# Minimum cost path on the whole globe?

Geographic Information Systems## How do you find the minimum cost of path?

**Min cost path using recursion:**

- If N is less than zero or M is less than zero then return Integer Maximum(Base Case)
- If M is equal to zero and N is equal to zero then return cost[M][N](Base Case)
- Return cost[M][N] + minimum of (minCost(M-1, N-1), minCost(M-1, N), minCost(M, N-1))

## What is the shortest path based on minimum cost?

**The minimum cost flow problem can be seen as a generalization of the shortest path and maximum flow problems**. That is, by suitably choosing costs, capacities, and supplies we can solve shortest path or maximum flow using any method which will solve min cost flow.

## What is the least-cost algorithm?

Least-cost-path algorithm

The most common cost distance task is to **determine the single path through the space between a given source location and a destination location that has the least total accumulated cost**.

## What is the cost of a path in a graph?

The cost of a path in a costed graph is **the sum of the cost of the edges that make up the path**. The cheapest path between two nodes is the path between them that has the lowest cost. For example, in the above costed graph, the cheapest path between node a and node f is [a,c,e,f] with cost 7+2+3, that is 12.

## What is the formula for minimum cost?

Using the equation **min = c – b^2/4a**, we can find the minimum cost. Once again, we plug in our numbers and get min = 10 – (0.5^2)/(4 * 0.01), which simplifies to min = 10 – 0.25 / 0.04 = 3.75. So, the minimum cost to produce tennis balls is $3.75.

## How do you calculate minimum flow network?

Turn the feasible flow into a minimum flow by **solving a max flow problem**. You need to find the maximum flow on the graph that has capacities equal to flow(e) – lower-bound(e), where flow(e) means flow from the feasible flow. This maximum flow subtracted from the feasible flow will be a minimum flow.

## Will A * always find the lowest cost path?

If the heuristic function is admissible – meaning that it never overestimates the actual cost to get to the goal –, **A* is guaranteed to return a least-cost path from start to goal**.

## Does Google Maps use shortest path?

It also takes parameters such as time requirement, distance, etc., optimizing and choosing the better nodes. So now, **Google Maps also uses this algorithm to calculate the shortest path**, owing to its high accuracy and ability to deal with huge chunks of data and mammoth graphs.

## How do you find all the shortest paths?

**Below are the steps:**

- Start BFS traversal from source vertex.
- While doing BFS, store the shortest distance to each of the other nodes and also maintain a parent vector for each of the nodes.
- Make the parent of source node as “-1”.
- Recover all the paths using parent array.

## How do you find the minimum cost in Prims algorithm?

Step 1: Determine the arbitrary starting vertex. Step 2: Keep repeating steps 3 and 4 until the fringe vertices (vertices not included in MST)remain. Step 3: Select an edge connecting the tree vertex and fringe vertex having the minimum weight. Step 4: Add the chosen edge to MST if it doesn’t form any closed cycle.

## How do you find the minimum cost of a spanning tree?

The cost of the spanning tree is **the sum of the weights of all the edges in the tree**. There can be many spanning trees. Minimum spanning tree is the spanning tree where the cost is minimum among all the spanning trees.

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