[leetcode]152. Maximum Product Subarray最大乘积子数组

Given an integer array nums, find the contiguous subarray within an array (containing at least one number) which has the largest product.

Example 1:

Input: [2,3,-2,4]

Output: 6

Explanation: [2,3] has the largest product 6.

Example 2:

Input: [-2,0,-1]

Output: 0

Explanation: The result cannot be 2, because [-2,-1] is not a subarray.

题意：

求最大乘积子数组

思路：

1. the sign(I mean,  if it is positive or negative) influence the product value

2. when iterating each item, it can be postive or negative

3. we use max[i] to stand for max product of ith item

4. we use min[i] to stand for min product of ith item

5. so function rule:

max[i]:    max(max[i -1]*nums[i], min[i-1]* nums[i], nums[i])

min[i]:     min(max[i -1]*nums[i], min[i-1]* nums[i], nums[i])

code

  public int maxProduct(int[] nums) {

         // initialize

         int[] max = new int[nums.length];

         int[] min = new int[nums.length];

         max[0] = nums[0];

         min[0] = nums[0];

         int result = nums[0];

         // max[i]: max product of ith item

         // min[i]: min product of ith item

         for(int i = 1; i < nums.length; i++){

             max[i] = Math.max(Math.max(max[i-1] * nums[i] , min[i-1]*nums[i]), nums[i]);

             min[i] = Math.min(Math.min(max[i-1] * nums[i] , min[i-1]*nums[i]), nums[i]);

             result = Math.max(result, max[i]);

         }

         return result;

     }