Top 10 Algorithms for Coding Interview Questions in 2025

In today’s highly competitive job market cracking coding interviews is crucial for securing positions at top tech companies. Algorithms form the backbone of most coding interview questions and understanding them thoroughly can make a huge difference in your performance. Whether you are preparing for interviews at companies like Google, Amazon, or Microsoft, mastering key algorithms is essential.

In this comprehensive guide we will go through the top 10 algorithms for coding interview questions that you must know to excel in your interviews. Along with a detailed explanation of each algorithm, we will provide at least 10 interview questions related to each to ensuring that you have a deep understanding of these concepts and are well-prepared.

Binary Search

Binary Search is one of the most efficient searching algorithms for sorted arrays or lists. By dividing the search interval in half and focusing only on the relevant half, binary search reduces the problem size exponentially with each step. This algorithm works on the principle of divide-and-conquer.

Time Complexity: O(log n)
Binary search is used in a wide range of problems like searching for an element, finding bounds, and many more. It is a highly efficient way of narrowing down search space.

Sample Coding Interview Questions of Binary Search

1. Find an element in a sorted array.
2. Implement binary search on a rotated sorted array.
3. Find the first and last position of an element in a sorted array.
4. Search for an element in a nearly sorted array.
5. Find the peak element in a 2D matrix.
6. Find the minimum element in a rotated sorted array.
7. Find the closest number to a target in a sorted array.
8. Find the kth smallest element in a sorted matrix.
9. Implement binary search for finding square root.
10. Search for an element in a matrix where each row and column is sorted.

Depth-First Search (DFS)

DFS is a graph traversal algorithm that explores a graph deeply by visiting the nodes of a graph or tree in a recursive manner. It goes deep into one branch until no further node is reachable, then backtracks and explores the next unvisited branch. DFS can be implemented using a stack or recursion.

Time Complexity: O(V + E), where V is vertices and E is edges.
DFS is particularly useful in problems where all nodes need to be visited or in tree-related problems like searching, finding paths, and checking for cycles.

Sample Coding Interview Questions for DFS

1. Implement DFS for a graph.
2. Find connected components in an undirected graph.
3. Topological sort using DFS.
4. Detect a cycle in a directed graph.
5. Solve the maze problem using DFS.
6. Check for path existence between two nodes in a graph.
7. Find the number of islands in a grid.
8. Perform DFS traversal of a binary tree.
9. Check if a graph is bipartite using DFS.
10. Find the longest path in a tree.

Breadth-First Search (BFS)

BFS is another graph traversal algorithm that explores the graph level by level. Starting from the root, it explores all the immediate neighbors before moving on to their neighbors. BFS is implemented using a queue.

Time Complexity: O(V + E)
BFS is mainly used to find the shortest path in an unweighted graph and is also effective for problems where nodes must be processed in layers.

Sample Coding Interview Questions for BFS

1. Implement BFS for a graph.
2. Find the shortest path in an unweighted graph.
3. Solve the shortest path in a binary maze.
4. Find the level of a given node in a tree.
5. Find the minimum number of moves to reach the target in a chessboard problem.
6. Perform BFS on a tree.
7. Count the number of connected components in a graph.
8. Find the minimum steps to reach a destination in a grid.
9. Detect cycles in a graph using BFS.
10. Determine if there is a path between two nodes.

Dynamic Programming (DP)

Dynamic Programming is a method for solving complex problems by breaking them down into simpler subproblems. It stores the results of solved subproblems to avoid redundant work, making it highly efficient. DP is used when a problem has overlapping subproblems and optimal substructure.

Time Complexity: Varies, depending on the problem.
DP helps solve problems that involve decision-making and recursion, particularly in optimization problems. It’s one of the most important concepts for coding interviews.

Sample Coding Interview Questions for Dynamic Programming

1. Find the nth Fibonacci number.
2. Solve the 0/1 Knapsack problem.
3. Longest Common Subsequence (LCS).
4. Longest Increasing Subsequence.
5. Coin change problem.
6. Matrix chain multiplication.
7. Edit distance between two strings.
8. Subset sum problem.
9. Minimum path sum in a grid.
10. Count the number of ways to climb stairs.

Merge Sort

Merge Sort is a divide-and-conquer algorithm that splits the array into two halves, recursively sorts them, and then merges them back together in sorted order. The merging process ensures that the result is sorted.

Time Complexity: O(n log n)
Merge Sort is important for efficiently sorting large datasets, especially when the dataset cannot fit into memory (external sorting).

Sample Coding Interview Questions for Merge Sort

1. Implement merge sort.
2. Sort an array using merge sort.
3. Merge two sorted arrays into one sorted array.
4. Sort a linked list using merge sort.
5. Find the median of two sorted arrays.
6. Count the inversions in an array.
7. Merge multiple sorted arrays into one.
8. Sort an array in O(n log n) time.
9. Find the kth largest element in an array using merge sort.
10. Sort an array using merge sort without extra space.

Quick Sort

Quick Sort is another divide-and-conquer algorithm that partitions the array into two subarrays around a pivot element. It recursively sorts these subarrays, ensuring that elements are placed in their correct positions.

Time Complexity: O(n log n) on average and O(n²) in the worst case.
Quick Sort is a highly efficient in-place sorting algorithm and particularly when working with large datasets.

Sample Coding Interview Questions

1. Implement quicksort.
2. Find the kth smallest element in an array.
3. Sort an array using quicksort.
4. Quickselect algorithm to find the kth smallest element.
5. Sort a linked list using quicksort.
6. Find the median of an unsorted array using quickselect.
7. Implement quicksort with a random pivot.
8. Check if an array is sorted using quicksort.
9. Find the intersection of two arrays using quicksort.
10. Sort a nearly sorted array using quicksort.

Greedy Algorithms

Greedy algorithms make locally optimal choices at each step in the hope of finding a global optimum. While these algorithms are often more efficient, they may not always lead to the optimal solution.

Time Complexity: Varies depending on the problem.
Greedy algorithms are useful in optimization problems, especially when they guarantee the optimal solution, like in Minimum Spanning Tree (MST) or shortest path problems.

Sample Coding Interview Questions

1. Activity selection problem.
2. Coin change problem with the minimum number of coins.
3. Huffman coding.
4. Fractional Knapsack problem.
5. Minimum Spanning Tree using Kruskal’s algorithm.
6. Job scheduling with deadlines.
7. Find the minimum number of intervals to cover all points.
8. Interval partitioning problem.
9. Find the maximum number of non-overlapping intervals.
10. Optimal job assignment using greedy algorithm.

8. Dijkstra’s Algorithm

Dijkstra’s Algorithm is used to find the shortest path in a weighted graph with non-negative edges. It uses a priority queue (min-heap) to select the node with the least distance and updates neighboring nodes.

Time Complexity: O(E log V)
Dijkstra’s algorithm is essential for solving graph-based problems where you need the shortest path in weighted graphs.

Sample Coding Interview Questions

1. Find the shortest path from a source node to all other nodes.
2. Find the shortest path from a source to a destination node.
3. Implement Dijkstra’s algorithm.
4. Find the longest path in a directed acyclic graph.
5. Shortest path in a weighted graph.
6. Find the shortest path in a graph with non-negative weights.
7. Shortest path with a given condition (e.g., certain number of hops).
8. Implement the A* algorithm using Dijkstra.
9. Solve the problem of finding the minimum spanning tree using Dijkstra.
10. Find the shortest path in a grid with weighted obstacles.

9. Floyd-Warshall Algorithm

The Floyd-Warshall algorithm is used to find the shortest paths between all pairs of nodes in a graph, which is helpful when you need to compute the shortest paths between many pairs of nodes.

Time Complexity: O(V³)
This algorithm is useful when you need to calculate the shortest paths between all pairs of vertices, especially when working with dense graphs.

Sample Coding Interview Questions

1. Find the shortest paths between all pairs of nodes.
2. Implement the Floyd-Warshall algorithm.
3. Detect negative weight cycles in a graph.
4. Find the shortest path between any two vertices.
5. Check if a graph is strongly connected using Floyd-Warshall.
6. Solve all-pairs shortest path problem using dynamic programming.
7. Find the maximum distance in a weighted graph using Floyd-Warshall.
8. Implement the shortest path between all nodes in a grid.
9. Apply the Floyd-Warshall algorithm to a directed graph.
10. Use Floyd-Warshall to find paths with fewer than a given number of edges.

10. Bellman-Ford Algorithm

The Bellman-Ford algorithm is used to find the shortest path from a single source node to all other nodes in a graph, even when there are negative weight edges. It can also detect negative weight cycles in a graph.

Time Complexity: O(VE)
Bellman-Ford is important because it works on graphs with negative edge weights, unlike Dijkstra’s algorithm, which only works with non-negative weights.

Sample Coding Interview Questions

1. Implement Bellman-Ford to find the shortest path.
2. Detect negative weight cycles in a graph.
3. Find the shortest path in a graph with negative edges.
4. Modify Bellman-Ford to handle multiple sources.
5. Check if a given graph has a negative weight cycle.
6. Find the shortest path using Bellman-Ford with edge relaxations.
7. Solve the shortest path problem in a graph with varying weights.
8. Find the shortest path in a directed acyclic graph.
9. Find the maximum path cost in a graph using Bellman-Ford.
10. Detect negative cycles using the Bellman-Ford algorithm.

Conclusion

Mastering these top 10 algorithms for coding interviews is key to acing your technical interviews. Whether it is searching and sorting, graph traversal, dynamic programming, or greedy algorithms, understanding the concepts and practicing problem-solving will give you the edge you need. Prepare for your coding interview by learning these algorithms, practicing with real-world problems, and sharpening your problem-solving skills. The journey may seem tough, but consistent practice will surely help you succeed.