(euler): #9

euler/src/9 - Special Pythagorean Triplet.ts

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+// a + b + c = 1000
+// we need a * b * c
+// pythagorean triplet: a < b < c
+// a^2 + b^2 = c^2
+
+const pythagoreanTriplet = (sum: number) => {
+    let a: number,
+        b = 1,
+        c: number;
+
+    for (; b < sum; b++) {
+        // let x = sum
+
+        // c = x - (a + b)
+        // a^2 + b^2 = (x - (a + b))^2
+        // a^2 + b^2 = a^2 + 2ab - 2ax + b^2 - 2bx + x^2
+        // 0 = 2ab - 2ax - 2bx + x^2
+
+        // 2bx - 2ab = x^2 - 2ax
+        // (x^2 / x) - 2a = 2b - (2ab / x)
+        // -2a = 2b - (2ab / x) - (x^2 / x)
+        // a = - (((x * 2b) - (x * x)) / ((2 * x) - (2 * b)))
+        a = -((sum * (2 * b) - sum * sum) / (2 * sum - 2 * b));
+
+        if (Math.floor(a) === a) {
+            c = sum - a - b;
+            break;
+        }
+    }
+
+    return { a, b, c };
+};
+
+const triplet = pythagoreanTriplet(1000);
+console.log(triplet);
+console.log(triplet.a * triplet.b * triplet.c);