Leetcode solving: 1518 Water Bottles
Given numBottles full water bottles, you can exchange numExchange empty water bottles for one full water bottle.
The operation of drinking a full water bottle turns it into an empty bottle.
Return the maximum number of water bottles you can drink.
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My other Leetcode solving videos (easy)
https://www.youtube.com/playlist?list=PLg9w7tItBlZt4oUpNyWU_0rOItlScu1_d
Leetcode solving videos (Medium):
https://www.youtube.com/playlist?list=PLg9w7tItBlZvMGxy-y1eXURPD6Ao6kkzA
Leetcode solving videos (Hard):
https://www.youtube.com/playlist?list=PLg9w7tItBlZt4JQmlkGD3M5idZn14NyL6
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https://www.youtube.com/watch?v=fBz7BEP0cTA
Introduction to infinite product
More complex analysis:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsYfYG6dUISItqsSRSXaX4B
0:00 start
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https://www.youtube.com/watch?v=227F6pnK-3M
analytic number theory: Mobius function
We introduce the Mobius function and prove the Mobius inversion formula
0:00 start
0:30 prove the Mobius inversion formula and key lemma
10:00 Merten's conjecture
12:00 try to bound sum from x less that n u(n)/n
Advanced mathematics list:
Analytic number theory:
https://www.youtube.com/playlist?list=PLg9w7tItBlZu2IdPFQkrvAsPs-V2B_dxk
Real analysis:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsaSW0zlQ7m0S3Ti51bYJg_
Group representation for finite group
https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9-
exact sequences
https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9
Ring theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u
group theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v
Category theory
https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi
Field theory in abstract algebra
https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN-
Mathematical analysis
https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh
...
https://www.youtube.com/watch?v=E4cHtkm3Fac
prove the Law of total Covariance
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My other list of Probability:
https://www.youtube.com/playlist?list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b
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Algorithm:
https://www.youtube.com/playlist?list=PLg9w7tItBlZuXLnZO0UrW-jU3euCn17EP
Advanced mathematics list:
Group representation for finite group
https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9-
exact sequences
https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9
Ring theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u
group theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v
Category theory
https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi
Field theory in abstract algebra
https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN-
Mathematical analysis
https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh
...
https://www.youtube.com/watch?v=XIkYOEtRWrc
Bounds on Binomial coefficient
Advanced mathematics list:
Analytic number theory:
https://www.youtube.com/playlist?list=PLg9w7tItBlZu2IdPFQkrvAsPs-V2B_dxk
Real analysis:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsaSW0zlQ7m0S3Ti51bYJg_
Group representation for finite group
https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9-
exact sequences
https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9
Ring theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u
group theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v
Category theory
https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi
Field theory in abstract algebra
https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN-
Mathematical analysis
https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh
...
https://www.youtube.com/watch?v=h2BJxpdn5zw
Canonical form 1: Triangular form
In this video, we use mathematical induction to prove that every matrix has a Triangular form if all the eigenvalues in its field.
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more video lists:
exact sequences
https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9
Ring theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u
group theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v
Category theory
https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi
Field theory in abstract algebra
https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN-
...
https://www.youtube.com/watch?v=2s4Qxqm5YIY
Prove Method of infinite Descent : no nontrivial solutions x^2+y^2=3z^2
More Method of infinite Descent:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsYlJQ_P_pqjJFhrygyAo2N
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more video lists:
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機率
Probability and discrete mathematics:
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Probability interview questions:
https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b
Probability theory:
https://www.youtube.com/watch?v=8s-nyRLBsDo&list=PLg9w7tItBlZsvciKHBx8lXXnCtQ7Ou4cV
Complex analysis:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsYfYG6dUISItqsSRSXaX4B
Combinatorics:
https://www.youtube.com/playlist?list=PLg9w7tItBlZvQt0YNfCqcULzrPme2ai7K
additive combinatorics:
https://www.youtube.com/playlist?list=PLg9w7tItBlZseUrmXgf_2yc2NI_obVUhB
微積分 高等微積分 代數
Calculus and advanced mathematics (abstract algebra):
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Real analysis
https://www.youtube.com/playlist?list=PLg9w7tItBlZumEJ4DacAKgstCvDHKtY63
Reduction formula in Calculus:
https://www.youtube.com/playlist?list=PLg9w7tItBlZubmhgkHoHvje1uOASnkcke
Integrals of trigonometric functions:
https://www.youtube.com/playlist?list=PLg9w7tItBlZuwEER2YvFV06ri6i1Cj3hh
(algebraic geometry)代數幾何筆記
https://www.youtube.com/playlist?list=PLg9w7tItBlZssQ4Smzgp_bk2rEszKaW0B
Linear algebra Proof:
https://www.youtube.com/playlist?list=PLg9w7tItBlZueH6LMeYzzwPMUlIaRhCZo
環論(ring theory):
https://www.youtube.com/playlist?list=PLg9w7tItBlZs9w4wrNAuv4oJdrt-sIWUP
Abstract Algebra:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsyZ0Ri0IDPYEwDxDXjCqB0
Group theory (群論):
https://www.youtube.com/playlist?list=PLg9w7tItBlZu4Qkxz2WSk4eYZmDAC8ZY0
Galois theory:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsepuNJ3tOnG238M03KrKaG
數論跟其他:
number theory and others:
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Riemann Zeta functions:
https://www.youtube.com/playlist?list=PLg9w7tItBlZu4ncqL53iPd1GmwKq8yYoM
Math related to pi:
https://www.youtube.com/playlist?list=PLg9w7tItBlZuzFft3Y5h1LRaNvAv7ruKe
Number theory:
https://www.youtube.com/playlist?list=PLg9w7tItBlZvGgPYrFxfGWaQgQBrLOOws
Set Theory:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsDqBUL-CIHcVVBs9EODL_J
High school math & AP calculus:
https://www.youtube.com/playlist?list=PLg9w7tItBlZv165XaBIyj03q3WSMMUqDo
Solving polynomial equation:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsheN8dz8LLPy99AaLb7_-7
工程數學 Engineering Mathematics:
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Laplace transformation:
https://www.youtube.com/playlist?list=PLg9w7tItBlZty21VgNOrLTKg3BM1sFmFE
...
https://www.youtube.com/watch?v=XMtxtJPTJIA