๐—ง๐—ฟ๐—ถ๐—ฎ๐—ป๐—ด๐—น๐—ฒ - ๐— ๐—ถ๐—ป๐—ถ๐—บ๐˜‚๐—บ ๐—ฃ๐—ฎ๐˜๐—ต ๐—ฆ๐˜‚๐—บ | ๐—ฉ๐—ถ๐˜€๐˜‚๐—ฎ๐—น๐—ถ๐˜‡๐—ฎ๐˜๐—ถ๐—ผ๐—ป | ๐—Ÿ๐—ฒ๐—ฒ๐˜๐—–๐—ผ๐—ฑ๐—ฒ ๐Ÿญ๐Ÿฎ๐Ÿฌ | ๐——๐˜†๐—ป๐—ฎ๐—บ๐—ถ๐—ฐ๐—ฃ๐—ฟ๐—ผ๐—ด๐—ฟ๐—ฎ๐—บ๐—บ๐—ถ๐—ป๐—ด | ๐—ฃ๐—ต๐—ฎ๐—ป๐—ถ ๐—ง๐—ต๐—ฎ๐˜๐—ถ๐—ฐ๐—ต๐—ฎ๐—ฟ๐—น๐—ฎ

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ะŸะพะบะฐะทะฐั‚ัŒ ะพะฟะธัะฐะฝะธะต
Finding minimum path sum for a given triangle using Dynamic Programming with Simple Visualization.

๐“๐ข๐ฆ๐ž ๐‚๐จ๐ฆ๐ฉ๐ฅ๐ž๐ฑ๐ข๐ญ๐ฒ : ๐Ž(๐ง^๐Ÿ)
We are iterating through all numbers in the triangle, in first row we have 1 number, in second row we have 2 numbers, likewise in nth row, we ll have n numbers.
Sum to n numbers 1 + 2 + 3 + ... + n = n(n-1)/2, which gives us time complexity of O(n^2)

๐’๐ฉ๐š๐œ๐ž ๐‚๐จ๐ฆ๐ฉ๐ฅ๐ž๐ฑ๐ข๐ญ๐ฒ: ๐Ž(๐ง)
We are using a single list called dp whose length is equal to the size of the last row of the triangle.
Hence, space complexity is O(n)

๐‚๐จ๐ฆ๐ฉ๐ฅ๐ž๐ญ๐ž ๐๐ฅ๐š๐ฒ๐ฅ๐ข๐ฌ๐ญ:

๐‹๐ž๐ž๐ญ๐œ๐จ๐๐ž ๐‡๐š๐ซ๐ ๐๐ฅ๐š๐ฒ๐ฅ๐ข๐ฌ๐ญ

๐‚๐จ๐ง๐ง๐ž๐œ๐ญ ๐ฐ๐ข๐ญ๐ก ๐ฆ๐ž:
ะ ะตะบะพะผะตะฝะดะฐั†ะธะธ ะฟะพ ั‚ะตะผะต
ะšะพะผะผะตะฝั‚ะฐั€ะธะธ
ะะฒั‚ะพั€

๐‚๐จ๐ฆ๐ฉ๐ฅ๐ž๐ญ๐ž ๐‹๐ž๐ž๐ญ๐œ๐จ๐๐ž ๐๐ฅ๐š๐ฒ๐ฅ๐ข๐ฌ๐ญ

๐‹๐ž๐ž๐ญ๐œ๐จ๐๐ž ๐‡๐š๐ซ๐ ๐๐ฅ๐š๐ฒ๐ฅ๐ข๐ฌ๐ญ

๐‹๐ž๐ž๐ญ๐œ๐จ๐๐ž ๐Œ๐ž๐๐ข๐ฎ๐ฆ ๐๐ฅ๐š๐ฒ๐ฅ๐ข๐ฌ๐ญ

๐‚๐จ๐ง๐ง๐ž๐œ๐ญ ๐ฐ๐ข๐ญ๐ก ๐ฆ๐ž:

PhaniThaticharla
ะะฒั‚ะพั€

GREAT VIDEO, YOU SAVED MY LIFE MY FRIEND FROM THE EAST

Ryan-ykki
ะะฒั‚ะพั€

Thank you it really took me a while to rap my head around it!

oakleyorbit
ะะฒั‚ะพั€

Great explanation, helped me understand clearly.

trjblq
ะะฒั‚ะพั€

This video actually helped me visualize the problem. Thanku for the explanation ๐Ÿ˜Š

PriyaSingh-duxc
ะะฒั‚ะพั€

Make program on farthest from zero bro

rajesho