Коммутативность — это свойство математических операций, при котором результат не изменяется при изменении порядка операндов. В этом уроке мы рассмотрим коммутативные операции в JavaScript и увидим, как они работают на практике.
Коммутативная операция — это операция, результат которой не зависит от порядка операндов. Например, сложение и умножение являются коммутативными операциями.
+)*)-)/)+)Сложение двух чисел является коммутативной операцией, так как a + b всегда равно b + a.
let a = 5;
let b = 3;
console.log(a + b); // 8
console.log(b + a); // 8 (порядок операндов не влияет на результат)
*)Умножение двух чисел также является коммутативной операцией, так как a * b всегда равно b * a.
let a = 4;
let b = 7;
console.log(a * b); // 28
console.log(b * a); // 28 (порядок операндов не влияет на результат)
-)Вычитание двух чисел не является коммутативной операцией, так как a - b не всегда равно b - a.
let a = 10;
let b = 3;
console.log(a - b); // 7
console.log(b - a); // -7 (порядок операндов влияет на результат)
/)Деление двух чисел также не является коммутативной операцией, так как a / b не всегда равно b / a.
let a = 12;
let b = 4;
console.log(a / b); // 3
console.log(b / a); // 0.3333... (порядок операндов влияет на результат)
Создадим пример, который демонстрирует проверку коммутативности различных операций.
HTML:
<!DOCTYPE html>
<html>
<head>
<title>Коммутативные операции в JavaScript</title>
<script>
let a = 6;
let b = 2;
// Проверка коммутативности сложения
let sum1 = a + b;
let sum2 = b + a;
console.log("Сложение: " + sum1 + " == " + sum2 + " ? " + (sum1 == sum2)); // true
// Проверка коммутативности умножения
let product1 = a * b;
let product2 = b * a;
console.log("Умножение: " + product1 + " == " + product2 + " ? " + (product1 == product2)); // true
// Проверка коммутативности вычитания
let difference1 = a - b;
let difference2 = b - a;
console.log("Вычитание: " + difference1 + " == " + difference2 + " ? " + (difference1 == difference2)); // false
// Проверка коммутативности деления
let quotient1 = a / b;
let quotient2 = b / a;
console.log("Деление: " + quotient1 + " == " + quotient2 + " ? " + (quotient1 == quotient2)); // false
</script>
</head>
<body>
<h1>Коммутативные операции в JavaScript</h1>
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Смешение коммутативных и некоммутативных операций: Не забывайте проверять свойства операций, так как не все операции коммутативны.
let a = 5;
let b = 3;
console.log(a - b == b - a); // false
console.log(a / b == b / a); // false
let result = 1 + 2 * 3; // результат будет 7, а не 9
let correctResult = (1 + 2) * 3; // результат будет 9
Понимание коммутативных операций является важной частью программирования на JavaScript. Эти операции упрощают работу с выражениями и позволяют писать более предсказуемый и читаемый код.
Пример выполнения:
let a = 8;
let b = 5;
// Проверка коммутативности сложения
let sum1 = a + b;
let sum2 = b + a;
console.log("Сложение: " + sum1 + " == " + sum2 + " ? " + (sum1 == sum2)); // true
// Проверка коммутативности умножения
let product1 = a * b;
let product2 = b * a;
console.log("Умножение: " + product1 + " == " + product2 + " ? " + (product1 == product2)); // true
// Проверка некоммутативности вычитания
let difference1 = a - b;
let difference2 = b - a;
console.log("Вычитание: " + difference1 + " == " + difference2 + " ? " + (difference1 == difference2)); // false
// Проверка некоммутативности деления
let quotient1 = a / b;
let quotient2 = b / a;
console.log("Деление: " + quotient1 + " == " + quotient2 + " ? " + (quotient1 == quotient2)); // false
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