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;
  const jumpMap = new Map();
  let queue = [0];
  let result = 0;

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

    if (!jumpMap.has(value)) {
      jumpMap.set(value, new Set());
    }

    jumpMap.get(value).add(index);
  }

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

    for (const pos of queue) {
      if (pos === n - 1) return result;

      const value = arr[pos];
      const jumpBack = pos - 1;
      const jumpForward = pos + 1;
      const candidates = jumpMap.get(value) ?? [];

      if (jumpBack >= 0 && jumpMap.has(arr[jumpBack])) {
        nextQueue.push(jumpBack);
      }

      if (jumpForward < n && jumpMap.has(arr[jumpForward])) {
        nextQueue.push(jumpForward);
      }

      jumpMap.delete(value);

      for (const nextPos of candidates) {
        nextQueue.push(nextPos);
      }
    }

    queue = nextQueue;
    result += 1;
  }

  return -1;
};