C++ Coding Test Course, Time Machine to Get There Fast

Recently, many companies are evaluating applicants’ algorithmic thinking and problem-solving abilities through coding tests. In this course, we will explain in detail the process of understanding and solving an interesting algorithm problem called “Time Machine to Fast Travel”. In particular, we will seek efficient and optimized solutions using the C++ language.

Problem Description

You have a time machine that can transcend time. However, this time machine operates according to specific rules. The rules for operating the time machine are as follows:

  • You are currently at time t, and this time is a positive integer.
  • You can move k seconds ahead, and k is limited to a maximum of C.
  • After each move, you can determine k again based on the new time t + k.
  • You need to reach the target time N by making several moves.

You need to write a program to find the minimum number of moves required to reach the target time N, given the current time t, the target time N, and the maximum moving time C.

Input Format

The first line contains the current time t (1 ≤ t ≤ 105), the target time N (t ≤ N ≤ 105), and the maximum moving time C (1 ≤ C ≤ 1000).

Output Format

Print the minimum number of moves required to reach the target time N.

Example

    Input
    5 10 3

    Output
    2

Explanation: The customer starts at time 5, moves 3 seconds ahead (time 8), then moves 2 seconds ahead (time 10), making a total of 2 moves to reach the target time 10.

Problem Solving Strategy

This problem can be solved using BFS (Breadth-First Search). BFS is a very useful algorithm for exploring the shortest path in graphs or trees. The graph in this problem can be thought of as nodes composed of the current time and the target time, where each move acts as an edge of the graph.

Steps of the BFS Algorithm

  1. Start the BFS using a queue. The initial state is set to the current time t.
  2. Remove the current time from the queue and check if you have reached the target time N.
  3. From the current time, try all possible moves (from 1 second to C seconds) to calculate the new time, and check if this new time can reach the target time N.
  4. If the new time equals the target time N, print the number of moves. Otherwise, add the new time to the queue and continue searching.

C++ Code Implementation

    #include 
    #include 
    #include 
    using namespace std;

    int minMoves(int t, int N, int C) {
        vector visited(N + 1, false);
        queue> q; // {current_time, moves}
        q.push({t, 0});
        visited[t] = true;

        while (!q.empty()) {
            auto [current_time, moves] = q.front();
            q.pop();

            if (current_time == N) {
                return moves;
            }

            for (int jump = 1; jump <= C; ++jump) {
                int next_time = current_time + jump;
                if (next_time > N) {
                    continue; // Ignore if it exceeds the target time
                }

                if (!visited[next_time]) {
                    visited[next_time] = true;
                    q.push({next_time, moves + 1});
                }
            }
        }

        return -1; // In case of unreachable
    }

    int main() {
        int t, N, C;
        cin >> t >> N >> C;
        cout << minMoves(t, N, C) << endl;
        return 0;
    }

Code Explanation

The above C++ code implements the BFS algorithm to solve the given problem.

  1. The minMoves function takes the current time, target time, and maximum moving time as arguments. This function returns the minimum number of moves required to reach the target time N.
  2. First, initialize an array visited to store the visited status and prepare the queue.
  3. Remove the current time from the queue, and if you have reached the target time, return the number of moves.
  4. Try all possible moves up to a maximum of C seconds from the current time, adding new times to the queue.
  5. This process repeats, and once you reach the target time, the corresponding move count will be printed.

Result Verification

The program needs to be benchmarked and verified by running various inputs to ensure the results are as expected. For example:

    Input
    1 5 2

    Output
    3

By providing this input, we can examine each move path and confirm that the optimal solution is achieved.

Conclusion

In this course, we explored the process of solving the "Time Machine to Fast Travel" problem using C++. We learned how to find the shortest path through the BFS algorithm and gained experience solving problems through actual code. This knowledge will be greatly helpful for real coding tests or algorithm problem-solving. We look forward to tackling more interesting problems in the next course!