Name: Score:
17 Multiple choice questions
Definition 1 of 17
w = (1, 2PI / n) = e^(2PI*i/n)
Loga (u / V)
Logb(b)
Loga (u)^n
Omega(w)
Definition 2 of 17
loga (u) + loga (v)
loga (u)^n
loga (uv)
logb(b^x)
omega(w)
Definition 3 of 17
Given r = common ratio and a = first term in series
=> a + ar + ar^2 + ar^3 + ... + ar^(n-1)
=> a * [(1 - r^n) / (1-r)]
DC: Geometric Series
Fft And Inverse Fft Formulas
Dc: Solving Recurrences - Master Theorem
Dc: Arithmetic Series
,Definition 4 of 17
FFT = Mn(w) x B
Inverse FFT = 1/n Mn(w^-1) x B
Euler's Formula
Omega(w)
FFT and Inverse FFT Formulas
Steps to Solve for Fft
Definition 5 of 17
e^ix = cosx + isinx
Steps To Solve For Fft
Surface Area
Euler's Formula
Dc: Arithmetic Series
Definition 6 of 17
1. Define the Input and Output.
2. Define entries in table, i.e. T(i) or T(i, j) is...
3. Define a Recurrence relationship - Based on a subproblem to the main problem. (hint: use a
prefix of the original input 1 < i < n).
4. Define the Pseudocode.
5. Define the Runtime of the algorithm. Use Time Function notation here => T(n) = T(n/2) + 1...
Steps to solve a Dynamic Programming Problem
loga (u)^n
Omega(w)
Steps to solve for FFT
, Definition 7 of 17
Input = x1, x2, ..., xn
1) Subproblem = x1, x2, ..., xi ; O(n)
2) Subproblem = xi, xi+1, ..., xj ; O(n^2)
Input = x1, x2, ..., xn; y1, y2, ..., ym
1) Subproblem = x1, x2, ..., xi; y1, y2, ..., yj ; O(mn)
Input = Rooted Binary Tree
1) Subproblem = Smaller rooted binary tree inside the Input.
DC: Geometric Series
FFT and Inverse FFT Formulas
DC Algorithms and Runtimes (6)
DP: Types of Subproblems (4)
Definition 8 of 17
loga (u) - loga (v)
logb(b)
loga (u / v)
omega(w)
loga (u)^n
17 Multiple choice questions
Definition 1 of 17
w = (1, 2PI / n) = e^(2PI*i/n)
Loga (u / V)
Logb(b)
Loga (u)^n
Omega(w)
Definition 2 of 17
loga (u) + loga (v)
loga (u)^n
loga (uv)
logb(b^x)
omega(w)
Definition 3 of 17
Given r = common ratio and a = first term in series
=> a + ar + ar^2 + ar^3 + ... + ar^(n-1)
=> a * [(1 - r^n) / (1-r)]
DC: Geometric Series
Fft And Inverse Fft Formulas
Dc: Solving Recurrences - Master Theorem
Dc: Arithmetic Series
,Definition 4 of 17
FFT = Mn(w) x B
Inverse FFT = 1/n Mn(w^-1) x B
Euler's Formula
Omega(w)
FFT and Inverse FFT Formulas
Steps to Solve for Fft
Definition 5 of 17
e^ix = cosx + isinx
Steps To Solve For Fft
Surface Area
Euler's Formula
Dc: Arithmetic Series
Definition 6 of 17
1. Define the Input and Output.
2. Define entries in table, i.e. T(i) or T(i, j) is...
3. Define a Recurrence relationship - Based on a subproblem to the main problem. (hint: use a
prefix of the original input 1 < i < n).
4. Define the Pseudocode.
5. Define the Runtime of the algorithm. Use Time Function notation here => T(n) = T(n/2) + 1...
Steps to solve a Dynamic Programming Problem
loga (u)^n
Omega(w)
Steps to solve for FFT
, Definition 7 of 17
Input = x1, x2, ..., xn
1) Subproblem = x1, x2, ..., xi ; O(n)
2) Subproblem = xi, xi+1, ..., xj ; O(n^2)
Input = x1, x2, ..., xn; y1, y2, ..., ym
1) Subproblem = x1, x2, ..., xi; y1, y2, ..., yj ; O(mn)
Input = Rooted Binary Tree
1) Subproblem = Smaller rooted binary tree inside the Input.
DC: Geometric Series
FFT and Inverse FFT Formulas
DC Algorithms and Runtimes (6)
DP: Types of Subproblems (4)
Definition 8 of 17
loga (u) - loga (v)
logb(b)
loga (u / v)
omega(w)
loga (u)^n
