# Share my simple Java code with explanation

• /*
define max[i]/min[i] as the max/min product of subarray ENDING WITH a[i].
max[i] = max(max[i-1]*a[i], min[i-1]*a[i], a[i])
min[i] = min(max[i-1]*a[i], min[i-1]*a[i], a[i])
we need to find max(max[i]), for 0 <= i < a.length
*/
public class Solution {
public int maxProduct(int[] nums) {
if (nums == null || nums.length == 0) { return 0; }
int max = nums[0];
int prevMin = nums[0], prevMax = nums[0];
for (int i = 1; i < nums.length; ++i) {
int prod1 = prevMin * nums[i];
int prod2 = prevMax * nums[i];
prevMin = Math.min(nums[i], Math.min(prod1, prod2));
prevMax = Math.max(nums[i], Math.max(prod1, prod2));
max = Math.max(prevMax, max);
}
return max;
}
}

• Could you share an explanation? Why does this work?

• /* define max[i]/min[i] as the max/min product of subarray ENDING WITH a[i]. max[i] = max(max[i-1]*a[i], min[i-1]*a[i], a[i]) min[i] = min(max[i-1]*a[i], min[i-1]*a[i], a[i]) we need to find max(max[i]), for 0 <= i < a.length */

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