LeetCode 488: Zuma Game

Explanation

To solve this problem, we can use a backtracking approach combined with some optimizations to reduce the search space. We will iterate through each possible insertion point in the board, try inserting a ball from our hand at that point, and recursively continue the process until we clear the board or run out of balls. To optimize the solution, we can prune the search space by skipping unnecessary insertions that won't lead to a solution. We need to keep track of the minimum number of balls used to clear the board.

Algorithm:

1. Define a recursive backtracking function that takes the board, hand, and the number of balls inserted so far.
2. Iterate through each position in the board and try inserting a ball from the hand at that position.
3. If the board becomes empty, update the minimum balls used if it's less than the current minimum.
4. If the current insertion does not lead to a solution, backtrack and try the next insertion.
5. Prune unnecessary insertions:
   • Skip inserting the same color ball consecutively to avoid redundant moves.
   • Skip inserting balls that won't be enough to clear the board based on the current minimum.
6. Return the minimum balls used to clear the board.

Time Complexity: O(N!), where N is the length of the board. The backtracking algorithm explores all possible permutations. Space Complexity: O(N) for the recursive call stack.

class Solution {
    public int findMinStep(String board, String hand) {
        // Java solution code here
    }
}