Distance and nearest neighbour दूरी और सबसे नज़दीकी पड़ोसी

1. How far apart are two fruits?

Draw each fruit as a dot: x = sweetness, y = weight. Similar fruits sit close together. The straight-line gap between two dots is the Euclidean distance — Pythagoras from Class 8!

distance = √((x1 - x2)² + (y1 - y2)²)

The same idea works with any number of features: for each feature, subtract, square, add them all up, then take the square root.

• [0, 0] to [3, 4] → √(9 + 16) = 5

                const a = [0, 0];
const b = [3, 4];
const d = Math.sqrt((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2);
console.log(d);
              

Challenge: Euclidean distance

Write distance(a, b) where a and b are arrays of the same length (any length: 2, 3, …). Return the Euclidean distance: the square root of the sum of squared differences.

2. The nearest neighbour

Here is a whole classifier in one sentence: a new fruit gets the label of the closest fruit we already know.

That is the nearest neighbour rule. “Training” is just remembering the examples; all the work happens when you predict:

1. measure the distance from the new point to every training point
2. find the smallest distance
3. return that point’s label

Our rows look like { point: [sweetness, weight], label: "mango" }. (Scale your features first — remember normalising — or weight will boss everyone around.)

Challenge: Mango or lemon?

distance is ready. Write nearestLabel(train, point): go through every row of train, find the row whose row.point is closest to point, and return its label.