Add backtracking solution to JumpGame.

Author: trekhleb

src/algorithms/uncategorized/jump-game/__test__/btJumpGame.test.js

@@ -0,0 +1,17 @@
+import btJumpGame from '../btJumpGame';
+
+describe('btJumpGame', () => {
+  it('should solve Jump Game problem in backtracking manner', () => {
+    expect(btJumpGame([1, 0])).toBeTruthy();
+    expect(btJumpGame([100, 0])).toBeTruthy();
+    expect(btJumpGame([2, 3, 1, 1, 4])).toBeTruthy();
+    expect(btJumpGame([1, 1, 1, 1, 1])).toBeTruthy();
+    expect(btJumpGame([1, 1, 1, 10, 1])).toBeTruthy();
+    expect(btJumpGame([1, 5, 2, 1, 0, 2, 0])).toBeTruthy();
+
+    expect(btJumpGame([1, 0, 1])).toBeFalsy();
+    expect(btJumpGame([3, 2, 1, 0, 4])).toBeFalsy();
+    expect(btJumpGame([0, 0, 0, 0, 0])).toBeFalsy();
+    expect(btJumpGame([5, 4, 3, 2, 1, 0, 0])).toBeFalsy();
+  });
+});

src/algorithms/uncategorized/jump-game/__test__/grdJumpGame.test.js

@@ -6,6 +6,7 @@ describe('grdJumpGame', () => {
     expect(grdJumpGame([100, 0])).toBeTruthy();
     expect(grdJumpGame([2, 3, 1, 1, 4])).toBeTruthy();
     expect(grdJumpGame([1, 1, 1, 1, 1])).toBeTruthy();
+    expect(grdJumpGame([1, 1, 1, 10, 1])).toBeTruthy();
     expect(grdJumpGame([1, 5, 2, 1, 0, 2, 0])).toBeTruthy();
 
     expect(grdJumpGame([1, 0, 1])).toBeFalsy();

src/algorithms/uncategorized/jump-game/btJumpGame.js

@@ -0,0 +1,42 @@
+/**
+ * BACKTRACKING approach of solving Jump Game.
+ *
+ * @param {number[]} numbers - array of possible jump length.
+ * @param {number} startIndex - index from where we start jumping.
+ * @param {number[]} currentJumps - current jumps path.
+ * @return {boolean}
+ */
+export default function btJumpGame(numbers, startIndex = 0, currentJumps = []) {
+  if (startIndex === numbers.length - 1) {
+    // We've jumped directly to last cell. This situation is a solution.
+    return true;
+  }
+
+  // Check what the longest jump we could make from current position.
+  // We don't need to jump beyond the array.
+  const maxJumpLength = Math.min(
+    numbers[startIndex], // Jump is within array.
+    numbers.length - 1 - startIndex, // Jump goes beyond array.
+  );
+
+  // Let's start jumping from startIndex and see whether any
+  // jump is successful and has reached the end of the array.
+  for (let jumpLength = maxJumpLength; jumpLength > 0; jumpLength -= 1) {
+    // Try next jump.
+    const nextIndex = startIndex + jumpLength;
+    currentJumps.push(nextIndex);
+
+    const isJumpSuccessful = btJumpGame(numbers, nextIndex, currentJumps);
+
+    // Check if current jump was successful.
+    if (isJumpSuccessful) {
+      return true;
+    }
+
+    // BACKTRACKING.
+    // If previous jump wasn't successful then retreat and try the next one.
+    currentJumps.pop();
+  }
+
+  return false;
+}

src/algorithms/uncategorized/jump-game/grdJumpGame.js

@@ -2,6 +2,7 @@
  * GREEDY approach of solving Jump Game.
  *
  * @param {number[]} numbers - array of possible jump length.
+ * @return {boolean}
  */
 export default function grdJumpGame(numbers) {
   // The "good" cell is a cell from which we may jump to the last cell of the numbers array.