Binary TreesBinary Trees36
❯
  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Inorder Traversal of a Binary Tree using Recursion
  4. 4Inorder Traversal of a Binary Tree using Iteration
  5. 5Postorder Traversal of a Binary Tree Using Recursion
  6. 6Postorder Traversal of a Binary Tree using Iteration
  7. 7Level Order Traversal of a Binary Tree using Recursion
  8. 8Level Order Traversal of a Binary Tree using Iteration
  9. 9Reverse Level Order Traversal of a Binary Tree using Iteration
  10. 10Reverse Level Order Traversal of a Binary Tree using Recursion
  11. 11Find Height of a Binary Tree
  12. 12Find Diameter of a Binary Tree
  13. 13Find Mirror of a Binary Tree
  14. 14Left View of a Binary Tree
  15. 15Right View of a Binary Tree
  16. 16Top View of a Binary Tree
  17. 17Bottom View of a Binary Tree
  18. 18Zigzag Traversal of a Binary Tree
  19. 19Check if a Binary Tree is Balanced
  20. 20Diagonal Traversal of a Binary Tree
  21. 21Boundary Traversal of a Binary Tree
  22. 22Construct a Binary Tree from a String with Bracket Representation
  23. 23Convert a Binary Tree into a Doubly Linked List
  24. 24Convert a Binary Tree into a Sum Tree
  25. 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
  26. 26Check if a Binary Tree is a Sum Tree
  27. 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
  28. 28Lowest Common Ancestor (LCA) in a Binary Tree
  29. 29Solve the Tree Isomorphism Problem
  30. 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
  31. 31Check if Two Binary Trees are Mirror Images
  32. 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
  33. 33Print All Paths in a Binary Tree with a Given Sum
  34. 34Find the Distance Between Two Nodes in a Binary Tree
  35. 35Find the kth Ancestor of a Node in a Binary Tree
  36. 36Find All Duplicate Subtrees in a Binary Tree
GraphsGraphs46
❯
  1. 1Breadth-First Search in Graphs
  2. 2Depth-First Search in Graphs
  3. 3Number of Provinces in an Undirected Graph
  4. 4Connected Components in a Matrix
  5. 5Rotten Oranges Problem - BFS in Matrix
  6. 6Flood Fill Algorithm - Graph Based
  7. 7Detect Cycle in an Undirected Graph using DFS
  8. 8Detect Cycle in an Undirected Graph using BFS
  9. 9Distance of Nearest Cell Having 1 - Grid BFS
  10. 10Surrounded Regions in Matrix using Graph Traversal
  11. 11Number of Enclaves in Grid
  12. 12Word Ladder - Shortest Transformation using Graph
  13. 13Word Ladder II - All Shortest Transformation Sequences
  14. 14Number of Distinct Islands using DFS
  15. 15Check if a Graph is Bipartite using DFS
  16. 16Topological Sort Using DFS
  17. 17Topological Sort using Kahn's Algorithm
  18. 18Cycle Detection in Directed Graph using BFS
  19. 19Course Schedule - Task Ordering with Prerequisites
  20. 20Course Schedule 2 - Task Ordering Using Topological Sort
  21. 21Find Eventual Safe States in a Directed Graph
  22. 22Alien Dictionary Character Order
  23. 23Shortest Path in Undirected Graph with Unit Distance
  24. 24Shortest Path in DAG using Topological Sort
  25. 25Dijkstra's Algorithm Using Set - Shortest Path in Graph
  26. 26Dijkstra’s Algorithm Using Priority Queue
  27. 27Shortest Distance in a Binary Maze using BFS
  28. 28Path With Minimum Effort in Grid using Graphs
  29. 29Cheapest Flights Within K Stops - Graph Problem
  30. 30Number of Ways to Reach Destination in Shortest Time - Graph Problem
  31. 31Minimum Multiplications to Reach End - Graph BFS
  32. 32Bellman-Ford Algorithm for Shortest Paths
  33. 33Floyd Warshall Algorithm for All-Pairs Shortest Path
  34. 34Find the City With the Fewest Reachable Neighbours
  35. 35Minimum Spanning Tree in Graphs
  36. 36Prim's Algorithm for Minimum Spanning Tree
  37. 37Disjoint Set (Union-Find) with Union by Rank and Path Compression
  38. 38Kruskal's Algorithm - Minimum Spanning Tree
  39. 39Minimum Operations to Make Network Connected
  40. 40Most Stones Removed with Same Row or Column
  41. 41Accounts Merge Problem using Disjoint Set Union
  42. 42Number of Islands II - Online Queries using DSU
  43. 43Making a Large Island Using DSU
  44. 44Bridges in Graph using Tarjan's Algorithm
  45. 45Articulation Points in Graphs
  46. 46Strongly Connected Components using Kosaraju's Algorithm

Rearrange Array Alternately with Positive and Negative Elements Optimal Approach

Arrays

Contents

ProblemExamplesVisualizationSolutionAlgorithmCodeTimeSpace

Problem Statement❯

Given an array of integers that contains both positive and negative numbers, your task is to rearrange the elements so that they appear in an alternating order of positive and negative values, starting with a positive number.

  • If there are extra positive or negative numbers, place them at the end of the array.
  • The relative order of elements is not required to be preserved.

If the array is empty or has only one type of number (only positive or only negative), it should be returned as-is.

Examples❯

Input Array Rearranged Output Description
[1, 2, -3, -4, 5, -6] [1, -3, 2, -4, 5, -6] Alternating positive and negative, starting with positiveVisualization
[-1, 2, -3, 4, -5, 6] [2, -1, 4, -3, 6, -5] Signs alternate starting with positive, values rearrangedVisualization
[1, 2, 3, 4] [1, 2, 3, 4] Only positive numbers, no rearrangement neededVisualization
[-1, -2, -3, -4] [-1, -2, -3, -4] Only negative numbers, no rearrangement neededVisualization
[1] [1] Single element array, returned as-isVisualization
[-1] [-1] Single negative number, returned as-isVisualization
[] [] Empty array, output is also emptyVisualization
[1, -2, 3, -4, 5, -6, 7] [1, -2, 3, -4, 5, -6, 7] One extra positive number at the endVisualization
[1, -2, -3, -4] [1, -2, -3, -4] More negatives than positives; remaining negatives stay at endVisualization

Visualization Player

Solution❯

To solve this problem, we need to rearrange the array such that the signs of the numbers alternate—starting with a positive number, followed by a negative, and so on. The aim is to do this efficiently without using extra space.

We handle this using an index-based placement strategy. We imagine two roles: one index (say posIndex) is in charge of placing positives at even indices (0, 2, 4...), and another index (say negIndex) is for placing negatives at odd indices (1, 3, 5...).

As we go through the array, we check if the current element is at the wrong place based on its sign. If it is, we place it in the correct index (posIndex or negIndex) and increment that index by 2. This ensures alternate placement of positives and negatives.

Handling Different Cases

  • Normal case: When the number of positives and negatives is roughly equal, this alternating pattern works perfectly, and we end up with a well-balanced array.
  • Unequal count: If one type (say, positives) is more than the other, then the extra values will be left over at the end. That’s okay and acceptable by the problem definition.
  • All positive or all negative: If there’s no opposite sign to alternate with, we simply return the array as-is. Nothing can be rearranged here.
  • Empty array: The result is also an empty array since there's nothing to rearrange.
  • Single element: Whether it’s positive or negative, it should be returned untouched because there's no second number to alternate with.

This approach is optimal as it rearranges the array in a single traversal and uses only constant extra space (O(1)).

Also, note that the relative order of the numbers does not matter. So swapping values to place them correctly is allowed and helps us achieve this in-place.

Algorithm Steps❯

  1. Given an array arr of integers containing both positive and negative numbers.
  2. We want to rearrange it such that the signs alternate, starting with a positive number.
  3. Initialize posIndex = 0 and negIndex = 1.
  4. Traverse the array once. For every positive element found at the wrong position (odd index), place it at posIndex and increment posIndex by 2.
  5. For every negative element found at the wrong position (even index), place it at negIndex and increment negIndex by 2.
  6. Repeat the process until both indices exceed the array length.

Code

Python
JavaScript
Java
C++
C
def rearrange_alternating_optimal(arr):
    n = len(arr)
    result = [0] * n
    pos_index, neg_index = 0, 1
    for num in arr:
        if num >= 0 and pos_index < n:
            result[pos_index] = num
            pos_index += 2
        elif num < 0 and neg_index < n:
            result[neg_index] = num
            neg_index += 2
    return result

# Sample Input
arr = [1, 2, 3, -4, -1, 4]
print("Rearranged Array:", rearrange_alternating_optimal(arr))

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(n)In the best case, where the array is already alternating with correct signs at correct indices, we still traverse the array once to validate, resulting in linear time.
Average CaseO(n)Each element in the array is visited once during the traversal to place it in the correct position, ensuring a single-pass solution.
Worst CaseO(n)Regardless of the initial arrangement of positive and negative numbers, the array is traversed once and elements are moved in constant time per element.

Space Complexity❯

O(n)

Explanation: Although the algorithm is optimal in time, it creates a new array to store elements in the correct alternating order, requiring space proportional to the input size.