knightsMetric.js

// How many steps a Knight takes on an infinite chessboard from O(0,0) to P (x,y)
// With O(1) time complexity

const knightsMetric = (x, y) => {
    let normalizedX = Math.abs(x);
    let normalizedY = Math.abs(y);

    // Normailze coordinates, so that 0 <= y <= x
    if(normalizedX < normalizedY) {
        [normalizedY, normalizedX] = [normalizedX, normalizedY]
    }
    
    // Handle exceptions
    if(normalizedX === 1 && normalizedY === 0) return 3
    if(normalizedX === 2 && normalizedY === 2) return 4

    const delta = normalizedX - normalizedY

    if(delta < normalizedY) {
        return delta + Math.floor((normalizedY - delta + 2) / 3) * 2;
    } else {
        const xbase = normalizedX - (normalizedY % 2) * 2;
        
        return Math.floor(xbase / 4) * 2 + xbase % 4 + normalizedY % 2;
    }
}