PHP Program to Find element at given index after a number of rotations
Last Updated :
23 Jul, 2024
An array consisting of N integers is given. There are several Right Circular Rotations of range[L..R] that we perform. After performing these rotations, we need to find an element at a given index.
Examples :
Input : arr[] : {1, 2, 3, 4, 5}
ranges[] = { {0, 2}, {0, 3} }
index : 1
Output : 3
Explanation : After first given rotation {0, 2}
arr[] = {3, 1, 2, 4, 5}
After second rotation {0, 3}
arr[] = {4, 3, 1, 2, 5}
After all rotations we have element 3 at given
index 1.
Method - 1: Brute-force Approach
The brute force approach is to actually rotate the array for all given ranges, finally return the element in at given index in the modified array.
Method - 2: Efficient Approach
We can do offline processing after saving all ranges.
Suppose, our rotate ranges are : [0..2] and [0..3]
We run through these ranges from reverse.
After range [0..3], index 0 will have the element which was on index 3.
So, we can change 0 to 3, i.e. if index = left, index will be changed to right.
After range [0..2], index 3 will remain unaffected.
So, we can make 3 cases :
If index = left, index will be changed to right.
If index is not bounds by the range, no effect of rotation.
If index is in bounds, index will have the element at index-1.
For better explanation:
10 20 30 40 50
Index: 1
Rotations: {0,2} {1,4} {0,3}
Answer:
Index 1 will have 30 after all the 3 rotations in the order {0,2} {1,4} {0,3}.
We performed {0,2} on A and now we have a new array A1.
We performed {1,4} on A1 and now we have a new array A2.
We performed {0,3} on A2 and now we have a new array A3.
Now we are looking for the value at index 1 in A3.
But A3 is {0,3} done on A2.
So index 1 in A3 is index 0 in A2.
But A2 is {1,4} done on A1.
So index 0 in A2 is also index 0 in A1 as it does not lie in the range {1,4}.
But A1 is {0,2} done on A.
So index 0 in A1 is index 2 in A.
On observing it, we are going deeper into the previous rotations
starting from the latest rotation.
{0,3}
|
{1,4}
|
{0,2}
This is the reason we are processing the rotations in reverse order.
Please note that we are not rotating the elements in the reverse order, just processing the index from reverse.
Because if we actually rotate in reverse order, we might get a completely different answer as in case of rotations the order matters.
PHP
<?php
// PHP code to rotate an array
// and answer the index query
// Function to compute the
// element at given index
function findElement($arr, $ranges,
$rotations, $index)
{
for ($i = $rotations - 1;
$i >= 0; $i--)
{
// Range[left...right]
$left = $ranges[$i][0];
$right = $ranges[$i][1];
// Rotation will not
// have any effect
if ($left <= $index &&
$right >= $index)
{
if ($index == $left)
$index = $right;
else
$index--;
}
}
// Returning new element
return $arr[$index];
}
// Driver Code
$arr = array(1, 2, 3, 4, 5);
// No. of rotations
$rotations = 2;
// Ranges according
// to 0-based indexing
$ranges = array(array(0, 2),
array(0, 3));
$index = 1;
echo findElement($arr, $ranges,
$rotations, $index);
// This code is contributed by ajit
?>
Complexity Analysis:
- Time Complexity: O(N), where N represents the given number of rotations.
- Auxiliary Space: O(1), no extra space is required, so it is a constant.
Please refer complete article on Find element at given index after a number of rotations for more details!
Similar Reads
DSA Tutorial - Learn Data Structures and Algorithms DSA (Data Structures and Algorithms) is the study of organizing data efficiently using data structures like arrays, stacks, and trees, paired with step-by-step procedures (or algorithms) to solve problems effectively. Data structures manage how data is stored and accessed, while algorithms focus on
7 min read
Quick Sort QuickSort is a sorting algorithm based on the Divide and Conquer that picks an element as a pivot and partitions the given array around the picked pivot by placing the pivot in its correct position in the sorted array. It works on the principle of divide and conquer, breaking down the problem into s
12 min read
Merge Sort - Data Structure and Algorithms Tutorials Merge sort is a popular sorting algorithm known for its efficiency and stability. It follows the divide-and-conquer approach. It works by recursively dividing the input array into two halves, recursively sorting the two halves and finally merging them back together to obtain the sorted array. Merge
14 min read
Bubble Sort Algorithm Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. This algorithm is not suitable for large data sets as its average and worst-case time complexity are quite high.We sort the array using multiple passes. After the fir
8 min read
Data Structures Tutorial Data structures are the fundamental building blocks of computer programming. They define how data is organized, stored, and manipulated within a program. Understanding data structures is very important for developing efficient and effective algorithms. What is Data Structure?A data structure is a st
2 min read
Breadth First Search or BFS for a Graph Given a undirected graph represented by an adjacency list adj, where each adj[i] represents the list of vertices connected to vertex i. Perform a Breadth First Search (BFS) traversal starting from vertex 0, visiting vertices from left to right according to the adjacency list, and return a list conta
15+ min read
Binary Search Algorithm - Iterative and Recursive Implementation Binary Search Algorithm is a searching algorithm used in a sorted array by repeatedly dividing the search interval in half. The idea of binary search is to use the information that the array is sorted and reduce the time complexity to O(log N). Binary Search AlgorithmConditions to apply Binary Searc
15 min read
Insertion Sort Algorithm Insertion sort is a simple sorting algorithm that works by iteratively inserting each element of an unsorted list into its correct position in a sorted portion of the list. It is like sorting playing cards in your hands. You split the cards into two groups: the sorted cards and the unsorted cards. T
9 min read
Dijkstra's Algorithm to find Shortest Paths from a Source to all Given a weighted undirected graph represented as an edge list and a source vertex src, find the shortest path distances from the source vertex to all other vertices in the graph. The graph contains V vertices, numbered from 0 to V - 1.Note: The given graph does not contain any negative edge. Example
12 min read
Selection Sort Selection Sort is a comparison-based sorting algorithm. It sorts an array by repeatedly selecting the smallest (or largest) element from the unsorted portion and swapping it with the first unsorted element. This process continues until the entire array is sorted.First we find the smallest element an
8 min read