Challenge: Constant Product AMM

Implement a constant product AMM with swap, liquidity, and price impact calculations.

Requirements

Implement three functions:

1. swap(reserveIn, reserveOut, inputAmount, fee)

Calculate output amount for a swap:

• Apply fee (e.g., 0.3% means fee = 0.003)
• Use constant product formula: x * y = k
• Return { outputAmount, newReserveIn, newReserveOut, priceImpact }

2. addLiquidity(reserveA, reserveB, depositA, depositB, totalLPTokens)

Calculate LP tokens minted:

• If pool is empty (totalLPTokens === 0), mint sqrt(depositA * depositB)
• Otherwise, mint proportional to deposit: min(depositA/reserveA, depositB/reserveB) * totalLPTokens
• Return { lpTokens, finalDepositA, finalDepositB }

3. calculatePriceImpact(inputAmount, reserveIn, reserveOut)

Calculate price impact percentage:

• Spot price: reserveOut / reserveIn
• Execution price: outputAmount / inputAmount
• Price impact: ((executionPrice / spotPrice) - 1) * 100
• Return price impact as a percentage (negative value means worse than spot)