You are given two integers red and blue representing the count of red and blue colored balls. You have to arrange these balls to form a triangle such that the 1st row will have 1 ball, the 2nd row will have 2 balls, the 3rd row will have 3 balls, and so on.All the balls in a particular row should be the same color, and adjacent rows should have different colors.Return the maximum height of the triangle that can be achieved. Example 1:Input: red = 2, blue = 4Output: 3Explanation:The only possible arrangement is shown above.Example 2:Input: red = 2, blue = 1Output: 2Explanation:The only possible arrangement is shown above.Example 3:Input: red = 1, blue = 1Output: 1Example 4:Input: red = 10, blue = 1Output: 2Explanation:The only possible arrangement is shown above. Constraints:1 <= red, blue <= 100
Question
You are given two integers red and blue representing the count of red and blue colored balls. You have to arrange these balls to form a triangle such that the 1st row will have 1 ball, the 2nd row will have 2 balls, the 3rd row will have 3 balls, and so on.All the balls in a particular row should be the same color, and adjacent rows should have different colors.Return the maximum height of the triangle that can be achieved. Example 1:Input: red = 2, blue = 4Output: 3Explanation:The only possible arrangement is shown above.Example 2:Input: red = 2, blue = 1Output: 2Explanation:The only possible arrangement is shown above.Example 3:Input: red = 1, blue = 1Output: 1Example 4:Input: red = 10, blue = 1Output: 2Explanation:The only possible arrangement is shown above. Constraints:1 <= red, blue <= 100
Solution
To solve this problem, we need to follow these steps:
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First, we need to understand that the maximum height of the triangle is determined by the total number of balls we have. The number of balls needed for each row increases by 1 for each new row. So, for a triangle of height h, we need 1+2+3+...+h balls. This sum can be calculated using the formula h*(h+1)/2.
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We start by calculating the maximum possible height if we had an unlimited number of balls. This can be done by solving the equation h*(h+1)/2 = red + blue for h. Since h must be an integer, we take the floor of the square root of 2*(red + blue).
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Now we have the maximum possible height, but we need to check if we have enough balls of each color to
Similar Questions
Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 9999 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square, whose each side contains exactly 22 balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is
You are given an integer limit and a 2D array queries of size n x 2.There are limit + 1 balls with distinct labels in the range [0, limit]. Initially, all balls are uncolored. For every query in queries that is of the form [x, y], you mark ball x with the color y. After each query, you need to find the number of distinct colors among the balls.Return an array result of length n, where result[i] denotes the number of distinct colors after ith query.Note that when answering a query, lack of a color will not be considered as a color. Example 1:Input: limit = 4, queries = [[1,4],[2,5],[1,3],[3,4]]Output: [1,2,2,3]Explanation:After query 0, ball 1 has color 4.After query 1, ball 1 has color 4, and ball 2 has color 5.After query 2, ball 1 has color 3, and ball 2 has color 5.After query 3, ball 1 has color 3, ball 2 has color 5, and ball 3 has color 4.Example 2:Input: limit = 4, queries = [[0,1],[1,2],[2,2],[3,4],[4,5]]Output: [1,2,2,3,4]Explanation:After query 0, ball 0 has color 1.After query 1, ball 0 has color 1, and ball 1 has color 2.After query 2, ball 0 has color 1, and balls 1 and 2 have color 2.After query 3, ball 0 has color 1, balls 1 and 2 have color 2, and ball 3 has color 4.After query 4, ball 0 has color 1, balls 1 and 2 have color 2, ball 3 has color 4, and ball 4 has color 5. Constraints:1 <= limit <= 1091 <= n == queries.length <= 105queries[i].length == 20 <= queries[i][0] <= limit1 <= queries[i][1] <= 109
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