title: Maximum Subarray Sum Using Prefix Sum
signature: class Solution {
  
      public Integer maximumSubarraySumUsingPrefixSum(ArrayList<Integer> arr, Integer n) {
test_code: import static java.util.Map.entry;  
  import java.util.*;
  import java.lang.*;
  // TESTING CODE 
  // ============================================
  class QuestionEvaluator {
      public static String validateSolution(ArrayList<Integer> arr, Integer n, Integer expected){
          try{
              Driver driver = new Driver();
              if (driver.run(arr, n,expected)){
                  return "PASSED";
              }
              return "FAILED";
              
          } catch (Exception exception_obj){
              return exception_obj.getClass().getSimpleName();
          }
  
      }
      public static void main(String[] args) {
          String result;
          result = validateSolution(new ArrayList<>(Arrays.asList(8, 9, 11, 17, 18, 19, 23, 24, 27, 30, 31, 31, 35, 44, 46, 47, 49, 51, 55, 58, 59, 61, 65, 67, 71, 71, 71, 71, 78, 78, 82, 91, 98)), 20, 633);
          System.out.println(String.format("%s%s","TEST-0...",result));    
      
          result = validateSolution(new ArrayList<>(Arrays.asList(-82, -28, -66, -52, -36, 36, -88, 52, -62, 46, 42, 26, -60, 18, -52, 38, 94, -68, 44, -94, 14, 36, -70)), 15, 114);
          System.out.println(String.format("%s%s","TEST-1...",result));    
      
          result = validateSolution(new ArrayList<>(Arrays.asList(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)), 19, 8);
          System.out.println(String.format("%s%s","TEST-2...",result));    
      
          result = validateSolution(new ArrayList<>(Arrays.asList(28, 36, 42, 42, 5, 52, 74, 86, 55, 82, 59, 81, 4, 90, 24, 34, 20, 99, 86, 25, 52, 48, 62, 5, 67, 83, 60, 72, 80, 73, 38, 55, 8, 70, 95)), 19, 999);
          System.out.println(String.format("%s%s","TEST-3...",result));    
      
          result = validateSolution(new ArrayList<>(Arrays.asList(-92, -52, -24, 36, 56)), 3, -24);
          System.out.println(String.format("%s%s","TEST-4...",result));    
      
          result = validateSolution(new ArrayList<>(Arrays.asList(0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0)), 13, 7);
          System.out.println(String.format("%s%s","TEST-5...",result));    
      
          result = validateSolution(new ArrayList<>(Arrays.asList(1, 1, 4, 4, 7, 7, 17, 18, 20, 26, 26, 32, 37, 38, 42, 44, 44, 46, 50, 53, 57, 58, 58, 60, 61, 61, 64, 74, 75, 77, 83, 83, 84, 84, 85, 87, 88, 90, 95, 96, 97, 98, 99, 99)), 25, 811);
          System.out.println(String.format("%s%s","TEST-6...",result));    
      
          result = validateSolution(new ArrayList<>(Arrays.asList(-86, 2, 26, 54, -16, 16, 48, 24, 50, -10, -32, -62, 48, -12, -66)), 13, 204);
          System.out.println(String.format("%s%s","TEST-7...",result));    
      
          result = validateSolution(new ArrayList<>(Arrays.asList(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)), 14, 0);
          System.out.println(String.format("%s%s","TEST-8...",result));    
      
          result = validateSolution(new ArrayList<>(Arrays.asList(58, 14, 79, 11, 31, 28, 61, 86, 25, 27, 75, 78, 32, 55, 86, 48, 15, 51, 6, 78, 23, 82, 16, 62, 35, 51, 91, 16, 79, 38, 97, 30, 23, 58, 95, 57, 82, 35, 57, 43, 22, 41, 58, 69, 25, 65, 13, 79)), 39, 1971);
          System.out.println(String.format("%s%s","TEST-9...",result));    
      
      }
  }
  
  class Driver{
      public boolean run(ArrayList<Integer> arr, Integer n, Integer expected){
  
          PLACEHOLDER_CLS_NAME sol = new PLACEHOLDER_CLS_NAME();
          return validateSolution(sol.PLACEHOLDER_FN_NAME(arr, n),expected);
      }
      
      public boolean validateSolution(Integer actual, Integer expected){
          return actual.equals(expected);
      }
  }
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
source_py: def maximum_subarray_sum_using_prefix_sum(arr, n):
      min_prefix_sum = 0
      res = (- math.inf)
      prefix_sum = []
      prefix_sum.append(arr[0])
      for i in range(1, n):
          prefix_sum.append((prefix_sum[(i - 1)] + arr[i]))
      for i in range(n):
          res = max(res, (prefix_sum[i] - min_prefix_sum))
          min_prefix_sum = min(min_prefix_sum, prefix_sum[i])
      return res
source_cpp: int maximum_subarray_sum_using_prefix_sum(vector<int> arr, int n) {
    int min_prefix_sum = 0;
    int res = numeric_limits < int > :: min ( );
    int prefix_sum [ n ];
    prefix_sum [ 0 ] = arr [ 0 ];
    for ( int i = 1;
    i < n;
    i ++ ) prefix_sum [ i ] = prefix_sum [ i - 1 ] + arr [ i ];
    for ( int i = 0;
    i < n;
    i ++ ) {
      res = max ( res, prefix_sum [ i ] - min_prefix_sum );
      min_prefix_sum = min ( min_prefix_sum, prefix_sum [ i ] );
    }
    return res;
  }