Heuristics are really helpful for making shortest path algorithms work better. They help steer the search in a smart way so that it can find the destination faster. Popular algorithms in graph theory, like Dijkstra’s Algorithm, Bellman-Ford Algorithm, and Floyd-Warshall Algorithm, can all use these heuristics to improve their performance.

What are Heuristics?

Heuristics are methods or tricks we use to make decisions, solve problems, or find solutions quicker than normal ways. They don’t always give the best answer, but they often help us get a good enough answer faster.

Examples in Shortest Path Algorithms:

1. A Algorithm*: This algorithm mixes Dijkstra's algorithm with heuristics. It uses a special formula for cost, which is usually written as $f(n) = g(n) + h(n)$. Here’s what that means:

   • $g(n)$ is the cost from the start point to point $n$.
   • $h(n)$ is the guess of the cost from point $n$ to the end point.

2. Greedy Best-First Search: This method uses a heuristic to decide which point to look at next. It does this by looking only at the estimated distance to the goal. This helps it find paths faster in certain situations.

By using heuristics, these algorithms can skip exploring paths that are not likely to lead to the goal. This can save a lot of time, especially in big graphs where checking every single path isn’t practical.