Cracking the Coding Interview, 4 Edition - 150 Programming Interview Questions and Solutions

Solutions to Chapter 19 | Moderate
19.7 You are given an array of integers (both positive and negative). Find the continuous
sequence with the largest sum. Return the sum.
EXAMPLE
SOLUTION
Input: {2, -8, 3, -2, 4, -10}
Output: 5 (i.e., {3, -2, 4} )
pg 89
A simple linear algorithm will work by keeping track of the current subsequence sum. If that
sum ever drops below zero, that subsequence will not contribute to the subsequent maximal
subsequence since it would reduce it by adding the negative sum.
1 public static int getMaxSum(int[] a) {
2 int maxsum = 0;
3 int sum = 0;
4 for (int i = 0; i < a.length; i++) {
5 sum += a[i];
6 if (maxsum < sum) {
7 maxsum = sum;
8 } else if (sum < 0) {
9 sum = 0;
10 }
11 }
12 return maxsum;
13 }
NOTE: If the array is all negative numbers, what is the correct behavior? Consider
this simple array {-3, -10, -5}. You could make a good argument that the
maximum sum is either: (A) -3 (if you assume the subsequence can’t be empty)
(B) 0 (the subsequence has length 0) or (C) MINIMUM_INT (essentially the error
case). We went with option B (max sum = 0), but there’s no “correct” answer. This
is a great thing to discuss with your interviewer to show how careful you are.
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Cracking the Coding Interview | Additional Review Problems