Problem Statement
Byteasar is playing a tabletop role-playing game with his friends. To determine the effectiveness of their heroes' actions the players use a rather unique set of dice. The i-th (0-based) die has dice[i] faces. They are numbered from 1 to dice[i] and the face number k shows k pips. When a die is cast, every face has equal probability to come out on top.
Byteasar's hero is now trying to unlock a safe containing treasure. In order to see if he succeeds, Byteasar has to guess a number M and then to roll all the dice. The safe will open if and only if M is precisely equal to the total number of pips on the topmost faces of all the dice. Obviously, the best strategy for Byteasar is to set M equal to the most probable outcome of the dice roll.
You are given the int[] dice. Return the value M such that the probability of the total number of pips being M is the highest possible. If there are multiple such values of M, return the smallest one.
Byteasar's hero is now trying to unlock a safe containing treasure. In order to see if he succeeds, Byteasar has to guess a number M and then to roll all the dice. The safe will open if and only if M is precisely equal to the total number of pips on the topmost faces of all the dice. Obviously, the best strategy for Byteasar is to set M equal to the most probable outcome of the dice roll.
You are given the int[] dice. Return the value M such that the probability of the total number of pips being M is the highest possible. If there are multiple such values of M, return the smallest one.
Definition
- Class:
- RollingDiceDivOne
- Method:
- mostLikely
- Parameters:
- int[]
- Returns:
- long
- Method signature:
- long mostLikely(int[] dice)
- (be sure your method is public)
Notes
- Please note that a die can have as few as one or two faces.
Constraints
- dice will contain between 1 and 50 elements, inclusive.
- Each element of dice will be between 1 and 109, inclusive.
Examples
{6, 6, 8}Returns: 11
The probability that the total number of pips on topmost faces of the three dice will be 11 is equal to 1/9.{10}Returns: 1
You should return the minimum possible answer.{2, 3, 4, 5}Returns: 9
{1, 10, 1}Returns: 3
{382828264, 942663792, 291832707, 887961277, 546603677, 545185615, 146267547, 6938117, 167567032, 84232402, 700781193, 452172304, 816532384, 951089120, 448136091, 280899512, 256093435, 39595226, 631504901, 154772240}Returns: 4366828428
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