Algorithms to facilitate longest (and shortest) path algorithms. Path cost is calculated by either summing or multiplying edge weights.
Floyd-Warshall algorithm has the ability to calculate longest path (ie. most profitable trade) calculations, albeit at the expensive cost of $O(n^3)$.
For multiplication based weights, we make use of the fact that product maximisation is equivalent to maximisation of log of weights, as per: $x*y = 2^{log2(x) + log2(y)}$.
For longest paths, weights have been multiplied by $-1$ and hence reused in shortest path algorithm.
NOTE: Floyd-Warshall can detect negative path cycles (ie. infinite arbitrage opportunities), which cause the latest price update to be ignored. Potential TBD - remove offending edge to remove negative cycles...
Sample usage of Floyd-Warshall calculator. All prices are in $10^{12}$, including self references, eg. cost of BNB -> BNB = $10^{12}$
```rust use bestpath::prelude::*; use bestpath::prelude::floyd_warshall::calculator::FloydWarshallCalculator;
let ingraph = &[
(
ProviderPair { pair: Pair { source: "BNB".toowned(), target: "USDT".toowned() }, provider: "CRYPTOCOMPARE".toowned() },
364190000000000u128
),
(
ProviderPair { pair: Pair { source: "USDT".toowned(), target: "ETH".toowned() }, provider: "COINGECKO".toowned() },
2745000000u128
),
];
let resout = FloydWarshallCalculator::calcbestpaths(ingraph);
let asnodes = resout.unwrap().intoiter().collect::
Best-path serves as a best trade finding mechanism for best-path-pallet.