Data update

Task/Fraction-reduction/JavaScript/fraction-reduction.js

@@ -0,0 +1,87 @@
+function indexOf(haystack, needle) {
+    for (let i = 0; i < haystack.length; i++) {
+        if (haystack[i] === needle) {
+            return i;
+        }
+    }
+    return -1;
+}
+
+function getDigits(n, le, digits) {
+    while (n > 0) {
+        const r = n % 10;
+        if (r === 0 || indexOf(digits, r) >= 0) {
+            return false;
+        }
+        le--;
+        digits[le] = r;
+        n = Math.floor(n / 10);
+    }
+    return true;
+}
+
+function removeDigit(digits, le, idx) {
+    const pows = [1, 10, 100, 1000, 10000];
+    let sum = 0;
+    let pow = pows[le - 2];
+    for (let i = 0; i < le; i++) {
+        if (i === idx) continue;
+        sum += digits[i] * pow;
+        pow /= 10;
+    }
+    return sum;
+}
+
+function main() {
+    const lims = [[12, 97], [123, 986], [1234, 9875], [12345, 98764]];
+    const count = [0, 0, 0, 0, 0];
+    const omitted = Array.from({ length: 5 }, () => new Array(10).fill(0));
+
+    for (let i = 0; i < lims.length; i++) {
+        const nDigits = new Array(i + 2).fill(0);
+        const dDigits = new Array(i + 2).fill(0);
+        for (let n = lims[i][0]; n <= lims[i][1]; n++) {
+            nDigits.fill(0);
+            const nOk = getDigits(n, i + 2, nDigits);
+            if (!nOk) {
+                continue;
+            }
+            for (let d = n + 1; d <= lims[i][1] + 1; d++) {
+                dDigits.fill(0);
+                const dOk = getDigits(d, i + 2, dDigits);
+                if (!dOk) {
+                    continue;
+                }
+                for (let nix = 0; nix < nDigits.length; nix++) {
+                    const digit = nDigits[nix];
+                    const dix = indexOf(dDigits, digit);
+                    if (dix >= 0) {
+                        const rn = removeDigit(nDigits, i + 2, nix);
+                        const rd = removeDigit(dDigits, i + 2, dix);
+                        if ((n / d) === (rn / rd)) {
+                            count[i]++;
+                            omitted[i][digit]++;
+                            if (count[i] <= 12) {
+                                console.log(`${n}/${d} = ${rn}/${rd} by omitting ${digit}'s`);
+                            }
+                        }
+                    }
+                }
+            }
+        }
+        console.log();
+    }
+
+    for (let i = 2; i <= 5; i++) {
+        console.log(`There are ${count[i - 2]} ${i}-digit fractions of which:`);
+        for (let j = 1; j <= 9; j++) {
+            if (omitted[i - 2][j] === 0) {
+                continue;
+            }
+            console.log(`${omitted[i - 2][j].toString().padStart(6)} have ${j}'s omitted`);
+        }
+        console.log();
+    }
+}
+
+main();