`range()` — start, stop, step — Hinglish notes

1.2.19 · Coding › Introduction to Programming (Python)

YEH HAI KYA

Count formula ko scratch se derive karna — YEH FORM KYUN?

Terms hain start, start+step, start+2·step, ….
Hum stop cross karne se pehle valid terms ki count chahte hain.
Cover karne wali "distance" hai stop - start; har step step cover karta hai. Divide karne par milta hai kitne steps fit hote hain: (stop - start) / step.
Kyunki stop excluded hai, hum upar round karte hain (ceil): thodi si bhi baaki distance technically ek aur term maangti hai boundary tak pahunchne/paas karne ke liye... lekin hum usse pehle rok lete hain, isliye count exactly woh ceiling hai.
Agar division negative hai (jaise galat direction mein ja rahe ho), koi terms fit nahi hote → max(0, …).

Ek handy integer-only version (ceil ke bina): step > 0 ke saath, $n = \frac{stop - start + step - 1}{step} (integer floor division)$

KAISE USE KARTE HAIN

Worked example Example 1 —

range(5)

list(range(5))      # [0, 1, 2, 3, 4]

Start = 0 kyun? Single-argument form mein start default se 0 hota hai. Yeh step kyun? Kyunki Python mein indexing 0 se shuru hoti hai, isliye loops positions ke saath align hote hain.
5 kyun nahi? stop = 5 excluded hai → hume exactly 5 numbers milte hain (0..4). Yeh step kyun? Half-open rule guarantee karta hai ki len(range(5)) == 5, koi off-by-one mental math nahi.

Worked example Example 2 —

range(2, 9, 2)

list(range(2, 9, 2))   # [2, 4, 6, 8]

2 se start kyun? Explicit start. $a_{0} = 2$ .
Yeh 10 nahi, 8 par kyun ruka? $a_{3} = 2 + 3 \cdot 2 = 8 < 9$ ✓, lekin $a_{4} = 10 \neq < 9$ ✗. Yeh step kyun? Hum $a_{k} < stop$ apply karte hain.
Count check karo: $n = ⌈(9 - 2) /2 ⌉ = ⌈ 3.5 ⌉ = 4$ ✓.

Worked example Example 3 —

range(10, 0, -2) se NEECHE count karna

list(range(10, 0, -2))  # [10, 8, 6, 4, 2]

0 kyun nahi aata? stop = 0 excluded; hum $a_{k} > 0$ use karte hain. $a_{5} = 0 \neq > 0$ ✗.
Negative step kyun? Peeche jaane ke liye. Yeh step kyun? step < 0 ke saath condition flip hokar $a_{k} > stop$ ho jaati hai, isliye hum neeche utarte hain.
Count: $n = ⌈(0 - 10) / (- 2)⌉ = ⌈ 5 ⌉ = 5$ ✓.

Worked example Example 5 — empty range

list(range(5, 5))     # []
list(range(5, 1))     # []   (start > stop, positive step)

Empty kyun? Koi bhi $a_{k}$ condition satisfy nahi karta. $n = max (0, negative or zero) = 0$ .

Common mistakes

Recall Feynman: ek 12-saal-ke bacche ko samjhao

Ek hopscotch grid imagine karo. start woh square hai jis par tum pehle kudते ho. step hai har hop kitna door hai. stop ek wall hai jis par tum nahi land kar sakte — jis moment tumhari agla hop wall ko hit ya pass kar de, tum ruk jaate ho. Toh range(2, 9, 2) ka matlab hai: 2 par shuru karo, har baar 2 squares kudo (2→4→6→8), aur 9 ki wall se pehle ruk jao. Python poora hopscotch ek saath nahi banaata; bas tumhare puchne par agla square batata hai. Isliye yeh ek million squares ke liye bhi fast hai.

Active recall

range() ke teen argument forms kya hain?

range(stop), range(start, stop), range(start, stop, step).

range(start, stop, step) mein, kya stop included hai?

Nahi — yeh excluded hai (half-open [start, stop)).

range(stop) mein default start aur step?

start = 0, step = 1.

Range ke k-ve term ka formula?

a_{k} = start + k \cdot step

Elements ki sankhya ka formula?

n = max (0, ⌈(stop - start) / step ⌉)

list(range(10, 0, -2)) ka output?

[10, 8, 6, 4, 2].

range(5, 5) kya deta hai?

[] (empty).

step = 0 ke saath kya hota hai?

ValueError — step non-zero hona chahiye.

range(10, 0) [] kyun deta hai?

Default step +1 hai, 10 se 0 tak upar nahi ja sakta.

Aisa range kaise banate hain jo N ko include kare?

range(start, N+1).

Kya range float arguments le sakta hai?

Nahi — TypeError; sirf integers.

Kya range object ek list hai?

Nahi — yeh ek lazy immutable sequence hai (demand par generate karta hai).

Connections

for loops — range() sabse common loop driver hai.
Lists and list() — range ko materialise karne ke liye wrap karo: list(range(...)).
Indexing and slicing — dono same half-open [start, stop) convention use karte hain.
Arithmetic sequences — a_k = start + k·step ek discrete arithmetic progression hai.
numpy.arange / linspace — range() ke float-capable cousins.
enumerate() — alternative jab tumhe index aur value dono chahiye.