Greedy Algorithm--Algorithms

Largest Number:

  Find max digit
  Append it to the number
  Remove it from the list of digits

  Repeat while there are digits in the list 

car fueling:

  Refill at the the closest gas station

  Refill at the farthest reachable gas station

  Go until there is no fuel 

MinRefills(x,n,L)

numRefills ←0,currentRefill←0

while currentRefill≤n:

  lastRe ll ←currentRe ll

  while (currentRefill≤nand x[currentRefill+1]−x[lastRefill]≤L):

      currentRefill ←currentRefill+1

  if currentRefill==lastRefill:

        return IMPOSSIBLE

  if currentRefill≤n:

        numRefills ←numRefills+1

return numRefills

O(n)

For unsorted data, Sort in O(n log n) + greedy in O(n) 

Greedy Algorithm

While knapsack is not fullChoose item i with maximumvi/wi

If item fits into knapsack, take all of it

Otherwise take so much as to fill the knapsack

Return total value and amounts taken 

Knapsack(W,w1,v1,...,wn,vn)

A ←[0,0,...,0],V←0

repeat ntimes:

  if W=0:

    return (V,A)

  select iwithwi>0andmaxvi/Wj

  a ←min(wi,W)

  V ←V+avi/wi

  wi←wi−a,A[i]←A[i]+a,W←W−a

return (V,A)

Better:

Knapsack(W,w1,v1,...,wn,vn)

A ←[0,0,...,0],V←0

for ifrom1ton:

  if W=0:

    return (V,A)

  a ←min(wi,W)

  V ←V+avi/wi

  wi←wi−a,A[i]←A[i]+a,W←W−a

return (V,A)