Cumulative algorithms

• A cumulative algorithm is one where you incrementally accumulate a larger value by repeatedly adding, multiplying, etc., and storing the result into a variable over and over.
• Key aspect of a cumulative algorithm: A loop, and a variable declared outside the loop whose value is modified inside the loop.
• Example: Cumulative algorithm to sum the numbers 1-100:

  int sum = 0;
  for (int i = 1; i <= 100; i++) {
      sum = sum + i;
  }
  System.out.println(sum);    // 5050
  

• Some of the following problems ask you to write cumulative algorithms.