Designing correct loops

Patterns

What a variable means

Most loops are not invented: they are assembled from a few pieces that reappear in every program. Each piece is a variable with an initialization before the loop, an update inside it and, above all, a meaning that holds after every iteration. Knowing the pieces by their meaning, and not by their form, is what allows them to be combined without error.

• A counter holds how many data items have been processed (or how many satisfy a condition). It is initialized to 0, because before the first iteration none has been processed, and it is updated with ++count, only when there is something to count.
• An accumulator holds the combination of the processed data: their sum, their product. It is initialized to the identity element of the operation (0 for the sum, 1 for the product), because the sum of no data is 0 and the product of no data is 1.
• A maximum holds the largest of the processed data, and a minimum, the smallest. The maximum of no data does not exist: that is why it is initialized with the first data item, and not with a number chosen at random.
• A sentinel is an input value that is not a data item but the signal that the data have ended. The pattern requires reading once before the loop and again at the end of the body, as the lesson Loops did when summing up to zero, so that the condition examines each value before it is processed, and the sentinel is never counted as data.
• A flag is a bool that tells whether something has ever happened among the processed data. It is initialized to false and becomes true the first time it happens; no later iteration sets it back to false.

An example with all the pieces

A rainfall log records the millimeters that fall each day. The program first reads a threshold, and then the measurements of several days, terminated by a negative number, which is not a possible measurement and serves as a sentinel; it writes how many measurements there are, their average, the maximum, how many days exceeded the threshold and whether there was any day without rain.

#include <iostream>#include <print>​int main(){    double threshold{};    std::cin >> threshold;    int count{0};          // counter: measurements processed    int aboveCount{0};     // counter: measurements above the threshold    double total{0.0};     // accumulator: sum of the measurements    double largest{0.0};   // maximum: meaningful only if count > 0    bool dryDay{false};    // flag: there was a day without rain    double value{};    std::cin >> value;    while (std::cin && value >= 0.0) {        if (count == 0 || value > largest) {            largest = value;        }        ++count;        total += value;        if (value > threshold) {            ++aboveCount;        }        if (value == 0.0) {            dryDay = true;        }        std::cin >> value;    }    if (count == 0) {        std::println("No measurements.");    } else {        std::println("Measurements: {}; average: {:.2f} mm", count, total / count);        std::println("Maximum: {:.1f} mm; days above {:.1f} mm: {}", largest, threshold, aboveCount);        std::println("Days without rain: {}", dryDay ? "yes" : "no");    }}

104.5 0 12.5 21.5 7.5 -1

Measurements: 5; average: 9.20 mmMaximum: 21.5 mm; days above 10.0 mm: 2Days without rain: yes

Four decisions deserve comment. The condition count == 0 || value > largest initializes the maximum with the first data item without a separate read: in the first iteration the counter is 0 and the assignment always happens; in the following ones, only if the data item exceeds the maximum. The comparison value == 0.0 is exact, because the value was read and not computed: the digit 0 is converted into the exact zero, and the caution of the lesson Floating-point numbers against == refers to results of operations. The loop condition includes std::cin, so that an input that ends without a sentinel also ends the loop. And the average is computed only if there are measurements: with count equal to 0, total / count would be $0/0$, which in floating point is not an error but the value “not a number”, which the program would write without warning.

Note that in each row of the figure every variable fulfills its meaning with respect to the measurements processed so far: total is their sum, largest their maximum, dryDay tells whether there was a zero among them. That property, which holds after every iteration, has a name.