I want to find a nonempty, contiguous subarray for a given input array of integers, that can have duplicate values. I tried the divide and conquer method to find the maximum consecutive subarray of an array, which returns a different result as expected. Please find the code below.
private static int maxSumRec(int[] a, int low, int high) {
int leftSum = 0, rightSum = 0;
int sum = 0;
if (low == high) { // Base case
return a[low];
}
int mid = (low + high) >> 1; // (low + high) / 2
int maxLeftSum = maxSumRec(a, low, mid);
int maxRightSum = maxSumRec(a, mid + 1, high);
//max-crossing-subarray
for (int i = mid; i >= low; i--) {
sum += a[i];
if (sum > leftSum) {
leftSum = sum;
}
}
sum = 0;
for (int i = mid + 1; i <= high; i++) {
sum += a[i];
if (sum > rightSum) {
rightSum = sum;
}
}
return max3(maxLeftSum, maxRightSum, (leftSum + rightSum));
}
private static int max3(int a, int b, int c) {
return a > b ? (a > c ? a : c) : (b > c ? b : c);
}
public static void main(String[] args) {
//INPUT
int a[] = {
-5, 71, 23, 41, 34, 1, 3, 6, 2, 91, 312, 42, 31, 67, 12, 10, 18, 56, 90, 21, 45, 47, 89, 1999999990,
78, -7, 76, 75, 74, 73, 72, 80, 24, 25, 61, 69, 84, 0, -1, 145, 1902, 200, 199, 198, 197, 196, 195, 194,
78, 77, 76, 75, 74, 73, 72, 80, 24, 25, 61, 69, 84, 0, -1, 145, 1902, 200, 199, 198, 197, 196, 195, 194,
5, 71, 23, 41, 34, 1, 3, 6, 2, 91, 312, 42, 31, 67, 12, 10, 18, 56, 90, 21, 45, 47, 89, 1999999990
};
int maxSum = maxSumRec(a, 0, a.length - 1);
System.out.println("Max sum is " + maxSum);
}
This code returns the result as 2000005400. The non recursive version of MCS returns a different result i.e. 2000010721 and its found from {1-94}. I'm unable to figure out the reason. Please let me know if there's a bug in the code.
The sum from 1 to 95 (it's :4000010711 ) is actually greater than the one from 1 to 94.
Your ints
are too long.
You need to use long
to get the right result.
Note:
int are between -2147483648 and 2147483647
int test=2147483647;
System.out.println(test);
System.out.println(test+1);
you will get:
2147483647
-2147483648
Try this :
public class Sample5 {
private static long maxSumRec(int[] a, int low, int high) {
long leftSum = 0, rightSum = 0;
long sum = 0;
if (low == high) { // Base case
return a[low];
}
int mid = (low + high)/2; // (low + high) / 2
long maxLeftSum = maxSumRec(a, low, mid);
long maxRightSum = maxSumRec(a, mid + 1, high);
//max-crossing-subarray
for (int i = mid; i >= low; i--) {
sum += a[i];
if (sum > leftSum) {
leftSum = sum;
}
}
sum = 0;
for (int i = mid + 1; i <= high; i++) {
sum += a[i];
if (sum > rightSum) {
rightSum = sum;
}
}
System.out.println("final left sum "+leftSum);
System.out.println("final right sum "+rightSum);
System.out.println("leftSum+rightSUM:"+(leftSum + rightSum));
return max3(maxLeftSum, maxRightSum, (leftSum + rightSum));
}
private static long max3(long a, long b, long c) {
return a > b ? (a > c ? a : c) : (b > c ? b : c);
}
private static int sum(int[] a,int i,int j){
int r=0;
for(int k=i;k<=j;k++){
r+=a[k];
}
return r;
}
public static void main(String[] args) {
//INPUT
int a[] = {
-5, 71, 23, 41, 34, 1, 3, 6, 2, 91, 312, 42, 31, 67, 12, 10, 18, 56, 90, 21, 45, 47, 89, 1999999990,
78, -7, 76, 75, 74, 73, 72, 80, 24, 25, 61, 69, 84, 0, -1, 145, 1902, 200, 199, 198, 197, 196, 195, 194,
78, 77, 76, 75, 74, 73, 72, 80, 24, 25, 61, 69, 84, 0, -1, 145, 1902, 200, 199, 198, 197, 196, 195, 194,
5, 71, 23, 41, 34, 1, 3, 6, 2, 91, 312, 42, 31, 67, 12, 10, 18, 56, 90, 21, 45, 47, 89, 1999999990
};
long maxSum = maxSumRec(a, 0, a.length-1);
System.out.println("Max sum is " + maxSum);
//WITH INTS
System.out.println("with ints, the sum 1 to 94 is " + sum(a,1,94));
System.out.println("with ints, the sum 1 to 95 is " + sum(a,1,95));
}
}
You will get :
final left sum 2000005311
final right sum 2000005400
leftSum+rightSUM:4000010711
Max sum is 4000010711
with ints, the sum 1 to 94 is 2000010721
with ints, the sum 1 to 95 is -294956585