1. Dynamic programming & Greedy algorithms

2. All the Torah on one leg
dynamic programming is a method for solving complex problems by breaking them down into simpler sub problems. Solve only once Often trade off with memory complexity

3. Guide lines Find recursive method
Discover that algorithm (top to bottom) is exponential time
If cause of exponential is repeating problems then Dynamic Programming is in order
Solve sub problems and keep there answer

4. Example Fibonacci sequence
function fib(n)
if n = 0 return 0
if n = 1 return 1
return fib(n − 1) + fib(n − 2)
if key n is not in map m
m[n] := fib(n − 1) + fib(n − 2)
return m[n]

5. Longest common subsequence
Find Longest common subsequence (not have to be continuous) sequence X: AGCAT(n elements) sequence Y: GAC(m elements) # combinations

6. Dynamic

7. function LCSLength(X[1. m], Y[1. n]) C = array(0. m, 0. n) for i := 0
function LCSLength(X[1..m], Y[1..n]) C = array(0..m, 0..n) for i := 0..m C[i,0] = 0 for j := 0..n C[0,j] = 0 for i := 1..m for j := 1..n if X[i] = Y[j] C[i,j] := C[i-1,j-1] + 1 else C[i,j] := max(C[i,j-1], C[i-1,j]) return C[m,n]

8. Example AGCAT GAC
"G" Row Completed Ø A G C T
(G)

9. Greedy algorithms
Solve local optimization in hope it will bring to global optimization Often trade off with the best answer possible

10. Huffman coding
Huffman coding is an entropy encoding algorithm used for lossless data compression Main idea encode repeating symbols in as short word Input: file containing symbols or chars Output: compressed file * Optimal!!!

11. Huffman(C) n<-length(C) % insert the group into priority queue Q<- C for i<-1 to n-1 do z<-allocate-node() x<-left[z]<-extract-min(Q) y<-right[z]<-extract-min(Q) f[z]<-f[x]+f[y] Insert(Q,z) return extract-min(Q)