Maximum Product Subarray
描述
Find the contiguous subarray within an array (containing at least one number) which has the largest product.
For example, given the array [2,3,-2,4],
the contiguous subarray [2,3] has the largest product = 6.
分析
这题跟“最大连续子序列和”非常类似，只不过变成了“最大连续子序列积”，所以解决思路也很类似。
仅仅有一个小细节需要注意，就是负负得正，两个负数的乘积是正数，因此我们不仅要跟踪最大值，还要跟踪最小值。
动规
- Java
- C++
// maximum-product-subarray
// 时间复杂度O(n)，空间复杂度O(1)
public class Solution {
public int maxProduct(int[] nums) {
int maxLocal = nums[0];
int minLocal = nums[0];
int global = nums[0];
for(int i = 1; i < nums.length; i++){
int temp = maxLocal;
maxLocal = Math.max(Math.max(nums[i] * maxLocal, nums[i]), nums[i] * minLocal);
minLocal = Math.min(Math.min(nums[i] * temp, nums[i]), nums[i] * minLocal);
global = Math.max(global, maxLocal);
}
return global;
}
}
// maximum-product-subarray
// 时间复杂度O(n)，空间复杂度O(1)
class Solution {
public:
int maxProduct(vector<int>& nums) {
int maxLocal = nums[0];
int minLocal = nums[0];
int global = nums[0];
for(int i = 1; i < nums.size(); i++){
int temp = maxLocal;
maxLocal = max(max(nums[i] * maxLocal, nums[i]), nums[i] * minLocal);
minLocal = min(min(nums[i] * temp, nums[i]), nums[i] * minLocal);
global = max(global, maxLocal);
}
return global;
}
};