Finish the tree logic in the transaction-chaining scheduler

Also completes the DB functions, makes Scheduler never instantiated, and
ensures tree roots have change outputs.

processor/primitives/src/payment.rs

@@ -1,3 +1,7 @@
+use std::io;
+
+use scale::{Encode, Decode, IoReader};
+
 use serai_primitives::{Balance, Data};
 use serai_coins_primitives::OutInstructionWithBalance;
 
@@ -27,6 +31,7 @@ impl<A: Address> Payment<A> {
   pub fn new(address: A, balance: Balance, data: Option<Vec<u8>>) -> Self {
     Payment { address, balance, data }
   }
+
   /// The address to pay.
   pub fn address(&self) -> &A {
     &self.address
@@ -39,4 +44,20 @@ impl<A: Address> Payment<A> {
   pub fn data(&self) -> &Option<Vec<u8>> {
     &self.data
   }
+
+  /// Read a Payment.
+  pub fn read(reader: &mut impl io::Read) -> io::Result<Self> {
+    let address = A::read(reader)?;
+    let reader = &mut IoReader(reader);
+    let balance = Balance::decode(reader).map_err(io::Error::other)?;
+    let data = Option::<Vec<u8>>::decode(reader).map_err(io::Error::other)?;
+    Ok(Self { address, balance, data })
+  }
+  /// Write the Payment.
+  pub fn write(&self, writer: &mut impl io::Write) -> io::Result<()> {
+    self.address.write(writer).unwrap();
+    self.balance.encode_to(writer);
+    self.data.encode_to(writer);
+    Ok(())
+  }
 }