1 2 12}
Finally in third set.
arr[] after this step --> {4 5 6 7 8 9 10 11 12 1 2 3}
Here is the code:
void leftRotate(int arr[], int d, int n)
{
int i, j, k, temp;
int gcd = gcd(d, n);
for (i = 0; i < gcd; i++)
{
/* move i-th values of blocks */
temp = arr[i];
j = i;
while(1)
{
k = j + d;
if (k >= n)
k = k - n;
if (k == i)
break;
arr[j] = arr[k];
j = k;
}
arr[j] = temp;
}
}
int gcd(int a,int b)
{
if(b==0)
return a;
else
return gcd(b, a%b);
}
Time complexity: O(n)
Auxiliary Space: O(1)
Method 3 - Rotate one by one:
righttRotate(arr[], d, n)
start
For i = 0 to i < d
Right rotate all elements of arr[] by one
end
To rotate by one, store arr[n-1] in a temporary variable temp, move arr[1] to arr[2], arr[2] to arr[3] …and finally temp to arr[0]
Let us take the same example arr[] = [1, 2, 3, 4, 5, 6, 7], d = 2, rotate arr[] by one 2 times. We get [7, 1, 2, 3, 4, 5, 6] after first rotation and [ 6, 7, 1, 2, 3, 4, 5] after second rotation.
Her is Code Snippet:
void leftRotate(int arr[], int d, int n)
{
int i;
for (i = 0; i < d; i++)
leftRotatebyOne(arr, n);
}
void leftRotatebyOne(int arr[], int n)
{
int i, temp;
temp = arr[n-n];
for (i = 0; i < n-1; i++)
arr[i] = arr[i+1];
arr[n - 1] = temp;
}
Time complexity: O(n*d)
Auxiliary Space: O(1)
The following code will do your job. This is for right rotate.
public void rightrotate(int[] nums, int k) {
k %= nums.length;
reverse(nums, 0, nums.length - 1);
reverse(nums, 0, k - 1);
reverse(nums, k, nums.length - 1);
}
public void reverse(int[] nums, int start, int end) {
while (start < end) {
int temp = nums[start];
nums[start] = nums[end];
nums[end] = temp;
start++;
end--;
}
}
If you want to do left rotate just use the following
public void leftrotate(int[] nums, int k) {
k %= nums.length;
reverse(nums, 0, k - 1);
reverse(nums, k, nums.length - 1);
reverse(nums, 0, nums.length - 1);
}
When k is negative, it rotates to the left.
Space is O(1) and time is O(n)
static void rotate(int[] num, int k) {
int n = num.length;
k = k % n;
if (k < 0) k += n;
int[] result = new int[n];
System.arraycopy(num, 0, result, k, n - k);
System.arraycopy(num, n - k, result, 0, k);
System.arraycopy(result, 0, num, 0, n);
}
ArrayUtil class is used to provide following utilities in primitive array
swap array elements
reverse array between startIndex and endIndex
leftRotate array by shift
Algorithm for array rotation by shift-
If we have to reverse array by shift value then take mod(%) with array length so that shift will become smaller than array length.
Reverse array between index 0 and shift-1
Reverse array between index shift and length-1.
Reverse complete array between index 0 and length-1.
Space Complexity: In-place Algorithm, No extra space needed so O(1).
Time Complexity : Array reversal of size k take O(k/2) i.e swapping k/2 pairs of elements.
Array Reversal time- O(k) for k size array.
Total time in Rotation-
O(1) ..........for step 1
O(shift) ......for step 2
O(n - shift) ...for step 3
O(n) ...........for step 4
Total Time for array Rotation: O(1) + O(shift) + O(n-shift) + O(n) = O(n)
public class Solution {
public static void main(String[] args) {
int k = 3;
int a[] = {1,2,3,4,5,6,7};
ArrayUtil.leftRotate(a, k);
for (int i : a)
System.out.println(i);
}
}
class ArrayUtil {
public static final boolean checkIndexOutOfRange(int[] array, int index) {
if (index < 0 || index > array.length)
return true;
return false;
}
public static final void swap(int[] array, int i, int j) {
if (checkIndexOutOfRange(array, i) || checkIndexOutOfRange(array, j))
return;
int t = array[i];
array[i] = array[j];
array[j] = t;
}
public static final void reverse(int[] array, int startIndex, int endIndex) {
if (checkIndexOutOfRange(array, startIndex) || checkIndexOutOfRange(array, endIndex))
return;
while (startIndex < endIndex) {
swap(array, startIndex, endIndex);
startIndex++;
endIndex--;
}
}
public static final void reverse(int[] array) {
reverse(array, 0, array.length - 1);
}
public static final void leftRotate(int[] array, int shift) {
int arrayLength = array.length;
if (shift >= arrayLength)
shift %= arrayLength;
reverse(array, 0, shift - 1);
reverse(array, shift, arrayLength - 1);
reverse(array);
}
}
Partial Code for ONE time array rotation
last=number_holder[n-1];
first=number_holder[0];
//rotation
number_holder[0]=last;
for(i=1;i<n;i++)
{
last=number_holder[i];
number_holder[i]=first;
first=last;
}
Display the array
for(i=1;i<n;i++)
{
System.out.println(number_holder[i]);
}
AFAIK, there are three ways to rotate an array with O(1) extra space, or put it another way, to swap two contiguous subarray.
reverse approach. reverse both part, then reverse all. most easy to code.
successively swap two contiguous block, until all items are in place.
juggling rotate, shell sort like. -- worse cache performance.
C++ has builtin function std::rotate(), which takes three iterator first, middle, last,
and return new_middle, which is where the old first element lies in the rotated
sequence.
I have checked the implementation on my computer, which use second approach I listed above.
(line 1246 in /usr/lib/gcc/i686-pc-cygwin/5.4.0/include/c++/bits/stl_algo.h).
Below is my implementation of rotate, with test program.
#include <iostream>
#include <vector>
// same logic with STL implementation, but simpler, since no return value needed.
template <typename Iterator>
void rotate_by_gcd_like_swap(Iterator first, Iterator mid, Iterator last) {
if (first == mid) return;
Iterator old = mid;
for (; mid != last;) {
std::iter_swap(first, mid);
++first, ++mid;
if (first == old) old = mid; // left half exhausted
else if (mid == last) mid = old;
}
}
// same logic with STL implementation
template <typename Iterator>
Iterator rotate_by_gcd_like_swap_then_return_new_mid(Iterator first, Iterator mid, Iterator last) {
if (first == mid) return last;
if (mid == last) return first;
Iterator old = mid;
for(;;) {
std::iter_swap(first, mid);
++first, ++mid;
if (first == old) old = mid;
if (mid == last) break;
}
Iterator result = first; // when first time `mid == last`, the position of `first` is the new `mid`.
for (mid = old; mid != last;) {
std::iter_swap(first, mid);
++first, ++mid;
if (first == old) old = mid;
else if (mid == last) mid = old;
}
return result;
}
int main() {
using std::cout;
std::vector<int> v {0,1,2,3,4,5,6,7,8,9};
cout << "before rotate: ";
for (auto x: v) cout << x << ' '; cout << '\n';
int k = 7;
rotate_by_gcd_like_swap(v.begin(), v.begin() + k, v.end());
cout << " after rotate: ";
for (auto x: v) cout << x << ' '; cout << '\n';
cout << "sz = " << v.size() << ", k = " << k << '\n';
}
Above solutions talk about shifting array elements either by reversing them or any other alternative.
I've unique solution. How about determining the starting position of element after n rotations. Once we know that, then simply insert elements from that index and increment counter using modulus operation. Using this method we can avoid using extra array operations and so on.
Here is my code:
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
void rotateLeft(int n,int r) {
vector<long int> vec(n);
int j = n;
// get the position of starting index after r left rotations.
while(r!=0) {
--j;
if(j==0)
j = n;
--r;
}
for(long int i=0;i<n;++i) {
// simply read the input from there and increment j using modulus operator.
cin>>vec[j];
j = (j+1)%n;
}
// print the array
for(long int i=0;i<n;++i)
cout<<vec[i]<<" ";
}
int rotateRight (int n,int r) {
// get the position of starting index after r left rotations.
int j = r % n;
vector<long int> vec(n);
for(int i=0;i<n;i++) {
cin>>vec[j];
j=(j+1)%n;
}
for(int i=0;i<n;i++)
cout<<vec[i]<<" ";
}
int main() {
long int n,r; // n stands from number of elements in array and r stands for rotations.
cin>>n>>r;
// Time Complexity: O(n+r) Space Complexity: O(1)
rotateLeft(n,r);
// Time Complexity: O(n) Space Complexity: O(1)
rotateRight(n,r);
return 0;
}
Python code:
def reverse(arr,start , end):
while(start <= end):
arr[start] , arr[end] = arr[end] , arr[start]
start = start+1
end = end-1
arr = [1,2,3,4,5,6,7]
n = 7
k = 2
reverse(arr,0,n-1)
# [7,6,5,4,3,2,1]
reverse(arr,0,n-1-k)
# [3,4,5,6,7,2,1]
reverse(arr,n-k,n-1)
# [3,4,5,6,7,1,2]
print arr
# [3, 4, 5, 6, 7, 8, 9, 1, 2]
In Ruby Its very simple, Please take a look, Its one line.
def array_rotate(arr)
i, j = arr.length - 1, 0
arr[j],arr[i], i, j = arr[i], arr[j], i - 1, j + 1 while(j<arr.length/2)
puts "#{arr}"
end
Input: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
Output: [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]
1.using a temp array and O(n) time
public static void rotateAnArrayUsingTemp(int arr[], int d, int n) {
int temp[] = new int[d];
int tempIndex = 0;
for (int i = 0; i < d; i++) {
temp[i] = arr[i];
}
for (int i = 0; i < arr.length - d; i++) {
arr[i] = arr[i + d];
}
for (int i = arr.length - d; i < arr.length; i++) {
arr[i] = temp[tempIndex++];
}
}
This is a simple solution to rotate an array.
public class ArrayRotate {
public int[] rotateArray(int array[], int k) {
int newArray[] = new int[array.length];
for (int i = 0; i < array.length; i++) {
newArray[(i + k) % array.length] = array[i];
}
System.arraycopy(newArray, 0, array, 0, array.length);
return newArray;
}
public static void main(String[] args) {
int array[] = { 1, 2, 3, 4, 5, 6, 7 };
ArrayRotate rotate = new ArrayRotate();
rotate.display(rotate.rotateArray(array, 3));
}
public void display(int array[]) {
for (int i : array) {
System.out.print(i + ",");
}
}
}
Runtime complexity is O(n)
There are several other algorithm to achieve the same.
using temp array
Rotate One By one
Juggling algorithm
reversal method
This solution is O(1) space and O(N) time. It is in C#, takes an array parameter and rotates it in place. The algorithm goes through the first s (the shift) elements, starting with the first element moves it to the s_th position, then moves the s_th to the 2s_th position etc. If each of the first s elements rotates back to itself then there will be (arrayLength / s) * s = arrayLength loops, and at the end the array will be rotated by s. If the first s elements do not rotate back themselves, then there will still be cycles, say if s = 4, there could be one cycle which is 1-3-1 and the second 2-4-2, the line - if (ind == indAtBeg), checks for a cycle and terminates the while loop. The variable loopCount increments, when there is a rotation starting at any of the first s elements.
public static void rotateArrayByS(int[] ar, int s)
{
int len = ar.Length, ind = 0, temp1 = ar[0],
temp2 /*temp1 and temp2 for switching elements*/,
loopCount /*rotations starting at the first s elemtns of ar*/ = 0;
s %= len;
while (loopCount < s)
{
int indAtBeg = ind;
temp1 = ar[ind];
bool done = false;
while (!done)
{
if (ind < s)
loopCount++;
ind = (ind + s) % len;
//cycle detected
if (ind == indAtBeg)
done = true;
//switch the elements
temp2 = ar[ind];
ar[ind] = temp1;
temp1 = temp2;
}
++ind;
}
}
#include <stdio.h>
int
main(void)
{
int arr[7] = {1,2,3,4,5,6,7};
int new_arr[7] = {0};
int k = 3;
int len = 7;
int i=0;
for (i = (len-1); i>=0; i--) {
if ((i+k) >= len) {
new_arr[(i+k-len)] = arr[i];
} else {
new_arr[(i+k)] = arr[i];
}
}
for (i=0;i<len;i++) {
printf("%d ", new_arr[i]);
}
return 0;
}
Time complexity O(n)
Space complexity O(2*n).
Thanks.
Here is the complete Java code for left and right array rotation by k steps
import java.util.*;
public class ArrayRotation {
private static Scanner sc;
public static void main(String[] args) {
int n,k;
sc = new Scanner(System.in);
System.out.print("Enter the size of array: ");
n = sc.nextInt();
int[] a = new int[n];
System.out.print("Enter the "+n+" elements in the list: ");
for(int i=0;i<n;i++)
a[i] = sc.nextInt();
System.out.print("Enter the number of left shifts to array: ");
k = sc.nextInt();
System.out.print("Array before "+k+" shifts: ");
display(a);
leftRoation(a,k);
System.out.println();
System.out.print("Array after "+k+" left shifts: ");
display(a);
rightRoation(a,k);
System.out.println();
System.out.print("Array after "+k+" right shifts: ");
display(a);
}
public static void leftRoation(int[] a, int k){
int temp=0, j;
for(int i=0;i<k;i++){
temp = a[0];
// j=0; // both codes work i.e. for loop and while loop as well
// while(j<a.length-1){
// a[j]=a[j+1];
// j++;
// }
for(j=0;j<a.length-1;j++)
a[j]=a[j+1];
a[j]=temp;
}
}
public static void rightRoation(int[] a, int k){
int temp=0, j;
for(int i=0;i<k;i++){
temp = a[a.length-1];
for(j=a.length-1;j>0;j--)
a[j]=a[j-1];
a[j]=temp;
}
}
public static void display(int[] a){
for(int i=0;i<a.length;i++)
System.out.print(a[i]+" ");
}
}
/****************** Output ********************
Enter the size of array: 5
Enter the 5 elements in the list: 1 2 3 4 5
Enter the number of left and right shifts to array: 2
Array before 2 shifts: 1 2 3 4 5
Array after 2 left shifts: 3 4 5 1 2
Array after 2 right shifts: 1 2 3 4 5 // here the left shifted array is taken as input and hence after right shift it looks same as original array.
**********************************************/
My solution... (a: the array, n : size of array, k: number of shifts) :
public static int[] arrayLeftRotation(int[] a, int n, int k) {
if (k == 0) return a;
for (int i = 0; i < k; i++) {
int retenue = a[0];
int[] copie = java.util.Arrays.copyOfRange(a, 1, n );
for (int y = 0; y <= copie.length - 1 ; y++) {
a[y] = copie[y];
}
a[n-1] = retenue;
}
return a;
}
Java implementation for right rotation
public int[] solution(int[] A, int K) {
int len = A.length;
//Create an empty array with same length as A
int arr[] = new int[len];
for (int i = 0; i < len; i++) {
int nextIndex = i + K;
if (nextIndex >= len) {
// wraps the nextIndex by same number of K steps
nextIndex = nextIndex % len;
}
arr[nextIndex] = A[i];
}
return arr;
}
>>> k = 3
>>> arr = [1,2,3,4,5,6,7]
>>> actual_rot = k % len(arr)
>>> left_ar = arr[:-actual_rot]
>>> right_ar = arr[-actual_rot:]
>>> result = right_ar + left_ar
>>> result
[5, 6, 7, 1, 2, 3, 4]
A better way to rotate an array by k steps is:
a = [1,2,3,4,5,6]
b = a[:]
k = 2
for i in range(len(a)):
a[(i + k) % len(a)] = b[i]## (rotate right by k steps)
#a[(i - k) % len(a)] = b[i]## (rotate left by k steps)
print(a)
o/p:
[6, 5, 1, 2, 3, 4]
how to rotate an array, IN this function first argument - array, the second argument is
a number or integer.
def rotLeft(a, d):
data = a
n = d
get = data[n:len(data)]
remains = data[0:n]
data.clear()
for i in get:
data.append(i)
for x in remains:
data.append(x)
return data
This is rotating the array to the right by k steps, where k is non-negative
for (int i = 0; i < k; i++) {
for (int j = nums.length - 1; j > 0; j--) {
int temp = nums[j];
nums[j] = nums[j - 1];
nums[j - 1] = temp;
}
}
return nums;
if (k > arr.length) {
k = k % arr.length;
}
int n = arr.length - k;
int count = 0;
outer:
for (int i = arr.length - 1; i >= n; i--) {
int temp = arr[i];
inner:
for (int j = i - 1; j >= 0; j--) {
arr[j + 1] = arr[j];
if (j == 0) {
int temp2 = arr[j];
arr[j] = temp;
i = arr.length;
count++;
if (count == k) {
break outer;
}
}
}
}
Here I have solved the same problem in go.
Try to run in go playground...
sample code.
func rotate(a []int, k int) {
for j := 0; j < k ; j++ {
temp := a[len(a)-1]
for i := len(a) - 1; i > 0; i-- {
a[i] = a[i-1]
}
a[0] = temp
}
}
If you are looking for the soltuion of Codility - Cyclic Rotation Problem then, here is the JavaScript code which gave 100% for me.
function solution(A, K) {
const L = A.length - (K % A.length); // to get the rotation length value below array length (since rotation of product of array length gives same array)
const A1 = A.slice(L); // last part of array which need to be get to front after L times rotation
const A2 = A.slice(0, L); // part which rotate L times to right side
const Result = [...A1, ...A2]; // reverse and join both array by spreading
return Result;
}
Rotate an array of n elements to the right by k steps.
For instance, with n = 7 and k = 3, the array [1,2,3,4,5,6,7] is rotated to [5,6,7,1,2,3,4].
In JS the solution will be 2 part, in two line:
function rotateArray(array,k){
// remove the rotation part
const splice = [...array].splice(0,k); //... for make a clone;
// add reversed version of the what left
return array.concat(splice.reverse()) from original array.
}
Related
Given an integer S and an array arr[], the task is to find the minimum number of elements whose sum is S, such that an element of the array can be chosen only once to get sum S.
Example:
Input: arr[] = {25, 10, 5}, S = 30
Output: 2
Explanation:
Minimum possible solution is 2, (25+5)
Example:
Input: arr[] = {2, 1, 4, 3, 5, 6}, Sum= 6
Output: 1
Explanation:
Minimum possible solution is 1, (6)
I have found similar solution here but it says element of array can be used multiple times.
I have this code from the link which uses an array element multiple times, but how to restrict this to use only once?
static int Count(int S[], int m, int n)
{
int [][]table = new int[m + 1][n + 1];
// Loop to initialize the array
// as infinite in the row 0
for(int i = 1; i <= n; i++)
{
table[0][i] = Integer.MAX_VALUE - 1;
}
// Loop to find the solution
// by pre-computation for the
// sequence
for(int i = 1; i <= m; i++)
{
for(int j = 1; j <= n; j++)
{
if (S[i - 1] > j)
{
table[i][j] = table[i - 1][j];
}
else
{
// Minimum possible for the
// previous minimum value
// of the sequence
table[i][j] = Math.min(table[i - 1][j],
table[i][j - S[i - 1]] + 1);
}
}
}
return table[m][n];
}
// Driver Code
public static void main(String[] args)
{
int arr[] = { 9, 6, 5, 1 };
int m = arr.length;
System.out.print(Count(arr, m, 11));
}
The idiomatic approach for this is to loop backwards when updating the table of previous results.
static int minElementsForSum(int[] elems, int sum){
int[] minElems = new int[sum + 1];
for(int i = 1; i <= sum; i++) minElems[i] = Integer.MAX_VALUE;
for(int elem: elems)
for(int i = sum; i >= elem; i--)
if(minElems[i - elem] != Integer.MAX_VALUE)
minElems[i] = Math.min(minElems[i], minElems[i - elem] + 1);
return minElems[sum];
}
Demo
So I am working on a Leetcode question and my code works for some cases but fails for certain cases.
Here is the question:
Given a n x n matrix where each of the rows and columns are sorted in ascending order, find the kth smallest element in the matrix.
Note that it is the kth smallest element in the sorted order, not the kth distinct element.
Example:
matrix = [[1, 5, 9], [10, 11, 13], [12, 13, 15]]
k = 8
return: 13
My approach is to use a minHeap, even if it stated that the array is sorted I still needed to make sure that I have it sorted from least to greatest value.
Here is my code:
class Solution {
public int kthSmallest(int[][] matrix, int k) {
int row = matrix.length;
int col = matrix[0].length;
int result = 0;
HashMap<Integer, Integer> map = new HashMap<>();
//populate HashMap
for (int i = 0; i < row; i++) {
for (int j = 0; j < col; j++) {
map.put(matrix[i][j],
map.getOrDefault(matrix[i][j], 0) + 1);
}
}
PriorityQueue<Map.Entry<Integer, Integer>> pq =
new PriorityQueue<>((n1, n2) -> n1.getValue() - n2.getValue());
pq.addAll(map.entrySet());
for (int i = 0; i < k && !(pq.isEmpty()); i++) {
result = pq.poll().getKey();
}
return result;
}
}
Here are my inputs:
Input 1: [[1,5,9],[10,11,13],[12,13,15]]
k = 8
Input 2: [[1,2],[1,3]]
k = 1
Here are the outputs:
Output 1: 13
Output 2: 2
Notice that the code works just fine for my first input where the 8th smallest element in the 2d-array is 13, but for the second input, the code is returning 2 as my first smallest element rather than returning 1.
Can someone please help me fix the code? I ask that you please not implement some fancy shorthand sorting technique e.g. Arrays.sort... it's not ideal for me as I am trying to learn how to implement heaps. Thanks a bunch :)
For solving this problem we can also binary search (a bit more efficient):
public class Solution {
public static final int kthSmallest(final int[][] matrix, final int k) {
int lo = matrix[0][0];
int hi = matrix[matrix.length - 1][matrix[0].length - 1] + 1;
while (lo < hi) {
final int mid = lo + (hi - lo) / 2;
int count = 0;
int col = matrix[0].length - 1;
for (int row = 0; row < matrix.length; ++row) {
while (col >= 0 && matrix[row][col] > mid) {
col--;
}
count += (col + 1);
}
if (count < k) {
lo = mid + 1;
} else {
hi = mid;
}
}
return lo;
}
}
You can use the flatMapToInt method to iterate over the rows of a 2d array in one stream:
public static void main(String[] args) {
int[][] matrix1 = {{1, 5, 9}, {10, 11, 13}, {12, 13, 15}};
int[][] matrix2 = {{1, 2}, {1, 3}};
System.out.println(kthSmallest(matrix1, 8)); // 13
System.out.println(kthSmallest(matrix2, 1)); // 1
}
public static int kthSmallest(int[][] matrix, int k) {
return Arrays.stream(matrix)
.flatMapToInt(Arrays::stream)
.skip(k - 1)
.findFirst()
.getAsInt();
}
public static int kthSmallest(int[][] matrix, int k) {
return Arrays
.stream(matrix)
.flatMapToInt(x -> Arrays.stream(x))
.sorted()
.skip(k-1)
.findFirst()
.getAsInt();
}
public static int kthSmallestNumber(int[][] matrix, int k) {
return Arrays.stream(matrix).flatMapToInt(x->Arrays.stream(x))
.distinct()
.sorted()
.skip(k-1)
.findFirst()
.getAsInt();
}
Problem: Given K sorted arrays of size N each, merge them and print the sorted output.
Sample Input-1:
K = 3, N = 4
arr[][] = { {1, 3, 5, 7},
{2, 4, 6, 8},
{0, 9, 10, 11}} ;
Sample Output-1:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
I know there is a way to do this problem using a priority queue/min heap, but I want to do it using the merge procedure from mergeSort. The idea seems straightforward enough...at each iteration, merge the remaining arrays in groups of two, such that the number of arrays gets halved at each iteration.
However, whenever halving leads to an odd number, this becomes problematic.
My idea is that whenever halving leads to an odd number, we take care of the extra array by merging it with the array formed from the last merge.
The code I have so far is below. This only works on one out of 30 test cases, however:
static int[] mergeArrays(int[][] arr) {
int k = arr.length;
int n = arr[0].length;
if(k < 2){
return arr[0];
}
boolean odd_k;
if(k%2){
odd_k = false;
}
else{
odd_k = true;
}
while(k > 1){
int o;
if(odd_k){
o = (k/2) + 1;
}
else{
o = k/2;
}
int[][] out = new int[o][];
for(int i=0; i < k; i = i + 2){
int[] a;
int[] b;
if(odd_k && i == (k-1)){
b = arr[i];
b = out[i-1];
}
else{
a = arr[i];
b = arr[i+1];
}
out[i] = mergeTwo(a, b);
}
k = k/2;
if(k % 2 == 0){
odd_k = false;
}
else{
odd_k = true;
}
arr = out;
}
return arr[0];
}
static int[] mergeTwo(int[] a, int[] b){
int[] c = new int[a.length + b.length];
int i, j, k;
i = j = k = 0;
while(i < a.length && j < b.length){
if(a[i] < b[j]){
c[k] = a[i];
i++;
k++;
}
else{
c[k] = b[j];
j++; k++;
}
}
if(i < a.length){
while(i < a.length){
c[k] = a[i];
i++; k++;
}
}
if(j < b.length){
while(j < b.length){
c[k] = b[j];
j++; k++;
}
}
return c;
}
We can shorten your mergeTwo implementation,
static int[] mergeTwo(int[] a, int[] b) {
int[] c = new int[a.length + b.length];
int i = 0, j = 0, k = 0; // declare and initialize on one line
while (i < a.length && j < b.length) {
if (a[i] <= b[j]) {
c[k++] = a[i++]; // increment and assign
} else {
c[k++] = b[j++]; // increment and assign
}
}
// No need for extra if(s)
while (i < a.length) {
c[k++] = a[i++];
}
while (j < b.length) {
c[k++] = b[j++];
}
return c;
}
And we can then fix your mergeArrays and shorten it by starting with the first row from the int[][] and then using mergeTwo to concatenate the arrays iteratively. Like,
static int[] mergeArrays(int[][] arr) {
int[] t = arr[0];
for (int i = 1; i < arr.length; i++) {
t = mergeTwo(t, arr[i]);
}
return t;
}
I then tested it with
public static void main(String[] args) {
int arr[][] = { { 1, 3, 5, 7 }, { 2, 4, 6, 8 }, { 0, 9, 10, 11 } };
System.out.println(Arrays.toString(mergeArrays(arr)));
}
And I get (as expected)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
As you say you have merged two arrays at a time. As it is inefficient you can merge all subarrays same time. What you have to do is to find the minimum from every subarray and remember the position of that element.
To do that we can use another array (say curPos) to remember the current position
private int[] merge(int[][] arr)
{
int K = arr.length;
int N = arr[0].length;
/** array to keep track of non considered positions in subarrays **/
int[] curPos = new int[K];
/** final merged array **/
int[] mergedArray = new int[K * N];
int p = 0;
while (p < K * N)
{
int min = Integer.MAX_VALUE;
int minPos = -1;
/** search for least element **/
for (int i = 0; i < K; i++)
{
if (curPos[i] < N)
{
if (arr[i][curPos[i]] < min)
{
min = arr[i][curPos[i]];
minPos = i;
}
}
}
curPos[minPos]++;
mergedArray[p++] = min;
}
return mergedArray;
Probably the easiest way to handle this is to use a queue of arrays. Initially, add all the arrays to the queue. Then, remove the first two arrays from the queue, merge them, and add the resulting array to the queue. Continue doing that until there is only one array in the queue. Something like:
for each array in list of arrays
queue.push(array)
while queue.length > 1
a1 = queue.pop()
a2 = queue.pop()
a3 = merge(a1, a2)
queue.push(a3)
result = queue.pop()
That simplifies things quite a bit, and the problem of "halving" goes away.
I was working my Algorithm's midterm review and I tried to implement all the pseudo codes by Java in order to have a better understanding of algorithm. But on the heap sort part, there was something wrong with my code. My input array is
{10,16,4,10,14,7,9,3,2,8,1}
and the first element just represents the number of elements that I would like to sort. In other words, the elements needed to be sorted start from index 1.
My output of build max-heap is :
16 14 10 8 7 9 3 2 4 1
And my output of heap sort is :
1 3 2 4 7 8 9 10 14 16
It seemed my build-max-heap part worked well but I couldn't find bugs in heap-sort part, either.
public class Midterm{
public static void main(String[] args){
int[] C = {10,16,4,10,14,7,9,3,2,8,1};
/*for convenience, the first element in array C represent the
number of elements needed to be heapified;
*/
Midterm heap = new Midterm();
int n = C.length - 1;
for (int i = (n / 2); i > 0; i--){
heap.maxHeapify(C, i, n);
}
int index = 1;
while(index <= n){
System.out.print(C[index] + " ");
index++;
}
System.out.println();
Midterm heap2 = new Midterm();
heap2.heapSort(C);
int index2 = 1;
while(index2 <= n){
System.out.print(C[index2] + " ");
index2++;
}
System.out.println();
}
public void heapSort(int[] A){
int n = A.length - 1;
for (int i = n; i >= 2; i--){
exchange(A, 1, i);
maxHeapify(A, 1, i - 1);
}
}
public void maxHeapify(int[] A, int i, int n){
int left = 2 *i, right = 2 * i + 1;
int largest;
if (left < n && A[left] > A[i]){
largest = left;
}else{
largest = i;
}
if (right < n && A[right] > A[largest]){
largest = right;
}
if (largest != i){
exchange(A, i, largest);
maxHeapify(A, largest,n);
}
}
private void exchange(int[] A, int i , int j){
int temp = A[i];
A[i] = A[j];
A[j] = temp;
}
}
There are 2 mistakes in your code:
1. The for loop for the heapsort goes from last element to first element, so
for (int i = n; i >= 2; i--){
should be:
for (int i = n; i >= 1; i--){
because the indices start from 0.
2. After performing a exchange(A, 1, i), the right call should be:
maxHeapify(A, 1, i)
check the below code.
public class HeapSort
{
public void sort(int arr[])
{
int n = arr.length;
// Build heap (rearrange array)
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
// One by one extract an element from heap
for (int i=n-1; i>=0; i--)
{
// Move current root to end
int temp = arr[0];
arr[0] = arr[i];
arr[i] = temp;
// call max heapify on the reduced heap
heapify(arr, i, 0);
}
}
// To heapify a subtree rooted with node i which is
// an index in arr[]. n is size of heap
void heapify(int arr[], int n, int i)
{
int largest = i; // Initialize largest as root
int l = 2*i + 1; // left = 2*i + 1
int r = 2*i + 2; // right = 2*i + 2
// If left child is larger than root
if (l < n && arr[l] > arr[largest])
largest = l;
// If right child is larger than largest so far
if (r < n && arr[r] > arr[largest])
largest = r;
// If largest is not root
if (largest != i)
{
int swap = arr[i];
arr[i] = arr[largest];
arr[largest] = swap;
// Recursively heapify the affected sub-tree
heapify(arr, n, largest);
}
}
/* A utility function to print array of size n */
static void printArray(int arr[])
{
int n = arr.length;
for (int i=0; i<n; ++i)
System.out.print(arr[i]+" ");
System.out.println();
}
// Driver program
public static void main(String args[])
{
int arr[] = {12, 11, 13, 5, 6, 7};
int n = arr.length;
HeapSort ob = new HeapSort();
ob.sort(arr);
System.out.println("Sorted array is");
printArray(arr);
}
}
I have wrote a program to shift an int array left, but cannot find a way to move it right. Could you take a look at my code and comment if you have any ideas how how to "rotate" my array right based on the number of spaces (int x), as currently it only moves left. Thanks
public void makeRight(int x) {
int[] anArray = {0, 1, 2, 3, 4, 5};
int counter = 0;
while (counter < x) {
int temp = anArray[0];
for (int i = 0; i < anArray.length - 1; i++) {
anArray[i] = anArray[i + 1];
}
anArray[anArray.length - 1] = temp;
counter++;
}
for (int i = 0; i < anArray.length; i++){
System.out.print(anArray[i] + " ");
}
}
Rotate an array right
public void makeRight( int x )
{
int[] anArray =
{ 0, 1, 2, 3, 4, 5 };
int counter = 0;
while ( counter < x )
{
int temp = anArray[anArray.length - 1];
for ( int i = anArray.length - 1; i > 0; i-- )
{
anArray[i] = anArray[i - 1];
}
anArray[0] = temp;
counter++;
}
for ( int i = 0; i < anArray.length; i++ )
{
System.out.print( anArray[i] + " " );
}
}
while (counter < x) {
int temp = anArray[anArray.length - 1];
for (int i = anArray.length - 1; i > 0; i--) {
anArray[i] = anArray[i - 1];
}
anArray[0] = temp;
counter++;
}
in my opinion basically you had done on most of the parts to rotate an array (right).
Just that the concept of
anArray[i] = secondArray[(i + x) % anArray.length];
And
anArray[(i + x) % anArray.length] = secondArray[i];
is a bit different.
There would be something like this
int[] anArray = {0, 1, 2, 3, 4, 5};
//int counter = 0;
//int x = 2;
int[] secondArray = new int[anArray.length];
for (int i = 0; i < anArray.length; i++) {
secondArray[(i + x) % anArray.length] = anArray[i];
}
for (int i = 0; i < secondArray.length; i++){
System.out.print(secondArray[i] + " ");
}
As for how the "%" works, Codility - CyclicRotation this link should had a clear explanation.
Below function can help you
public static void rightRotateArray(int[] a, int requiredIterations) {
// right-rotate [a] by k moves
// totalActiveIterations by MOD
// => because every n(a.length) rotations ==> we receive the same array
int totalActiveIterations = requiredIterations % a.length;
for (int i = 0; i < totalActiveIterations; i++) {
// make lastElement as BKP temp
int temp = a[a.length - 1];
// make other elements => each one equal previous one [starting by lastElement]
for (int j = (a.length - 1); j >= 1; j--) {
a[j] = a[j - 1];
}
// make 1stElement equal to (BKP as temp = lastElement)
a[0] = temp;
}
}
Something like this should work
private void shiftArrayRight() {
int endElementvalue = element[element - 1];
int[] startElements = Arrays.copyOfRange(element, 0 , element.length - 1);
element[0] = endElementvalue;
for(int i = 0, x = 1; i < startElements.length; i++, x++) {
element[x] = startElements[i];
}
System.out.println(Arrays.toString(element);
}
The other answers are merely code dumps, with zero explanations. Here's an algorithm I came up with:
We rotate the array in place. Observe that the target position of every element is given by (index + k) modulo size. For range 0 to k - 1, we recursively swap each element with the one in its target position as long as the target position is greater than the current position. This is because since we are incrementally progressing from lower to higher indices, a smaller target index indicates that the corresponding element had already been swapped.
Example:
Rotate [1, 2, 3, 4, 5, 6] by 3
Index to target index:
0 to 3
1 to 4
2 to 5
3 to 0
4 to 1
5 to 2
swap(0, 3) => [4, 2, 3, 1, 5, 6]
swap(0, 0) => return
swap(1, 4) => [4, 5, 3, 1, 2, 6]
swap(1, 1) => return
swap(2, 5) => [4, 2, 6, 1, 2, 3]
swap(2, 2) => return
Done!
Another example:
Rotate [2, 3, 4, 1] by 1
Index to target index:
0 to 1
1 to 2
2 to 3
3 to 0
swap(0, 1) => [3, 2, 4, 1]
swap(0, 2) => [4, 2, 3, 1]
swap(0, 3) => [1, 2, 3, 4]
swap(3, 0) => return
Done!
Code:
static void rotateRight(int[] xs, int k) {
swap(0, 0, xs, k);
}
private static void swap(int original, int current, int[] xs, int k) {
int target = (original + k) % xs.length;
if (target > current) {
int tmp = xs[current];
xs[current] = xs[target];
xs[target] = tmp;
swap(target, current, xs, k);
}
}
public static List<int> rotateLeft(int d, List<int> arr)
{
int listSize = arr.Count();
int[] newArr = new int[listSize];
for(int oldIndex=0; oldIndex< listSize; oldIndex++)
{
int newIndex = (oldIndex + (listSize - d))% listSize;
newArr[newIndex] = arr[oldIndex];
}
List<int> newList = new List<int>(newArr);
return newList;
}
the easiest way is to use c++ 11 and above, in Codility test for Cyclicrotation.
imagine doing it in earlier versions, Duh!
#include <algorithm>
#include <iterator>
vector<int> solution(vector<int> &A, int K) {
if (A.size() == 0) {
return A;
}
for (int i=0;i<K;i++) {
//Create auciliary array
std::vector<int> aux(A.size());
//copy array to be rotated there by means of C++11
std::copy(std::begin(A), std::end(A), std::begin(aux));
//insert last element from aux to begining of the array
A.insert(A.begin(), aux.end()-1, aux.end());
//remove last element which is already become first
A.pop_back();
}
return A;
}
Just change the code like this
public void makeRight(int x) {
int[] anArray = {0, 1, 2, 3, 4, 5};
int counter = 0;
while(counter< x){
int temp = anArray[anArray.length - 1];
for (int i = anArray.length - 1; i > 0; i--) {
anArray[i] = anArray[i - 1];
}
anArray[0] = temp;
counter++;
}
for (int i = 0; i < anArray.length; i++)
System.out.print(anArray[i] + " ");
}