Race Car in C++

Suppose we have a car, that starts at position 0 and speed +1 on an infinite number line. The car runs automatically according to a sequence of instructions A: for accelerate and R − for reverse. When we get an instruction "A", our car does the following −

• position := position + speed, then speed = speed * 2.

When we get an instruction "R", our car does the following −

• if speed is positive then speed = -1,
• otherwise speed = 1.

For example, after executing the instructions "AAR", our car goes to positions 0->1->3->3, and speed goes to 1->2->4->-1.

Now suppose we have some target position; we have to find the length of the shortest sequence of instructions to get there.

So, if the input is like target = 6, then the output will be 5 as one of the possible sequence is AAARA, the position sequence will be 0->1->3->7->7->6

To solve this, we will follow these steps −

• Define one set visited
• Define one queue q
• insert { 0, 1 } into q
• for initialize level := 0, when not q is empty, update (increase level by 1), do −
  • for initialize k := size of q, when k > 0, update (decrease k by 1), do −
    • Define one pair curr := front element of q, delete element from q
    • if first of curr is same as target, then −
      • return level
    • forward := first of curr + second of curr
    • forwardSpeed := second of curr * 2
    • key := convert forward to string concatenate " * " concatenate convert forwardSpeed to string
    • if forward > 0 and |forward - target| < target and not key is not in visited, then −
      • insert key into visited
      • insert { forward, forwardSpeed } into q
    • key := convert first of curr to string concatenate " * " concatenate 0 when second of curr > 0, otherwise -1
    • if curr.first > 0 and |target - curr.first| < target and key is not in visited, then −
      • insert key into visited
      • insert { curr.first, (if curr.second > 0, then -1, otherwise 1 }) into q
• return -1

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
   int racecar(int target) {
      unordered_set < string > visited;
      queue < pair <int ,int> > q;
      q. push({0, 1});
      for(int level = 0; !q.empty(); level++){
         for(int k = q.size(); k > 0; k-- ){
            pair <int, int> curr = q.front();
            q.pop();
            if(curr.first == target) return level;
            int forward = curr.first + curr.second;
            int forwardSpeed = curr.second * 2;
            string key = to_string(forward) + "*" + to_string(forwardSpeed);
            if(forward > 0 && abs(forward - target) < target && !visited.count(key)){
               visited.insert(key);
               q.push({forward, forwardSpeed});
            }
            key = to_string(curr.first) + "*" + to_string(curr.second > 0 ? - 1: 1);
            if(curr.first > 0 && abs(target - curr.first) < target && !visited.count(key)){
               visited.insert(key);
               q.push({curr.first, curr.second > 0 ? - 1: 1});
            }
         }
      }
      return -1;
   }
};
main(){
   Solution ob;
   cout << (ob.racecar(6));
}

Input

6

Output

5