Questions tagged [backtracking]

5 questions
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How to solve 5x5 grid with 16 diagonals?

I have a grid 5x5 and I have to fill 16 little squares with a diagonal Rules You cannot place more than 1 diagonal in each square The diagonals cannot touch each other (example bellow) Click here to view the solution But what I seek here is a…
BrunoLM
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Shattering Orbs - Expected cuts in a hanging chain of Orbs to arrive at the Highest Orb (Probability Question)

Question - 7 orbs are labeled 1−7 and are linked linearly in a vertical stack from the ceiling with orb 1 being a part of the ceiling and orb 7 being closest to the floor. Each orb is attached to adjacent orbs by a chain link. At each time step, one…
1
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1 answer

Polynomial Growth Observed in a New Graph Coloring Algorithm: Insight or Oversight?

Hello MathExchange community, I have developed a graph coloring algorithm that has demonstrated impressive results in initial tests. However, before drawing any concrete conclusions, I'm looking for insights from experts in the field. Brief Overview…
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Confusion about Armijo's rule

I am currently working on line search algorithms and read about Armijo's Rule. The rule is given for a fixed $\beta \in (0,1)$ and $\eta >1$ we choose $\alpha \geq 0$ such that $$ f(x+\alpha\cdot d) \leq f(x) + \beta\cdot \nabla f(x)^t\cdot d\cdot…
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Newton Method with backtracking line search

I have a school exercise where I am supposed to implement the Newton method with and without a backtracking line search. The first one converges quite rapidly but, when I add the backtracking line search part, it does not... Here's what I did, could…