# Write a greedy algorithm to generate shortest path tree

How to implement the above algorithm? We choose another 2p coin.

### Dijkstra algorithm python

Our next step is repeatedly choosing a coin for as long as we can use that coin. There's no 30p coin in pound sterling , how do you calculate how much change to return? It then goes to 10p. There isn't much to it. Now, let's see what our Greedy algorithm does. To update the distance values, iterate through all adjacent vertices. We now need to return 5p. We'll start with the denominations. Let's take it. In our example when we start the loop. We now need to return 3p. The vertices included in SPT are shown in green colour. It does this for 50p. In total, our algorithm selected these coins to return as change: value, how many we return as change 10, 1 5, 1 2, 2 1, 1 Let's code something.

The distance value of vertex 6 and 8 becomes finite 15 and 9 respectively. It does this for 50p.

## Prims algorithm

Now pick the vertex with minimum distance value. We now need to return 1p. This algorithm works quite well in real life. The vertex 0 is picked, include it in sptSet. In the change giving algorithm, we can force a point at which it isn't optimal globally. Does Greedy Always Work? Counting Change Using Greedy Imagine you're a vending machine.

Given denominations and an amount to give change, we want to return a list of how many times that coin was returned. Update the distance values of adjacent vertices of 1.

## Dijkstras shortest path algorithm example

Following subgraph shows vertices and their distance values, only the vertices with finite distance values are shown. Assign distance value as 0 for the source vertex so that it is picked first. The distance value of vertex 6 and 8 becomes finite 15 and 9 respectively. The vertices included in SPT are shown in green colour. There's no 30p coin in pound sterling , how do you calculate how much change to return? It then goes to 10p. First, we need to define the problem. We pick 1x 20p.

The optimal solution is 2x 15p. The algorithm needs to return change of 10p.

We now need to return 10p. The vertex 0 is picked, include it in sptSet. We now need to return 5p. We'll start with the denominations.

It then goes to 10p. In our example when we start the loop.

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