LeetCode //C - 789. Escape The Ghosts

789. Escape The Ghosts

You are playing a simplified PAC-MAN game on an infinite 2-D grid. You start at the point [0, 0], and you are given a destination point $target=[x_{target},y_{target}]$ that you are trying to get to. There are several ghosts on the map with their starting positions given as a 2D array ghosts, where $ghosts[i]=[x_i,y_i]$ represents the starting position of the $i^{th}$ ghost. All inputs are integral coordinates.

Each turn, you and all the ghosts may independently choose to either move 1 unit in any of the four cardinal directions: north, east, south, or west, or stay still. All actions happen simultaneously.

You escape if and only if you can reach the target before any ghost reaches you. If you reach any square (including the target) at the same time as a ghost, it does not count as an escape.

Return true if it is possible to escape regardless of how the ghosts move, otherwise return false.
 

Example 1:

Input: ghosts = [[1,0],[0,3]], target = [0,1]
Output: true
Explanation: You can reach the destination (0, 1) after 1 turn, while the ghosts located at (1, 0) and (0, 3) cannot catch up with you.

Example 2:

Input: ghosts = [[1,0]], target = [2,0]
Output: false
Explanation: You need to reach the destination (2, 0), but the ghost at (1, 0) lies between you and the destination.

Example 3:

Input: ghosts = [[2,0]], target = [1,0]
Output: false
Explanation: The ghost can reach the target at the same time as you.

Constraints:

• 1 <= ghosts.length <= 100
• ghosts[i].length == 2
• $-10^4<=x_i,y_i<=10^4$
• There can be multiple ghosts in the same location.
• target.length == 2
• $-10^4<=x_{target},y_{target}<=10^4$

From: LeetCode
Link: 789. Escape The Ghosts

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Solution:

Ideas:

• Manhattan Distance is used because both player and ghosts move in cardinal directions.

• You calculate:

  • The distance from the player’s start point [0,0] to the target.
  • The distance from each ghost to the target.

• If any ghost can reach the target in fewer or equal steps than the player, then escape is impossible.

• Otherwise, you can always reach the target first, regardless of how the ghosts move.

Code:

// Helper function to calculate Manhattan distance
int manhattanDistance(int* point1, int* point2) {
    return abs(point1[0] - point2[0]) + abs(point1[1] - point2[1]);
}

bool escapeGhosts(int** ghosts, int ghostsSize, int* ghostsColSize, int* target, int targetSize) {
    // Distance for player from (0,0) to target
    int playerDist = abs(target[0]) + abs(target[1]);

    // Check if any ghost can reach the target before or at the same time as player
    for (int i = 0; i < ghostsSize; i++) {
        int ghostDist = abs(ghosts[i][0] - target[0]) + abs(ghosts[i][1] - target[1]);
        if (ghostDist <= playerDist) {
            return false;
        }
    }
    return true;
}