feat(router): Add Smart Routing to route payments efficiently (#2665)

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
Co-authored-by: shashank_attarde <shashank.attarde@juspay.in>
Co-authored-by: Aprabhat19 <amishaprabhat@gmail.com>
Co-authored-by: Amisha Prabhat <55580080+Aprabhat19@users.noreply.github.com>

crates/euclid/src/backend.rs

@@ -0,0 +1,25 @@
+pub mod inputs;
+pub mod interpreter;
+#[cfg(feature = "valued_jit")]
+pub mod vir_interpreter;
+
+pub use inputs::BackendInput;
+pub use interpreter::InterpreterBackend;
+#[cfg(feature = "valued_jit")]
+pub use vir_interpreter::VirInterpreterBackend;
+
+use crate::frontend::ast;
+
+#[derive(Debug, Clone, serde::Serialize)]
+pub struct BackendOutput<O> {
+    pub rule_name: Option<String>,
+    pub connector_selection: O,
+}
+
+pub trait EuclidBackend<O>: Sized {
+    type Error: serde::Serialize;
+
+    fn with_program(program: ast::Program<O>) -> Result<Self, Self::Error>;
+
+    fn execute(&self, input: BackendInput) -> Result<BackendOutput<O>, Self::Error>;
+}