#1824 - Minimum Sideway Jumps
Problem Description
There is a 3 lane road of length n that consists of n + 1 points labeled from 0 to n. A frog starts at point 0 in the second lane and wants to jump to point n. However, there could be obstacles along the way.
You are given an array obstacles of length n + 1 where each obstacles[i] (ranging from 0 to 3) describes an obstacle on the lane obstacles[i] at point i. If obstacles[i] == 0, there are no obstacles at point i. There will be at most one obstacle in the 3 lanes at each point.
- For example, if obstacles[2] == 1, then there is an obstacle on lane 1 at point 2.
The frog can only travel from point i to point i + 1 on the same lane if there is not an obstacle on the lane at point i + 1. To avoid obstacles, the frog can also perform a side jump to jump to another lane (even if they are not adjacent) at the same point if there is no obstacle on the new lane.
- For example, the frog can jump from lane 3 at point 3 to lane 1 at point 3.
Return the minimum number of side jumps the frog needs to reach any lane at point n starting from lane 2 at point 0.
Note: There will be no obstacles on points 0 and n.
Solution
/**
* @param {number[]} obstacles
* @return {number}
*/
var minSideJumps = function(obstacles) {
const n = obstacles.length;
let dp = [1, 0, 1];
for (let i = 1; i < n; i++) {
const currentObstacle = obstacles[i];
const nextDp = [Infinity, Infinity, Infinity];
for (let lane = 1; lane <= 3; lane++) {
if (lane === currentObstacle) continue;
nextDp[lane - 1] = dp[lane - 1];
for (let fromLane = 1; fromLane <= 3; fromLane++) {
if (fromLane !== lane && fromLane !== currentObstacle) {
nextDp[lane - 1] = Math.min(nextDp[lane - 1], dp[fromLane - 1] + 1);
}
}
}
dp = nextDp;
}
return Math.min(...dp);
};