DS Exercises · DS_part2

The intermediate band: data with defects, statistics derived from other statistics, and honest tie handling.

PF-DS-07 · Range-Check Filter

Level: Foundational · Lectures: L07/L09 · Prerequisites: DS-02 Problem: Read n, then n integers (sensor values). Print the kept values on one line (those in −50..60 inclusive), then dropped: <k>. Formula first: predicate keep(v) ⇔ −50 ≤ v ≤ 60; kept values compact left-to-right into the same array (no second array). Edge cases: nothing kept (print an empty line, then dropped: n); all kept (dropped: 0); n = 0. Sample: 6 21 999 -7 60 61 0 → kept line 21 -7 60 0 / dropped: 2 Hints: this is the filter-compact half of PF-E-072's remove — here the rule is physical plausibility, not an exact value.

PF-DS-08 · Variance and Standard Deviation

Level: Intermediate · Lecture: L17 · Prerequisites: DS-05 Problem: Read n then n doubles. Print mean (2 dp), variance (2 dp, population form), stddev (2 dp). Formula first: var = Σ(xi − mean)² / n, std = √var. Use the two-pass form (compute mean first, then the squared deviations). State in a comment why the one-pass "sum of squares" shortcut (Σx²/n − mean²) is numerically riskier for large values. Edge cases: n = 1 → variance 0.00, stddev 0.00 (define it, print it, do not crash); constant data. Sample: 6 2 4 4 4 9 4 → mean 4.50, variance 4.58, stddev 2.14 (population form; verify the mean by hand first: 27/6 = 4.5). Hints: <cmath> sqrt is allowed (taught with isPrime's √n bound); sums of squares of doubles stay double; no integer casts here.

PF-DS-09 · Missing-Data Report (file, NA field)

Level: Intermediate · Lecture: L29 · Prerequisites: DS-06 Problem: File readings_na.txt holds lines station value, where value may be a number or the token NA. Print loaded, missing, invalid (non-numeric or wrong field count), then mean of loaded values (1 dp). NA is a recorded gap (its own class) — never mean it, never call it invalid. Formula first: mean over loaded only; class counts must sum to line count (loaded + missing + invalid = lines) — assert it in a comment and check by hand in the test table. Edge cases: empty file (all zeros, mean n/a, exit 0); missing file → exit 2; blank lines ignored (not counted in any class). Dataset: datasets/readings_na.txt (15 non-blank lines: 11 loaded, 2 missing, 2 invalid; mean 21.05 — and the class identity 11 + 2 + 2 = 15 holds, which your test table must confirm). Hints: getline + istringstream; token == "NA" before numeric parse.

PF-DS-10 · Weighted Mean

Level: Intermediate · Lectures: L13–L17 · Prerequisites: DS-03 Problem: Read n, then n pairs score weight (weights ≥ 0, at least one positive). Print the weighted mean (2 dp). Formula first: weighted mean = Σ(xi·wi) / Σwi — NOT Σxi/n. The denominator is the weight total, not the count; getting this wrong is the whole point of the exercise. Edge cases: all weights zero → no weights (exit 0, no division!); a weight of exactly 0 (legal: the score is ignored by the math — verify it is). Sample: 3 90 2 80 1 70 1 → 82.50 (not 82.75, and not the unweighted 80!); with a zero weight 3 90 0 80 1 70 1 → 82.50 still (the zero-weight pair contributes to neither numerator nor denominator). Hints: accumulate sumXW and sumW in one loop; both double (scores may be non-integer later).

PF-DS-11 · Sort and Rank

Level: Intermediate · Lecture: L24 · Prerequisites: DS-05 Problem: Read n then n scores. After sorting ascending, print rank of <value> queries? No — print, for the ORIGINAL order, each score's rank band (1-based position in the sorted list, smallest rank on ties). Formula first: rank(x) = 1 + |{y : y < x}| (competition ranking: 2 2 4 → ranks 1 1 3). Edge cases: all equal (every rank 1); single element (rank 1). Input: n, n values, then queries? Keep it programmatic: after sorting, print two lines: sorted values and their rank bands, space-separated. Sample: input 5 70 85 85 60 90 → sorted 60 70 85 85 90 / ranks 1 2 3 3 5 Hints: ranks come from positions; a value's rank can be found while sorting or by counting smaller elements — either, stated in a comment. Avoid duplicating: PF-CS-059 (stable ranking with ties) was a design study; this is a concrete implementation with a precise rank formula.

PF-DS-12 · Mode with Honest Ties

Level: Intermediate · Lecture: L18 · Prerequisites: DS-06 Problem: Read n then n integers in 1..100. Print mode: <v> and, if several values share the maximum frequency, print ALL of them ascending on a second line tied: ... (omit the line if unique). Also print freq: <k>. Formula first: mode = argmax_c f(c); ties are reported, not hidden — an honest report lists every maximizer. Edge cases: every value distinct (max frequency 1 — a weak claim; print it anyway with tied: listing all n values? No: if all frequencies are 1, print mode: none — say why in a comment); n = 0. Sample: 9 4 6 4 7 6 4 7 7 9 → counts 4:3, 6:2, 7:3, 9:1 → mode: 4 / tied: 4 7 / freq: 3 Hints: counts array of 100 slots with index shift; two scans: find max frequency, then list maximizers ascending.