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What algorithm do miners use to validate individual transactions in a broadcasted solution before accepting it to their blockchain?

For a node to accept an invalid transaction, that is, one with an invalid UTXO, inexistent balance or already spent balance, that node should need to slightly change the code and, by doing that, it ...
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What algorithm do miners use to validate individual transactions in a broadcasted solution before accepting it to their blockchain?

Fully validating nodes have parsed the complete blockchain in order to autonomously determine the set of Unspent Transaction Outputs (UTXOs). When such a full node learns about a new block it checks ...
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What algorithm do miners use to validate individual transactions in a broadcasted solution before accepting it to their blockchain?

All nodes, not just miners, check that the inputs to transactions in a block have not already been spent. All full nodes (wallets such as Bitcoin core) keep track of unspent transaction outputs (UTXOs)...
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