Question

Give an example of a dynamic programming algorithm which solves the following problem:

Input. Two strings w1 and w2
Output. Yes if w1 contains all the letters of w2 in order, no otherwise.
(example problem instance and solutions)
Input. w1="abccba", w2="bba"
Output. Yes
Input. w1="abcabc", w2="bba"
Output. No

You do not need to prove the algorithm is correct. But you should analyze its runtime.

Answer 1

The algorithm is given as:

function boolean contains(String str1, String str2) {

m = str1.length()

n = str2.length()

j = 0

for i = 0 to i < m such that j < n do

if str1[i] == str2[j] then

j++

end if

end loop

if (j == n) then

print "Yes"

else

print "No"

end if

}

Time complexity: O(m) where m is the length of str1.