8.3 Add Magic Index

Author: another-guy

__tests__/8-3-magic-index.spec.ts

@@ -0,0 +1,17 @@
+import { magicIndex } from '../src/cracking-the-coding-interview/8-recursion-and-dynamic-programming/8-3-magic-index';
+
+describe(magicIndex.name, () => {
+  [
+    { array: [ 0, 2, 4, 5, 6 ], expectedIndex: 0 },
+    { array: [ -1, 1, 4, 5, 6 ], expectedIndex: 1 },
+    { array: [ -1, 0, 2, 5, 6 ], expectedIndex: 2 },
+    { array: [ -1, 0, 1, 3, 6 ], expectedIndex: 3 },
+    { array: [ -1, 0, 1, 2, 4 ], expectedIndex: 4 },
+    { array: [ -1, 0, 1, 2, 3 ], expectedIndex: null },
+    { array: [], expectedIndex: null },
+  ].forEach(({ array, expectedIndex }) => {
+    it(`Should return ${expectedIndex} for ${JSON.stringify(array)}`, () => {
+      expect(magicIndex(array)).toEqual(expectedIndex);
+    });
+  });
+});

src/cracking-the-coding-interview/8-recursion-and-dynamic-programming/8-2-robot-in-a-grid.ts

@@ -3,25 +3,25 @@ export type Move = 'down' | 'right';
 export type X = 'x';
 export type _ = ' ';
 
-export function findPathRecursively(grid: Grid, r?: number, c?: number): Move[] | null {
+export function findPathRecursively(grid: Grid, rowIndex?: number, columnIndex?: number): Move[] | null {
   if (!grid || !grid.length) return null;
 
-  r = r != null ? r : grid.length - 1;
-  c = c != null ? c : grid[0].length - 1;
+  rowIndex = rowIndex != null ? rowIndex : grid.length - 1;
+  columnIndex = columnIndex != null ? columnIndex : grid[0].length - 1;
 
-  const canGoUp = r > 0 && grid[r - 1][c] === ' ';
-  const canGoLeft = c > 0 && grid[r][c - 1] === ' ';
-  if (r === 0 && c === 0) {
-    return grid[r][c] === 'x' ? null : [];
+  const canGoUp = rowIndex > 0 && grid[rowIndex - 1][columnIndex] === ' ';
+  const canGoLeft = columnIndex > 0 && grid[rowIndex][columnIndex - 1] === ' ';
+  if (rowIndex === 0 && columnIndex === 0) {
+    return grid[rowIndex][columnIndex] === 'x' ? null : [];
   }
 
   if (canGoUp) {
-    const pathToUpper = findPathRecursively(grid, r - 1, c);
+    const pathToUpper = findPathRecursively(grid, rowIndex - 1, columnIndex);
     if (pathToUpper) return [...pathToUpper, 'down'];
   }
 
   if (canGoLeft) {
-    const pathToLeft = findPathRecursively(grid, r, c - 1);
+    const pathToLeft = findPathRecursively(grid, rowIndex, columnIndex - 1);
     if (pathToLeft) return [...pathToLeft, 'right'];
   }
 

src/cracking-the-coding-interview/8-recursion-and-dynamic-programming/8-3-magic-index.ts

@@ -0,0 +1,16 @@
+export function magicIndex(
+  array: number[],
+  lowIndex: number = 0,
+  highIndex = array.length - 1,
+): number | null {
+  if (!array.length) return null;
+
+  if (lowIndex === highIndex) return array[lowIndex] === lowIndex ? lowIndex : null;
+
+  const index = lowIndex + Math.floor((highIndex - lowIndex) / 2);
+  const value = array[index];
+
+  if (value === index) return index;
+  else if (value < index) return magicIndex(array, index + 1, highIndex);
+  else return magicIndex(array, lowIndex, index - 1);
+}