Maximum Product Subarray (M)
题目
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
在给定数组中找到一个子数组，使其积最大。
思路
动态规划。sm[i]表示以nums[i]为结尾的子数组能得到的最小乘积，lg[i]表示以nums[i]为结尾的子数组能得到的最大乘积。可以得到递推式：
[sm[i]=min(nums[i], nums[i]*sm[i-1], nums[i]*lg[i-1])\
lg[i]=max(nums[i], nums[i]*sm[i-1], nums[i]*lg[i-1])
]
代码实现
Java
class Solution {
public int maxProduct(int[] nums) {
int ans = nums[0];
int[] sm = new int[nums.length];
int[] lg = new int[nums.length];
sm[0] = nums[0];
lg[0] = nums[0];
for (int i = 1; i < nums.length; i++) {
sm[i] = Math.min(nums[i], Math.min(nums[i] * sm[i - 1], nums[i] * lg[i - 1]));
lg[i] = Math.max(nums[i], Math.max(nums[i] * sm[i - 1], nums[i] * lg[i - 1]));
ans = Math.max(ans, lg[i]);
}
return ans;
}
}