I have this "cost matrix" in R that represents the "cost" of going from any location to any other location (for a total of 5 locations):

```
X<-matrix(rnorm(25) , nrow = 5)
rownames(X) <- colnames(X) <- c("Location 1", "Location 2", "Location 3", "Location 4", "Location 5")
Location 1 Location 2 Location 3 Location 4 Location 5
Location 1 0.4501251 2.30029903 -0.26950735 0.1723589 0.5045694
Location 2 1.1208198 1.38557818 0.25250596 -0.6174514 -0.5324785
Location 3 0.4181011 0.01103208 0.83713132 -0.7649082 -0.5619196
Location 4 0.9372365 -1.04258420 0.08397031 0.1611555 1.8356483
Location 5 1.0201278 -0.56020913 1.14815210 1.0362332 -2.2052776
```

I would like to find out the "Greedy Shortest Path" that starts from "Location 1" and ends at "Location 1" while visiting each location exactly once.

I think this would look something like this (R getting the minimum value for each row in a matrix, and returning the row and column name) - this code returns the smallest value in each row of the matrix:

```
result <- t(sapply(seq(nrow(X)), function(i) {
j <- which.min(X[i,])
c(paste(rownames(X)[i], colnames(X)[j], sep='/'), X[i,j])
}))
```

When I look at the results:

```
print(result)
[,1] [,2]
[1,] "Location 1/Location 3" "-0.269507349140081"
[2,] "Location 2/Location 4" "-0.617451368699149"
[3,] "Location 3/Location 4" "-0.764908186347014"
[4,] "Location 4/Location 2" "-1.04258420123991"
[5,] "Location 5/Location 5" "-2.20527763537575"
```

I think this is telling me that the "Greedy Shortest Path" (starting from "Location 1") is : 1 to 3, 3 to 4, 4 to 2, 2 to 4 ... but then I get stuck in a "2 to 4, 4 to 2" loop for ever.

- Can someone please show me how I can find the "Greedy Shortest Path" that starts from "Location 1"?

By doing this manually:

- Starting at Location 1, the "shortest greedy path" is to Location 4
- From Location 4, the "shortest greedy path" is to Location 3
- From Location 3, the "shortest greedy path" is to Location 5
- From Location 5, the "shortest greedy path" is to Location 2 (since we have already been to Location 3 and Location 4, and we can not re-visit the current Location i.e. Location 5, and can not visit Location 1 since there is still a Location we haven't visited)
- From Location 2, we now have no choice but to return to Location 1 and finish the journey

I would look to produce the following output:

```
Path : (1,4), (4,3), (3,5), (5,2), (2,1)
Total Distance = -0.8441315 + (-0.7244259) + (-0.3775706) + 0.3796208 + 0.3015059 = -1.265001
```

- Could someone please show me how to modify my code to get this final output?

Thank you!

**Note:** In my real data, all diagonal elements of the Matrix are 0