CPMagical CP Library

Problem solution · Java

Maximize Value of Function in a Ball Passing Game

Maximize Value of Function in a Ball Passing Game: a Java solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Direct simulation
Source
walkccc LeetCode Solutions
Length
44 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Direct simulation

For Maximize Value of Function in a Ball Passing Game, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 44 lines of Java from the credited upstream file 2836.java.
  • The implementation visibly relies on sequence storage.
  • 5 loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeMaximize Value of Function in a Ball Passing Game · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public long getMaxFunctionValue(List<Integer> receiver, long k) {    final int n = receiver.size();    final int m = (int) (Math.log(k) / Math.log(2)) + 1;    long ans = 0;    // jump[i][j] := the the node you reach after jumping 2^j steps from i    int[][] jump = new int[n][m];    // sum[i][j] := the sum of the first 2^j nodes you reach when jumping from i    long[][] sum = new long[n][m];     for (int i = 0; i < n; ++i) {      jump[i][0] = receiver.get(i);      sum[i][0] = receiver.get(i);    }     // Calculate binary lifting.    for (int j = 1; j < m; ++j)      for (int i = 0; i < n; ++i) {        final int midNode = jump[i][j - 1];        //   the the node you reach after jumping 2^j steps from i        // = the node you reach after jumping 2^(j - 1) steps from i        // + the node you reach after jumping another 2^(j - 1) steps        jump[i][j] = jump[midNode][j - 1];        //   the sum of the first 2^j nodes you reach when jumping from i        // = the sum of the first 2^(j - 1) nodes you reach when jumping from i        // + the sum of another 2^(j - 1) nodes you reach        sum[i][j] = sum[i][j - 1] + sum[midNode][j - 1];      }     for (int i = 0; i < n; ++i) {      long currSum = i;      int currPos = i;      for (int j = 0; j < m; ++j)        if ((k >> j & 1) == 1) {          currSum += sum[currPos][j];          currPos = jump[currPos][j];        }      ans = Math.max(ans, currSum);    }     return ans;  }}

Keep practising

Did this explanation save you time? I'm a Grade 11 student building this free library to make difficult algorithms easier to understand.

Buy me a coffee ↗