TIM AU YEUNG HKOI 2012 Greedy. Try some cases Make a guess local optimum -> global optimum Not really a specific algorithm  Practice more  By feelings.

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Presentation transcript:

TIM AU YEUNG HKOI 2012 Greedy

Try some cases Make a guess local optimum -> global optimum Not really a specific algorithm  Practice more  By feelings

Example 1: Coins 7 kinds of coins: $0.1, $0.2, $0.5, $1, $2, $5, $10 Find minimum number of coins needed to pay $n Try n = 3.6  $2, $1, $0.5, $0.1 Try n = 18  $10, $5, $2, $1 Every time use the coin of highest value

Example 2: Subarray Sum Given a one-dimensional array of numbers (containing at least one positive number) Find the nonempty contiguous subarray which has the largest sum  Calculate maximum subarray ending at each position  simple example of DP (will be taught later) If all numbers are non-positive?

Example 3: Bridge and Torch Four people come to a river in the night. There is a narrow bridge, but it can only hold two people. Person A can cross the bridge in 1 minute, B in 2 minutes, C in 5 minutes, and D in 8 minutes. When two people cross the bridge together, they must move at the slower person's pace. What is the minimum time required for all four people to cross the river?

Example 3: Bridge and Torch N people  1) AB Go A Back, YZ Go B Back  2) AZ Go A Back, AY Go A Back N-2 people

Example 4: Yogurt factory POJ 2393 C_i: cost to produce one unit of yogurt in week i S: fee to store one unit of unused yogurt per week Y_i: units of yogurt demanded in week i (Yogurt produced in week i and already in storage, can be used to meet yogurt demand for that week)  Week i: sell yogurt produced in week j (j<=i)  minC = min(C_i, minC + S)

Example 5: Persistent Numbers POJ2325 Given a number n, find the smallest number that can reach n by repeatedly multiplying the digits e.g > 378 -> 168 -> 48 -> … 48 can be reached from 679 There may be No Solution!  Factorize n by 9, 8, 7, 6, 5, 4, 3, 2 in order  Distribute them from low-value digit to high-value digit

Greedy Practice List POJ 2709 POJ 1042 POJ 1065 POJ 2586 POJ 1328 POJ 1018 HKOJ 1019 HKOJ 1137 HKOJ 2014

If (Greedy_fails) Fail for boundary cases  Special solution deal with them Fail for many cases  Don’t be greedy  Think of other algorithm

Greedy Conclusion Guess Try some cases Hard to prove or disprove Easy to code Efficient Practice more!