22a. Recursion Practice 5

1. (count-w) Find how many “w” letters there are in a word. Signature: count-w: string -> number.

2. (p7) Find the smallest power of 7 that is at least a given number. (So find the smallest $k$ so that $7^k \ge \text{number}$.) Signature: p7: number -> number.

    (check-expect (p7 1) 0)
    (check-expect (p7 7) 1)
    (check-expect (p7 8) 2)
    (check-expect (p7 49) 2)
    (check-expect (p7 50) 3)
   

3. (eyeball) Find how many pairs of consecutive zeros there are in a number. Signature: eyeball: number -> number.

    (check-expect (eyeball 0) 0)
    (check-expect (eyeball 00) 0)
    (check-expect (eyeball 1007008) 2)
    (check-expect (eyeball 30008) 2)
   

   Explanations: the number 00 is really just 0, so there is only one zero. The number 30008 has two pairs of consecutive zeros: 3 00 08 and 30 00 8.

More Practice

4. (no-z) Remove all z’s from a string. no-z: string -> string

    (check-expect (no-z "whazzlez") "wale")
   

5. (cq) Count how many times a given letter appears in a word. cq: string(letter) string(word) -> number One special case: when asked to count the number of “q” in a word, only count “q” letters immediately followed by “u”.

    (check-expect (cq "k" "kraken") 2)
    (check-expect (cq "q" "queue q que") 2)
   

6. (pink) Change every appearance of “pink” in the string to “blue”. Signature: pink: string -> string.

    (check-expect (pink "pink pink") "blue blue")
   

   Advanced: leave the first appearance alone.

    (check-expect (pink-advanced "pink pink pink") "pink blue blue")