Zero Se Path Constraint

Kuch bhi symbolic nahi. Sirf normal Python.

def f(x):
    if x > 10:
        print("BADA")
    else:
        print("CHHOTA")

• f(50) → BADA
• f(3) → CHHOTA

Bas ek cheez notice karo: 50 aur 3 ne alag-alag lines chalayi.

"Kaun si lines chali" — usko path kehte hain. Matlab raasta jo program ne liya. Is program me do paths hain.

BADA wale path pe kaun si values jaati hain? 11, 12, 13, ... — list khatam hi nahi hoti.

To infinite numbers likhne ki jagah, hum ek chhoti condition likh dete hain: x > 10. Ye ek line un saari values ko pakad leti hai.

CHHOTA me x <= 10 isliye aaya kyunki else ka matlab hi hai "jab x > 10 sach nahi hai" — yaani ulta.

Ye poore chapter ki sabse badi galti hai. Ek baar pakka kar lo.

def g(y):
    if y < 5:  print("A")
    else:      print("B")

def k(x):
    if x > 10:
        if x < 50:
            print("MILA")

• x = 5 → pehla if fail. ❌
• x = 70 → pehla paar, dusra fail. ❌
• x = 30 → dono paar. ✅ MILA

To MILA ka constraint hai dono conditions ek saath:

def n():
    a = input()          # pehla number
    if a > 0:
        b = input()      # DUSRA number
        if b > 0:
            print("DONO POSITIVE")

a > 0 ∧ a > 0 nahi likha — kyunki dusra input() ek naya number laata hai. Jaise ATM do baar PIN maange: dono baar alag cheez, chahe sawaal same ho.

Agar program 10 baar input maange to a, b, c, d… naam khatam ho jaayenge. Isliye naam dete hain r₀, r₁, r₂, r₃… — r matlab read, aur number matlab kaunsa-wala read. Ginti zero se shuru.

10 baar chahiye to 10 if likhne padenge — pagal ho jaoge. To loop likh dete hain:

while True:
    r = input()
    if r <= 0:
        break        # ← BAHAR nikal jao

Ye wahi kaam kar raha hai jo Step 06 wale nested if kar rahe the. Bas short me.

Nested if wala program 3 input ke baad apne aap khatam ho gaya tha. Loop apne aap nahi rukta — usko rokna padta hai, break se.

Maan lo loop 3 baar chala, phir ruk gaya:

Loop 2 baar chala, par aakhri wala r₂ hai — r₁ nahi. Teeno case saath rakh ke dekho:

• Loop 2 baar chala → > 0 waale r₀ aur r₁ → yaani 0 se 1 tak
• Loop 3 baar chala → > 0 waale r₀, r₁, r₂ → yaani 0 se 2 tak

Har baar aakhri number ek kam. Aur rokne waala hamesha usse agla.

Maan lo loop n baar chala — n matlab koi bhi number: 2, 5, 100, kuch bhi. Upar wale pattern se seedha:

Isko chhota likhne ke liye ek symbol use karte hain: ⋀

// Add positive inputs until a zero or negative integer is read.
int sumUntilZero(int a) {
    int sum = a;
    while (true) {           // constant — ye branch hai hi nahi
        x = sym_input();      // har baar naya: r₀, r₁, r₂ …
        if (x <= 0) {         // ← ASLI branch
            break;
        }
        sum = sum + x;
    }
    return sum;
}

"Choose the appropriate path constraint (PC) for the while loop with a sequence of n true outcomes followed by a false."