Week-16 (Final)

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What is Lorem Ipsum? Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s,

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What is Lorem Ipsum? Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s,

bg right:50% h:400px

What is Lorem Ipsum? Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s,

bg left:50% h:400px

What is Lorem Ipsum? Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s,

bg h:400px

What is Lorem Ipsum? Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s,

bg left:50% h:800px

What is Lorem Ipsum? Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s,

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\begin{aligned} \begin{matrix} compute m [i, i + 1] \\ \underset{(n - 1) values}{\underset{⏟}{{m [1, 2], m [2, 3], \dots, m [n - 1, n]}}} \end{matrix} & {\begin{cases} ℓ = 2 \\ for i = 1 to n - 1 do \\ m [i, i + 1] = \infty \\ for k = i to i do \\ ⋮ \end{cases} \\ \begin{matrix} compute m [i, i + 2] \\ \underset{(n - 2) values}{\underset{⏟}{{m [1, 3], m [2, 4], \dots, m [n - 2, n]}}} \end{matrix} & {\begin{cases} ℓ = 3 \\ for i = 1 to n - 2 do \\ m [i, i + 2] = \infty \\ for k = i to i + 1 do \\ ⋮ \end{cases} \\ \begin{matrix} compute m [i, i + 3] \\ \underset{(n - 3) values}{\underset{⏟}{{m [1, 4], m [2, 5], \dots, m [n - 3, n]}}} \end{matrix} & {\begin{cases} ℓ = 4 \\ for i = 1 to n - 3 do \\ m [i, i + 3] = \infty \\ for k = i to i + 2 do \\ ⋮ \end{cases} \end{aligned}

\begin{aligned} OPTIMAL-BST-COST (p, n) \\ for i \leftarrow 1 to n do \\ c [i, i - 1] \leftarrow 0 \\ c [i, i] \leftarrow p [i] \\ R [i, j] \leftarrow i \\ P S [1] \leftarrow p [1] ⟸ P S [i] \to prefix-sum (i) : Sum of all p [j] values for j \leq i \\ for i \leftarrow 2 to n do \\ P S [i] \leftarrow p [i] + P S [i - 1] ⟸ compute the prefix sum \\ for d \leftarrow 1 to n - 1 do ⟸ BSTs with d + 1 consecutive keys \\ for i \leftarrow 1 to n - d do \\ j \leftarrow i + d \\ c [i, j] \leftarrow \infty \\ for r \leftarrow i to j do \\ q \leftarrow m i n {c [i, r - 1] + c [r + 1, j]} + P S [j] - P S [i - 1]} \\ if q < c [i, j] then \\ c [i, j] \leftarrow q \\ R [i, j] \leftarrow r \\ return c [1, n], R \end{aligned}

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$E n d - O f - W e e k - 16 - M o d u l e$

Last update: March 6, 2022