dist[i][j] = shortest distance from i to j

For each intermediate vertex k:
  For each pair (i, j):
    dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j])
                 └── direct path ─┘  └─── via k ────────┘

flowchart LR
    subgraph Direct["Direct: i → j<br/>weight = 5"]
        i1["i"] -->|"5"| j1["j"]
    end

    subgraph Via["Via k: i → k → j<br/>weight = 2 + 1 = 3"]
        i2["i"] -->|"2"| k2["k"]
        k2 -->|"1"| j2["j"]
    end

    Direct --> Compare{"min(5, 3) = 3"}
    Via --> Compare

    style i1 fill:#7c3aed,color:#fff
    style j1 fill:#4f46e5,color:#fff
    style i2 fill:#7c3aed,color:#fff
    style k2 fill:#059669,color:#fff
    style j2 fill:#4f46e5,color:#fff
    style Compare fill:#6366f1,color:#fff

function floydWarshall(graph) {
  // graph: adjacency matrix (Infinity for no edge)
  const V = graph.length;
  const dist = graph.map(row => [...row]); // copy

  for (let k = 0; k < V; k++) {
    for (let i = 0; i < V; i++) {
      if (dist[i][k] === Infinity) continue; // skip impossible
      for (let j = 0; j < V; j++) {
        if (dist[k][j] === Infinity) continue;
        dist[i][j] = Math.min(dist[i][j], dist[i][k] + dist[k][j]);
      }
    }
  }

  return dist;
}

// Example
const INF = Infinity;
const G = [
  [0,   3,   INF, 7],
  [3,   0,   2,   INF],
  [INF, 2,   0,   1],
  [7,   INF, 1,   0],
];

const result = floydWarshall(G);
// result[0][3] = min(7, 3+2+1=6) = 6 (via B and C)