## Chapter 5 — The quick-check print is one matrix ### Lesson map Lesson 05. Map, example, EX051. ```mermaid flowchart TD D["Twelve keys, five cells each"] --> S["Sum each column"] D --> A["all of five ones"] S --> P["10, 8, 8, 11, 9 out of 12"] A --> C["3 of 12; worst FB07"] P --> Q{"Is a column rate the all-five count?"} C --> Q Q -->|No| K["Keep the embedded print"] ``` One dictionary. Five predicates. Two different summaries. ### Logical drawing ```text updates<=14d 10/12 encrypted 8/12 standard user 8/12 screen lock 11/12 backup<=7d 9/12 laptops passing all five: 3/12; worst: FB07 ``` ### Learning outcomes After this chapter, you should be able to: 1. Read each line of the embedded print as a defined reduction of the same dictionary. 2. Separate a column total from the count of rows that pass every predicate. 3. Refuse a note that replaces this run with Friday's update story. ### 5.1 Five reductions of one dictionary, and no second run. `lab_quickcheck.py` stores twelve keys, `FB01` through `FB12`. Each value is a list of five integers, and each integer is only `1` or `0`. The list order is fixed by `checks`: updates within fourteen days, disk encryption, a standard everyday account, a screen lock, and a backup within seven days. The script then does three reductions and nothing else. The first reduction walks column `i` and sums it. Because a yes is the integer `1`, the sum is a count. Those five counts are the five rates in the print: `10/12`, `8/12`, `8/12`, `11/12`, and `9/12`. The denominator is `len(laptops)`, which is 12. The front-desk computer is not a key in this dictionary, so it cannot change the denominator. The second reduction keeps a key only when `all(v)` is true, that is, when every cell is `1`. Three keys qualify: `FB01`, `FB08`, and `FB12`. The print therefore says `laptops passing all five: 3/12`. A laptop with four yes cells is absent from that count. The column rates can look healthy while the conjunction stays small, and both statements are true of this same object. The third reduction chooses `min(laptops, key=lambda k: sum(laptops[k]))`. It returns the key whose five cells add to the smallest total. `FB07` adds to 1. No other key adds to 1, so this run never has to break a tie. The print's `worst: FB07` is that minimum. It is not a judgement written by hand beside the table, and it is not a claim about the laptop's age. Age is a later sentence in the prose. Chapter 1 then tells a different story about updates. By Friday, the prose says, all twelve laptops show updates within fourteen days. That sentence is not a second execution of the script. The embedded lists still contain a `0` in the updates column for `FB03` and for `FB07`. A reader who pastes `12/12` over the first printed line is reporting a quantity this program did not compute. The same refusal applies to the closing note that twelve of twelve laptops later pass all five. Chapter 4 can narrate a later reading. It does not edit this dictionary. ### 5.2 Worked example | Sentence offered as a result | What computed it | Decision | |---|---|---| | `encrypted 8/12` | Column sum | Keep it on this print | | `laptops passing all five: 3/12` | `all` on each row | Keep it on this print | | `worst: FB07` | Minimum of the five-cell sums | Keep it | | "The script now prints 12 of 12 on every line." | No rerun is in the file | Refuse | > **Synthetic case.** Fenwick's twelve lists are the only machine output. Friday's update note is prose. ### Errors and limits A column can move in a later week while this embedded file stays as first recorded. Do not repair the print to match the story. ### Apply - **EX051 — One instrument.** The print shows 10, 8, 8, 11 and 9 out of 12, then 3 of 12 and worst FB07. May Friday's update sentence, or the later twelve-of-twelve note, replace that print? *Rubric:* 3 = no; the dictionary stays; column sums stay 10, 8, 8, 11 and 9; the conjunction stays 3 of 12; FB07 stays the unique minimum sum; do not edit the script;; 2 = the print stays and the later notes stay prose;; 1 = one line;; 0 = none. ### Continue studying — lesson 05 (chapter 05 of 20) [← Chapter 04](#ch-04) · [Course chapter index](../SUBJECTS.md) · [Chapter 06 →](#ch-06) Continue to the next authored lesson. ## Worked answers **EX051.** No. The dictionary stays. Column sums stay 10, 8, 8, 11 and 9 out of 12. The conjunction stays 3 of 12. FB07 stays the unique minimum. Do not edit the script.