ALGORITHM READING NOTE

Dijkstra's Algorithm

Dijkstra finds single-source shortest paths in a graph with non-negative edge weights by repeatedly finalizing the unsettled node with the smallest known distance.

TYPEAlgorithmCATEGORYGraphsDEPTHAdvancedTYPICAL COMPLEXITYO((V+E) log V) with heap

SHORT INTERVIEW ANSWER

Start with this mental model

Dijkstra finds single-source shortest paths in a graph with non-negative edge weights by repeatedly finalizing the unsettled node with the smallest known distance.

SIMPLE EXPLANATION

How it works, without unnecessary jargon

Initialize source distance to 0 and others to infinity.

Use a min-priority queue; when an edge u→v gives a cheaper route, relax v and update its distance.

EXECUTION

Read the algorithm as a sequence of decisions

Define directed/undirected and weighted/unweighted assumptions.

Choose the graph representation.

Track algorithm state and handle disconnected/cyclic cases explicitly.

A small example to keep in mind

Read a tiny input by hand and write down the state after every important operation. For Dijkstra's Algorithm, the goal is to make the invariant visible rather than to memorize code.

READABLE JAVASCRIPT IMPLEMENTATIONJavaScript

// Pseudocode-like JavaScript. Use a real min-heap in production.
function dijkstra(graph, start) {
  const dist = new Map([[start, 0]]);
  const pq = [[0, start]];

  while (pq.length) {
    pq.sort((a, b) => a[0] - b[0]);
    const [cost, node] = pq.shift();
    if (cost !== dist.get(node)) continue;

    for (const [next, weight] of graph[node] ?? []) {
      const candidate = cost + weight;
      if (candidate < (dist.get(next) ?? Infinity)) {
        dist.set(next, candidate);
        pq.push([candidate, next]);
      }
    }
  }
  return dist;
}

How to read this code

Do not memorize the syntax. Follow the state that changes on each line and connect it to the invariant described above.

COMPLEXITY

O((V+E) log V) with heap

Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.

WHEN TO USE IT

Good fit

Use the algorithm only when its graph assumptions match the problem.

COMMON MISTAKES

What usually goes wrong

Using it with negative edge weights.
Forgetting stale entries when using a heap without decrease-key.

HOW TO EXPLAIN IT IN AN INTERVIEW

A professional answer shape

State the non-negative-weight requirement and explain relaxation. With a binary heap and adjacency list, a common complexity is O((V+E) log V).

Problem→Core idea→Invariant / state→Big-O→Trade-off

QUICK INTERVIEW CHECK

What problem does Dijkstra's Algorithm solve?

Dijkstra finds single-source shortest paths in a graph with non-negative edge weights by repeatedly finalizing the unsettled node with the smallest known distance.

What should I mention about complexity?

Its typical cost here is O((V+E) log V) with heap, but a complete answer should connect that cost to the representation, input constraints and the dominant operations.

What is the most common mistake?

Using it with negative edge weights.

Continue readingGraph representationDFS/BFSPriority queues

// Pseudocode-like JavaScript. Use a real min-heap in production. function dijkstra(graph, start) { const dist = new Map([[start, 0]]); const pq = [[0, start]]; while (pq.length) { pq.sort((a, b) => a[0] - b[0]); const [cost, node] = pq.shift(); if (cost !== dist.get(node)) continue; for (const [next, weight] of graph[node] ?? []) { const candidate = cost + weight; if (candidate < (dist.get(next) ?? Infinity)) { dist.set(next, candidate); pq.push([candidate, next]); } } } return dist; }