1345. Jump Game IV

Description

Given an array of integers arr, you are initially positioned at the first index of the array.

In one step you can jump from index i to index:

• i + 1 where: i + 1 < arr.length.
• i - 1 where: i - 1 >= 0.
• j where: arr[i] == arr[j] and i != j.

Return the minimum number of steps to reach the last index of the array.

Notice that you can not jump outside of the array at any time.

 

Example 1:

Input: arr = [100,-23,-23,404,100,23,23,23,3,404]
Output: 3
Explanation: You need three jumps from index 0 --> 4 --> 3 --> 9. Note that index 9 is the last index of the array.

Example 2:

Input: arr = [7]
Output: 0
Explanation: Start index is the last index. You do not need to jump.

Example 3:

Input: arr = [7,6,9,6,9,6,9,7]
Output: 1
Explanation: You can jump directly from index 0 to index 7 which is last index of the array.

 

Constraints:

• 1 <= arr.length <= 5 * 104
• -108 <= arr[i] <= 108

 

Solutions

Solution: Breadth-First Search

• Time complexity: O(n)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number[]} arr
 * @return {number}
 */
const minJumps = function (arr) {
  const n = arr.length;

  if (n === 1) return 0;
  const arrMap = new Map();

  for (let index = 0; index < n; index++) {
    const value = arr[index];

    if (!arrMap.has(value)) {
      arrMap.set(value, []);
    }
    const indices = arrMap.get(value);

    indices.push(index);
  }

  let queue = [0];
  let result = 0;

  const isValidIndex = index => index > -1 && index < n && arrMap.has(arr[index]);

  while (queue.length) {
    const nextQueue = [];

    result += 1;

    for (const index of queue) {
      const value = arr[index];
      const forwardIndex = index + 1;
      const backIndex = index - 1;

      if (forwardIndex === n - 1 || backIndex === n - 1) return result;
      if (isValidIndex(forwardIndex)) {
        nextQueue.push(forwardIndex);
      }
      if (isValidIndex(backIndex)) {
        nextQueue.push(backIndex);
      }

      for (const nextIndex of arrMap.get(value) ?? []) {
        if (nextIndex === n - 1) return result;
        nextQueue.push(nextIndex);
      }
      arrMap.delete(value);
    }
    queue = nextQueue;
  }
  return -1;
};