You are given a 0-indexed integer array receiver of length n and an integer k.
There are n players having a unique id in the range [0, n - 1] who will play a ball passing game, and receiver[i] is the id of the player who receives passes from the player with id i. Players can pass to themselves, i.e. receiver[i] may be equal to i.
You must choose one of the n players as the starting player for the game, and the ball will be passed exactly k times starting from the chosen player.
For a chosen starting player having id x, we define a function f(x) that denotes the sum of x and the ids of all players who receive the ball during the k passes, including repetitions. In other words, f(x) = x + receiver[x] + receiver[receiver[x]] + ... + receiver(k)[x].
Your task is to choose a starting player having id x that maximizes the value of f(x).
Return an integer denoting the maximum value of the function.
\n\nNote: receiver may contain duplicates.
\n
Example 1:
\n\n| Pass Number | \n\t\t\tSender ID | \n\t\t\tReceiver ID | \n\t\t\tx + Receiver IDs | \n\t\t
|---|---|---|---|
| \n\t\t\t | \n\t\t\t | \n\t\t\t | 2 | \n\t\t
| 1 | \n\t\t\t2 | \n\t\t\t1 | \n\t\t\t3 | \n\t\t
| 2 | \n\t\t\t1 | \n\t\t\t0 | \n\t\t\t3 | \n\t\t
| 3 | \n\t\t\t0 | \n\t\t\t2 | \n\t\t\t5 | \n\t\t
| 4 | \n\t\t\t2 | \n\t\t\t1 | \n\t\t\t6 | \n\t\t
\nInput: receiver = [2,0,1], k = 4\nOutput: 6\nExplanation: The table above shows a simulation of the game starting with the player having id x = 2. \nFrom the table, f(2) is equal to 6. \nIt can be shown that 6 is the maximum achievable value of the function. \nHence, the output is 6. \n\n\n
Example 2:
\n\n| Pass Number | \n\t\t\tSender ID | \n\t\t\tReceiver ID | \n\t\t\tx + Receiver IDs | \n\t\t
|---|---|---|---|
| \n\t\t\t | \n\t\t\t | \n\t\t\t | 4 | \n\t\t
| 1 | \n\t\t\t4 | \n\t\t\t3 | \n\t\t\t7 | \n\t\t
| 2 | \n\t\t\t3 | \n\t\t\t2 | \n\t\t\t9 | \n\t\t
| 3 | \n\t\t\t2 | \n\t\t\t1 | \n\t\t\t10 | \n\t\t
\nInput: receiver = [1,1,1,2,3], k = 3\nOutput: 10\nExplanation: The table above shows a simulation of the game starting with the player having id x = 4. \nFrom the table, f(4) is equal to 10. \nIt can be shown that 10 is the maximum achievable value of the function. \nHence, the output is 10. \n\n\n
\n
Constraints:
\n\n1 <= receiver.length == n <= 1050 <= receiver[i] <= n - 11 <= k <= 1010x and for every i in the range [0, ceil(log2k)], we can determine the last receiver's id and compute the sum of player ids who receive the ball after 2i passes, starting from x.last_receiver[x][i] = the last receiver's id after 2i passes, and sum[x][i] = the sum of player ids who receive the ball after 2i passes. For all x in the range [0, n - 1], last_receiver[x][0] = receiver[x], and sum[x][0] = receiver[x].i in range [1, ceil(log2k)], last_receiver[x][i] = last_receiver[last_receiver[x][i - 1]][i - 1] and sum[x][i] = sum[x][i - 1] + sum[last_receiver[x][i - 1]][i - 1], for all x in the range [0, n - 1].x, we can now go through the powers of 2 in the binary representation of k and make jumps corresponding to each power, using the pre-computed values, to compute f(x).f(x) from each player id.Compiled with clang 11 using the latest C++ 20 standard.
Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
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