(1) for i 1 to n-1 2) for j=i+1 to n 3】 iE(A[i打>A[j1) (4) exchange A[i]and A[il How many times is the comparison Ali]Alj]made in Line 3? critical operation Principle 1.1 (Sum Principle) The size of a union of a family of mutually disjoint finite sets is the sum of the sizes of the sets. Us. IS:l
critical operation
操作计数与子集计数 相同的情况,不同的抽象: 在排序的例子里,对任意含两个元素的子 集,我们需要做一次比较 则比较次数等于个元素的集合所有的两 个元素的子集的个数。 ()= n(n-1) 2
操作计数 与 子集计数 相同的情况,不同的抽象: 在排序的例子里,对任意含两个元素的子 集,我们需要做一次比较 则比较次数等于n个元素的集合所有的两 个元素的子集的个数
你能再解释一下抽象的过程吗? (1) for i 1 to r (2】 for j 1 to m (3) S=0 (4 for k 1 to n (5) SS A[i,k]B[k,] (6) C[i,j打=s How many multiplications (expressed in terms of r.m.and n)does this pseudocode carry out in total among all the iterations of Line 5? 7=U Tl= U=∑ISl=∑=mn i-l 乘法原则是否是必须明确给出的呢?
你能再解释一下抽象的过程吗? 乘法原则是否是必须明确给出的呢?
(1) for i =1 to n-1 (2) minval A[i] (3) minindex i (4) for j=i to n (5) if (A[j]minval) (6) minval A[j] (7) minindex j (8) exchange A[i]and A[minindex] (9) bigjump =0 (10) for i 2 to n (11) if(A[i]>2*A[i-1]) (12) bigjump bigjump 1 这个算法需要执行多少次比较操作?
这个算法需要执行多少次比较操作?
乘法原则的两个版本不一样吗? 其实,我们还有 一个乘法原理: 做一件事情有m Principle 1.3 (Product Principle) 个步骤,如果完 The size of a union of m disjoint sets, each of size n is mn. 成第涉的方法有 1种,那么完成这 件事情的方法有 问题3: Principle 1.4 (Product Principle,Version 2) If a set S of lists of length m has the properties that *i2*.*im种方 通俗地 1.there are i different first elements of lists in S.and 法 说说1.4 2.for eachI and each choice of the firstj-I elements of a 是什么 list in S,there are i;choices of elements in position j of those lists. 意思? then there are ii=i lists in S
乘法原则的两个版本不一样吗? 其实,我们还有 一个乘法原理: 做一件事情有m 个步骤,如果完 成第j步的方法有 i j种,那么完成这 件事情的方法有 i1 *i2 *……*im种方 法
从数1ist到数函数 How many functions are there from a two-element set to a three-element set? How many functions are there from a three-element set to a two-element set? How many functions are there from a m-element set to a n-element set? T(m,n)=n*T(m-1,n) T(1,n)=n T(m,n)=nm
从数list到数函数 How many functions are there from a two-element set to a three-element set? How many functions are there from a three-element set to a two-element set? How many functions are there from a m-element set to a n-element set? T(m,n)=n*T(m-1,n) … T(1,n)=n T(m,n)=n m
问题4;这与数函数有什么关系? Principle 1.4 (Product Principle,Version 2) If a set S of lists of length m has the properties that 1.there are i different first elements of lists in S,and 2.for each>I and each choice of the first j-I elements of a list in S.there are i choices of elements in position j of those lists, then there are ii.=is lists in S. 用B中元素构造长度为3的ist。 每个ist其实就是一个A到T的函数! 这个ist有多少种可能性? A集合 B集合 ·如果A=m,B=n呢?
A集合 B集合 • 用B中元素构造长度为3的list。 • 每个list其实就是一个A到T的函数! • 这个list有多少种可能性? • 如果|A|=m,|B|=n呢?