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In this approach, we simulate the pouring process using a 2D array, where each element represents a glass and stores the amount of champagne in it. We iterate over each row, calculating the overflow and distributing it equally to the glasses directly below the current glass.
Time Complexity: O(n^2) where n is the number of rows traversed. Space Complexity: O(n^2) for the 2D array used to simulate the champagne distribution.
1function champagneTower(poured, query_row, query_glass) {
2 let tower = Array.from({ length: 101 }, () => Array(101).fill(0));
3 tower[0][0] = poured;
4 for (let i = 0; i < 100; i++) {
5 for (let j = 0; j <= i; j++) {
6 if (tower[i][j] >= 1) {
7 let overflow = (tower[i][j] - 1) / 2;
8 tower[i + 1][j] += overflow;
9 tower[i + 1][j + 1] += overflow;
10 }
11 }
12 }
13 return Math.min(1.0, tower[query_row][query_glass]);
14}
15
16console.log(champagneTower(2, 1, 1).toFixed(5));In this JavaScript implementation, a 2D array 'tower' is used to model the pyramid of glasses. The code iteratively checks each glass, calculating overflows and updating the respective glasses below.
We use a linear array 'dp' to hold the champagne amounts for each glass in the current row, updating in place to manage the overflow process effectively as we advance through the rows.