Factorial Of Large Numbers - (Microsoft, MakeMyTrip, Adobe):Explanation ➕ Live Coding 🧑🏻‍💻👩🏻‍💻

[@sameerswankar]

Ive watched soo many videos b4 but cudnt grasp the concept, bro ur explaination was solid and clear... Keep it up

[@codestorywithMIK]

Thank you so much Sameer ❤️
Means a lot to me

[@rex_incognito1]

best explanation of this problem on yt hands down

[@thekindspill]

I didn't find a better video than this one for this problem. This is insanely good

[@anandpandey918]

Clear All Your Doubts :
class Solution {
static ArrayList factorial(int n){
ArrayListfactorial = new ArrayList();
factorial.add(1);
int carry = 0;
for(int num = 2 ; num = 0;i--){
int product=(factorial.get(i) * num) + carry;
carry = product / 10;
factorial.set(i,product % 10);
}
while(carry != 0){
factorial.add(0,carry%10);
carry=carry/10;
}
}
return factorial;
}
}
/*
Dry run for n = 15:
Initial state:
n = 15
factorial = [1]
carry = 0
-----------------------------------------------------------------
num = 2
Inner Loop:
i = 0: factorial[0] * 2 + carry = 1 * 2 + 0 = 2, carry = 0, factorial = [2] // 2!=2
Carry distribution loop is skipped since carry is 0.
num = 3
Inner Loop:
i = 0: factorial[0] * 3 + carry = 2 * 3 + 0 = 6, carry = 0, factorial = [6] // 3!=6
Carry distribution loop is skipped.
num = 4
Inner Loop:
i = 0: factorial[0] * 4 + carry = 6 * 4 + 0 = 24, carry = 2, factorial = [4]
Carry distribution loop:
Adding carry digits to the beginning: factorial = [2, 4], carry = 0 // 4!=24
num = 5
Inner Loop:
i = 1: factorial[1] * 5 + carry = 4 * 5 + 0 = 20, carry = 2, factorial = [2, 0]
i = 0: factorial[0] * 5 + carry = 2 * 5 + 2 = 12, carry = 1, factorial = [2, 0]
Carry distribution loop:
Adding carry digits to the beginning: factorial = [1, 2, 0], carry = 0 // 5!=120
num = 6
Inner Loop:
i = 2: factorial[2] * 6 + carry = 0 * 6 + 0 = 0, carry = 0, factorial = [1, 1, 0]
i = 1: factorial[1] * 6 + carry = 2 * 6 + 0 = 12, carry =1, factorial = [1, 2, 0]
i = 0: factorial[0] * 6 + carry = 1 * 6 + 1 = 7, carry = 0, factorial = [7, 2, 0] //6!=720
Carry distribution loop is skipped.
num = 7
Inner Loop:
i = 2: factorial[2] * 7 + carry = 0 * 7 + 0 = 0, carry = 0, factorial = [7, 2, 0]
i = 1: factorial[1] * 7 + carry = 2 * 7 + 0 = 14, carry = 1, factorial = [7, 4, 0]
i = 0: factorial[0] * 7 + carry = 7 * 7 + 1 = 50, carry = 5, factorial = [0, 4, 0]
Carry distribution loop:
Adding carry digits to the beginning: factorial = [5, 0, 4, 0], carry = 0 //7!=5040
num = 8
Inner Loop:
i = 3: factorial[3] * 8 + carry = 0 * 8 + 0 = 0, carry = 0, factorial = [5, 0, 4, 0]
i = 2: factorial[2] * 8 + carry = 4 * 8 + 0 = 32, carry = 3, factorial = [5, 0, 2, 0]
i = 1: factorial[1] * 8 + carry = 0 * 8 + 3 = 3, carry = 0, factorial = [5, 3, 2, 0]
i = 0: factorial[0] * 8 + carry = 5 * 8 + 0 = 40, carry = 4, factorial = [0, 3, 2, 0]
Carry distribution loop:
Adding carry digits to the beginning: factorial = [4, 0, 3, 2, 0], carry = 0 //8!=40320
num=9
Inner Loop:
i = 4: factorial[4] * 9 + carry = 0 * 9 + 0 = 0, carry = 0, factorial =[4, 0, 3, 2, 0]
i = 3: factorial[3] * 9 + carry = 2 * 9 + 0 = 18, carry = 1, factorial =[4, 0, 3, 8, 0]
i = 2: factorial[2] * 9 + carry = 3 * 9 + 1 = 28, carry = 2, factorial =[4, 0, 8, 8, 0]
i = 1: factorial[1] * 9 + carry = 0 * 9 + 2 = 2, carry = 0, factorial =[4, 2, 8, 8, 0]
i = 0: factorial[0] * 9 + carry = 4 * 9 + 0 = 36, carry = 3, factorial =[6, 2, 8, 8, 0]
Carry distribution loop:
Adding carry digits to the beginning: factorial =[3, 6, 2, 8, 8, 0], carry = 0 //9!=362880
num=10
Inner Loop:
i = 5: factorial[5] * 10 + carry = 0 * 10 + 0 = 0, carry = 0, factorial=[3, 6, 2, 8, 8, 0]
i = 4: factorial[4] * 10 + carry = 8 * 10 + 0 = 80, carry = 8, factorial=[3, 6, 2, 8, 0, 0]
i = 3: factorial[3] * 10 + carry = 8 * 10 + 8 = 88, carry = 8, factorial=[3, 6, 2, 8, 0, 0]
i = 2: factorial[2] * 10 + carry = 2 * 10 + 8 = 28, carry = 2, factorial=[3, 6, 8, 8, 0, 0]
i = 1: factorial[1] * 10 + carry = 6 * 10 + 2 = 62, carry = 6, factorial=[3, 2, 8, 8, 0, 0]
i = 0: factorial[0] * 10 + carry = 3 * 10 + 6 = 36, carry = 3, factorial=[6, 2, 8, 8, 0, 0]
Carry distribution loop:
Adding carry digits to the beginning: factorial =[3, 6, 2, 8, 8, 0, 0], carry = 0 //10!=3628800
num=11
Inner Loop:
i = 6: factorial[6] * 11 + carry = 0 * 11 + 0 = 0, carry = 0, factorial=[3, 6, 2, 8, 8, 0, 0]
i = 5: factorial[5] * 11 + carry = 0 * 11 + 0 = 0, carry = 0, factorial=[3, 6, 2, 8, 8, 0, 0]
i = 4: factorial[4] * 11 + carry = 8 * 11 + 0 = 88, carry = 8, factorial=[3, 6, 2, 8, 8, 0, 0]
i = 3: factorial[3] * 11 + carry = 8 * 11 + 8 = 96, carry = 9, factorial=[3, 6, 2, 6, 8, 0, 0]
i = 2: factorial[2] * 11 + carry = 2 * 11 + 9 = 31, carry = 3, factorial=[3, 6, 1, 6, 8, 0, 0]
i = 1: factorial[1] * 11 + carry = 6 * 11 + 3 = 69, carry = 6, factorial=[3, 9, 1, 6, 8, 0, 0]
i = 0: factorial[0] * 11 + carry = 3 * 11 + 6 = 39, carry = 3, factorial=[9, 9, 1, 6, 8, 0, 0]
Carry distribution loop:
Adding carry digits to the beginning: factorial =[3, 9, 9, 1, 6, 8, 0, 0], carry = 0 //11!=39916800
num=12
Inner Loop:
i = 7: factorial[7] * 12 + carry = 0 * 12 + 0 = 0, carry = 0, factorial=[3, 9, 9, 1, 6, 8, 0, 0]
i = 6: factorial[6] * 12 + carry = 0 * 12 + 0 = 0, carry = 0, factorial=[3, 9, 9, 1, 6, 8, 0, 0]
i = 5: factorial[5] * 12 + carry = 8 * 12 + 0 = 0, carry = 9, factorial=[3, 9, 9, 1, 6, 6, 0, 0]
i = 4: factorial[4] * 12 + carry = 6 * 12 + 9 = 81, carry = 8, factorial=[3, 9, 9, 8, 1, 6, 0, 0]
i = 3: factorial[3] * 12 + carry = 1 * 12 + 8 = 20, carry = 2, factorial=[3, 9, 9, 0, 1, 6, 0, 0]
i = 2: factorial[2] * 12 + carry = 9 * 12 + 2 = 110, carry =11, factorial=[3, 9, 0, 0, 1, 6, 0, 0]
i = 1: factorial[1] * 12 + carry = 9 * 12 + 11 =119, carry =11, factorial=[3, 9, 0, 0, 1, 6, 0, 0]
i = 0: factorial[0] * 12 + carry = 3 * 12 + 11 = 47, carry = 4, factorial=[7, 9, 0, 0, 1, 6, 0, 0]
Carry distribution loop:
Adding carry digits to the beginning: factorial =[4, 7, 9, 0, 0, 1, 6, 0, 0] //12!=479001600
num=13
Inner Loop:
i = 8: factorial[8] * 13 + carry = 0 * 13 + 0 = 0, carry = 0, factorial=[4, 7, 9, 0, 0, 1, 6, 0, 0]
i = 7: factorial[7] * 13 + carry = 0 * 13 + 0 = 0, carry = 0, factorial=[4, 7, 9, 0, 0, 1, 6, 0, 0]
i = 6: factorial[6] * 13 + carry = 6 * 13 + 0 = 78, carry = 7, factorial=[4, 7, 9, 0, 0, 1, 8, 0, 0]
i = 5: factorial[5] * 13 + carry = 1 * 13 + 7 = 20, carry = 2, factorial=[4, 7, 9, 0, 0, 0, 8, 0, 0]
i = 4: factorial[4] * 13 + carry = 0 * 13 + 2 = 2, carry = 0, factorial=[4, 7, 9, 0, 2, 0, 8, 0, 0]
i = 3: factorial[3] * 13 + carry = 0 * 13 + 0 = 0, carry =0, factorial=[4, 7, 9, 0, 2, 0, 8, 0, 0]
i = 2: factorial[2] * 13 + carry = 9 * 13 + 0 =117, carry =11, factorial=[4, 7, 7, 0, 2, 0, 8, 0, 0]
i = 1: factorial[1] * 13 + carry = 7 * 13 + 11 = 102, carry = 10,factorial=[4, 2, 7, 0, 2, 0, 8, 0, 0]
i = 0: factorial[0] * 13 + carry = 4 * 13 + 10 = 62, carry = 6, factorial=[2, 2, 7, 0, 2, 0, 8, 0, 0]
Carry distribution loop:
Adding carry digits to the beginning: factorial=[6, 2, 2, 7, 0, 2, 0, 8, 0, 0] //13!=6227020800
num=14
Inner Loop:
i = 9: factorial[9] * 14 + carry = 0 * 14 + 0 = 0, carry = 0, factorial=[6, 2, 2, 7, 0, 2, 0, 8, 0, 0]
i = 8: factorial[8] * 14 + carry = 0 * 14 + 0 = 0, carry = 0, factorial=[6, 2, 2, 7, 0, 2, 0, 8, 0, 0]
i = 7: factorial[7] * 14 + carry = 8 * 14 + 0 = 112, carry = 11, factorial=[6, 2, 2, 7, 0, 2, 0, 2, 0, 0]
i = 6: factorial[6] * 14 + carry = 0 * 14 + 11 = 11, carry = 1, factorial=[6, 2, 2, 7, 0, 2, 1, 2, 0, 0]
i = 5: factorial[5] * 14 + carry = 2 * 14 + 1 = 29, carry = 2, factorial=[6, 2, 2, 7, 0, 9, 1, 2, 0, 0]
i = 4: factorial[4] * 14 + carry = 0 * 14 + 2 = 2, carry =0, factorial=[6, 2, 2, 7, 2, 9, 1, 2, 0, 0]
i = 3: factorial[3] * 14 + carry = 7 * 14 + 0 = 98, carry =9, factorial=[6, 2, 2, 8, 2, 9, 1, 2, 0, 0]
i = 2: factorial[2] * 14 + carry = 2 * 14 + 9 = 37, carry = 3,factorial=[6, 2, 7, 8, 2, 9, 1, 2, 0, 0]
i = 1: factorial[1] * 14 + carry = 2 * 14 + 3 = 31, carry = 3, factorial=[6, 1, 7, 8, 2, 9, 1, 2, 0, 0]
i = 0: factorial[0] * 14 + carry = 6 * 14 + 3 = 87, carry = 8, factorial=[7, 1, 7, 8, 2, 9, 1, 2, 0, 0]
Carry distribution loop:
Adding carry digits to the beginning: factorial=[8, 7, 1, 7, 8, 2, 9, 1, 2, 0, 0] //14!=87178291200
num=15
Inner Loop:
i = 10: factorial[10] * 15 + carry = 0 * 15 + 0 = 0, carry = 0, factorial=[8, 7, 1, 7, 8, 2, 9, 1, 2, 0, 0]
i = 9: factorial[9] * 15 + carry = 0 * 15 + 0 = 0, carry = 0, factorial=[8, 7, 1, 7, 8, 2, 9, 1, 2, 0, 0]
i = 8: factorial[8] * 15 + carry = 2 * 15 + 0 = 30, carry = 3, factorial=[8, 7, 1, 7, 8, 2, 9, 1, 0, 0, 0]
i = 7: factorial[7] * 15 + carry = 1 * 15 + 3 = 18, carry = 1, factorial=[8, 7, 1, 7, 8, 2, 9, 8, 0, 0, 0]
i = 6: factorial[6] * 15 + carry = 9 * 15 + 1 = 136, carry = 13,factorial=[8, 7, 1, 7, 8, 2, 6, 8, 0, 0, 0]
i = 5: factorial[5] * 15 + carry = 2 * 15 + 13 = 43, carry =4, factorial=[8, 7, 1, 7, 8, 3, 6, 8, 0, 0, 0]
i = 4: factorial[4] * 15 + carry = 8 * 15 + 4 = 124, carry =12, factorial=[8, 7, 1, 7, 4, 3, 6, 8, 0, 0, 0]
i = 3: factorial[3] * 15 + carry = 7 * 15 + 12 = 117, carry = 11,factorial=[8, 7, 1, 7, 4, 3, 6, 8, 0, 0, 0]
i = 2: factorial[2] * 15 + carry = 1 * 15 + 11 = 26, carry = 2,factorial=[8, 7, 6, 7, 4, 3, 6, 8, 0, 0, 0]
i = 1: factorial[1] * 15 + carry = 7 * 15 + 2 = 107, carry = 10,factorial=[8, 7, 6, 7, 4, 3, 6, 8, 0, 0, 0]
i = 0: factorial[0] * 15 + carry = 8 * 15 + 10 = 130, carry = 13,factorial=[0, 7, 6, 7, 4, 3, 6, 8, 0, 0, 0]
Carry distribution loop:
Adding carry digits to the beginning:
Iteration 1:
factorial=[3, 0, 7, 6, 7, 4, 3, 6, 8, 0, 0, 0]
Iteration 2:
factorial=[1, 3, 0, 7, 6, 7, 4, 3, 6, 8, 0, 0, 0] //15!=1307674368000
therefore 15!=[1, 3, 0, 7, 6, 7, 4, 3, 6, 8, 0, 0, 0 i.e 1307674368000
*/

[@parasagrawal2927]

iski time complexity jada h

[@souravjoshi2293]

One of the finest videos on this problem. No one can teach like you bro

[@nagmakhan3165]

Amazing explanation

[@DevOpskagyaan]

Best explanation for this problem on UA-cam

[@ugcwithaddi]

No one can beat his teaching style

[@Mohd-12335]

bhaiya great explanation..

[@akshayraj6732]

sab samjh aagaya bhai bas carry wala thoda sa upar se chala gaya

[@sahiltyagi1999]

Thanks Bro.really thanks

[@codestorywithMIK]

Thank you for watching 😇❤️

[@sharadkumar6658]

great solution bro.😇

[@pranavmaiya4386]

bro please update the DSA sheet man i beg you , they have really good problem not going to lie but the sheet is incomplete .

[@codestorywithMIK]

Sure. Give me a week time. I am travelling this weekend. Will update ♥️🙏

[@AnkitJain-w3l]

Day 2