fix alphabet indexAt and stringAt

Author: chieveit

src/core/alphabet.js

@@ -12,13 +12,14 @@ const alphabets = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', '
 export function stringAt(index) {
   let str = '';
   let cindex = index;
-  while (cindex >= alphabets.length) {
+  // Each loop iteration converts a base-26 (alphabet length) digit to a
+  // character [A-Z]. Because it works from least to most significant digit,
+  // each new character must be added to the FRONT of the string being built.
+  do {
+    str = alphabets[parseInt(cindex, 10) % alphabets.length] + str;
     cindex /= alphabets.length;
     cindex -= 1;
-    str += alphabets[parseInt(cindex, 10) % alphabets.length];
-  }
-  const last = index % alphabets.length;
-  str += alphabets[last];
+  } while (cindex >= 0);
   return str;
 }
 
@@ -30,12 +31,23 @@ export function stringAt(index) {
  */
 export function indexAt(str) {
   let ret = 0;
-  for (let i = 0; i < str.length - 1; i += 1) {
+  // Each loop iteration converts a digit from a base-26 [A-Z] string to a
+  // base 10 integer, working from most to least significant base-26 digit.
+  for (let i = 0; i < str.length; i += 1) {
+    // Calculate offset from 'A', which has character code 65
     const cindex = str.charCodeAt(i) - 65;
     const exponet = str.length - 1 - i;
-    ret += (alphabets.length ** exponet) + (alphabets.length * cindex);
+    // 'A' is interpreted as 0 when in the 0th digit, but as 1 when in any
+    // other digit. Therefore, we will increment cindex so that [0-25] is
+    // remapped to [1-26] for all digits, then decrement the result after the
+    // loop completes by 1 to remap the 0th digit back to [0-25].
+    // For example:
+    // 'AA' will be converted to (base-26) 11 by the loop,
+    // then decremented to (base-26) 10 before being returned,
+    // which expressed in base-10 is 26.
+    ret += (cindex + 1) * (alphabets.length ** exponet);
   }
-  ret += str.charCodeAt(str.length - 1) - 65;
+  ret -= 1;
   return ret;
 }
 

test/core/alphabet_test.js

@@ -11,54 +11,30 @@ import {
 describe('alphabet', () => {
   describe('.indexAt()', () => {
     it('should return 0 when the value is A', () => {
-      assert.equal(indexAt('A'), 0);
+      assert.equal(indexAt('A'), 1 * 26 ** 0 - 1);
     });
-    it('should return 25 when the value is Z', () => {
-      assert.equal(indexAt('Z'), 25);
+    it('should return 27 when the value is AB', () => {
+      assert.equal(indexAt('AB'), 1 * 26 ** 1 + 2 * 26 ** 0 - 1);
     });
-    it('should return 26 when the value is AA', () => {
-      assert.equal(indexAt('AA'), 26);
+    it('should return 730 when the value is ABC', () => {
+      assert.equal(indexAt('ABC'), 1 * 26 ** 2 + 2 * 26 ** 1 + 3 * 26 ** 0 - 1);
     });
-    it('should return 52 when the value is BA', () => {
-      assert.equal(indexAt('BA'), 52);
-    });
-    it('should return 54 when the value is BC', () => {
-      assert.equal(indexAt('BC'), 54);
-    });
-    it('should return 78 when the value is CA', () => {
-      assert.equal(indexAt('CA'), 78);
-    });
-    it('should return 26 * 26 when the value is ZA', () => {
-      assert.equal(indexAt('ZA'), 26 * 26);
-    });
-    it('should return 26 * 26 + 26 when the value is AAA', () => {
-      assert.equal(indexAt('AAA'), (26 * 26) + 26);
+    it('should return 19009 when the value is ABCD', () => {
+      assert.equal(indexAt('ABCD'), 1 * 26 ** 3 + 2 * 26 ** 2 + 3 * 26 ** 1 + 4 * 26 ** 0 - 1);
     });
   });
   describe('.stringAt()', () => {
     it('should return A when the value is 0', () => {
-      assert.equal(stringAt(0), 'A');
-    });
-    it('should return Z when the value is 25', () => {
-      assert.equal(stringAt(25), 'Z');
-    });
-    it('should return AA when the value is 26', () => {
-      assert.equal(stringAt(26), 'AA');
-    });
-    it('should return BC when the value is 54', () => {
-      assert.equal(stringAt(54), 'BC');
-    });
-    it('should return CB when the value is 78', () => {
-      assert.equal(stringAt(78), 'CA');
+      assert.equal(stringAt(1 * 26 ** 0 - 1), 'A');
     });
-    it('should return ZA when the value is 26 * 26', () => {
-      assert.equal(stringAt(26 * 26), 'ZA');
+    it('should return AB when the value is 27', () => {
+      assert.equal(stringAt(1 * 26 ** 1 + 2 * 26 ** 0 - 1), 'AB');
     });
-    it('should return Z when the value is 26 * 26 + 1', () => {
-      assert.equal(stringAt((26 * 26) + 1), 'ZB');
+    it('should return ABC when the value is 730', () => {
+      assert.equal(stringAt(1 * 26 ** 2 + 2 * 26 ** 1 + 3 * 26 ** 0 - 1), 'ABC');
     });
-    it('should return AAA when the value is 26 * 26 + 26', () => {
-      assert.equal(stringAt((26 * 26) + 26), 'AAA');
+    it('should return ABCD when the value is 19009', () => {
+      assert.equal(stringAt(1 * 26 ** 3 + 2 * 26 ** 2 + 3 * 26 ** 1 + 4 * 26 ** 0 - 1), 'ABCD');
     });
   });
   describe('.expr2xy()', () => {