feat : maximum subarray product

Author: ekgns33

maximum-product-subarray/ekgns33.java

@@ -0,0 +1,45 @@
+class Solution {
+  public int maxProduct(int[] nums) {
+    int n = nums.length;
+    int[][] product = new int[2][n];
+    product[0][0] = nums[0];
+    product[1][0] = nums[0];
+    int max = nums[0];
+    for(int i = 1; i < n; i++) {
+      product[0][i] = Math.max(product[0][i-1]*nums[i], Math.max(nums[i], nums[i] * product[1][i-1]));
+      product[1][i] = Math.min(product[0][i-1]*nums[i], Math.min(nums[i], nums[i] * product[1][i-1]));
+      max =Math.max(max, product[0][i]);
+    }
+    return max;
+  }
+}
+/**
+
+
+ brute force :
+ nested for loop
+ tc : O(n^2)
+ sc : O(1)
+
+ better sol :
+ maintain min and max
+ tc : O(n)
+ sc : O(n)
+
+ compare with prev Min * cur, prevMax * cur, cur
+ we have to keep track of minimum value that can lead to maximum value
+ when there are negative values later.
+
+ 2 3  -2 4
+ 2 6  -2   4
+ 2 2 -12 -48
+
+ -2  0 -1
+ -2  0  0
+ -2  0 -1
+
+ 2 3 -2  5     7   -100
+ 2 6 -2  5    35   210000
+ 2 3 -6 -30 -210.    -35
+
+ */