Day24

class Solution {
    public double champagneTower(int k, int r, int c) {
        // If no champagne is poured, the glass is empty.
        if(k==0)
           return 0.0;

        // Create a 2D array to represent the glasses pyramid.
        double [][]matrix=new double[r+1][c+2];
        // Put all the poured champagne in the top glass.
        matrix[0][0]=k;   

        for(int i=0;i<r;i++){
            for(int j=0;j<=c;j++){
                if(matrix[i][j]>1.0){
                    // Calculate excess champagne and distribute it equally to the glasses below.
                    double spare=matrix[i][j]-1;
                    // Set the current glass to hold exactly one cup.
                    matrix[i][j]=1;
                    // Distribute excess to the left glass below.
                    matrix[i+1][j]+=spare/2;
                    // Distribute excess to the right glass below.
                    matrix[i+1][j+1]+=spare/2;
                }
            }
        }
        // Check the value in the desired glass (r, c).
        double res=matrix[r][c];
        // Ensure that the value doesn't exceed 1, as each glass can hold a maximum of one cup.
        return Math.min(res,1.0);
        
    }
}