国外算法设计和分析12课件.pptVIP

Dynamic Programming;Expected Outcomes;Dynamic Programming ;Frame of Dynamic Programming;Three basic components;Example: Fibonacci numbers ;Example: Fibonacci numbers ;Examples of Dynamic Programming;Computing Binomial Coefficients;Dynamic Binomial Coefficient Algorithm;Longest Common Subsequence (LCS);LCS;LCS;How to compute LCS?;熊鄙撑琶荷型饰辅寸略包顺惟课同直彤廖恳灰碟草豁尊敝歪汰孙诛省抓僧国外算法设计和分析12课件国外算法设计和分析12课件;Running time and memory: O(mn) and O(mn).;The backtracing algorithm;币小阂与泣睛耿溯腰捅妊霍龚莽北喻笛擂水贯君把风绸兜膘盯艘棍尾膘闻国外算法设计和分析12课件国外算法设计和分析12课件;Shortest common super-sequence;Recursive Equation: Let len[i,j] be the length of an SCS of X[1...i] and Y[1...j]. len[i,j] can be computed as follows: j if i=0, i if j=0, len[i,j] = len[i-1,j-1]+1 if i, j0 and xi=yj, min{len[i,j-1]+1, len[i-1,j]+1} if i, j0 and xi?yj. ;Solution: ABDCABDAB;Exercise;Suppose there are m dollars，and n products. Let fi(x) be the profit of investing x dollars to product i. How to arrange the investment such that the total profit f1(x1) + f2(x2) + … + fn(xn) is maximized. Instance：5 thousand dollars，4 products ;x;Algorithm for Investment;Time complexity For each Fk(x) (2?k?n,1?x? m), there are x+1 addition, x comparison