|
| 1 | +--- |
| 2 | +id: maximum-product-subarray |
| 3 | +title: Maximum Product Subarray |
| 4 | +sidebar_label: 0152 Maximum Product Subarray |
| 5 | +tags: |
| 6 | + - Array |
| 7 | + - Dynamic Programming |
| 8 | + - LeetCode |
| 9 | + - Python |
| 10 | + - Java |
| 11 | + - C++ |
| 12 | +description: "This is a solution to the Maximum Product Subarray problem on LeetCode." |
| 13 | +--- |
| 14 | + |
| 15 | +## Problem Description |
| 16 | + |
| 17 | +Given an integer array nums, find a subarray that has the largest product, and return the product. |
| 18 | + |
| 19 | +The test cases are generated so that the answer will fit in a 32-bit integer. |
| 20 | + |
| 21 | +### Examples |
| 22 | + |
| 23 | +**Example 1:** |
| 24 | + |
| 25 | +``` |
| 26 | +Input: nums = [2,3,-2,4] |
| 27 | +Output: 6 |
| 28 | +Explanation: [2,3] has the largest product 6. |
| 29 | +``` |
| 30 | + |
| 31 | +**Example 2:** |
| 32 | + |
| 33 | +``` |
| 34 | +Input: nums = [-2,0,-1] |
| 35 | +Output: 0 |
| 36 | +Explanation: The result cannot be 2, because [-2,-1] is not a subarray. |
| 37 | +``` |
| 38 | + |
| 39 | +### Constraints |
| 40 | + |
| 41 | +- $1 <= nums.length <= 2 * 10**4$ |
| 42 | +- $10 <= nums[i] <= 10$ |
| 43 | +- $The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.$ |
| 44 | + |
| 45 | + |
| 46 | +#### Code in Different Languages |
| 47 | + |
| 48 | +<Tabs> |
| 49 | + <TabItem value="Python" label="Python"> |
| 50 | + <SolutionAuthor name="@mahek0620"/> |
| 51 | + ```python |
| 52 | + class Solution(object): |
| 53 | + def maxProduct(self, nums): |
| 54 | + """ |
| 55 | + :type nums: List[int] |
| 56 | + :rtype: int |
| 57 | + """ |
| 58 | + if not nums: |
| 59 | + return 0 |
| 60 | + |
| 61 | + max_prod = nums[0] |
| 62 | + min_prod = nums[0] |
| 63 | + result = max_prod |
| 64 | + |
| 65 | + for num in nums[1:]: |
| 66 | + if num < 0: |
| 67 | + max_prod, min_prod = min_prod, max_prod |
| 68 | + |
| 69 | + max_prod = max(num, max_prod * num) |
| 70 | + min_prod = min(num, min_prod * num) |
| 71 | + |
| 72 | + result = max(result, max_prod) |
| 73 | + |
| 74 | + return result |
| 75 | + |
| 76 | + |
| 77 | + |
| 78 | + ``` |
| 79 | + |
| 80 | + </TabItem> |
| 81 | + <TabItem value="Java" label="Java"> |
| 82 | + <SolutionAuthor name="@mahek0620"/> |
| 83 | + ```java |
| 84 | + class Solution { |
| 85 | + public int maxProduct(int[] nums) { |
| 86 | + if (nums.length == 0) |
| 87 | + return 0; |
| 88 | + |
| 89 | + int maxProd = nums[0]; |
| 90 | + int minProd = nums[0]; |
| 91 | + int result = maxProd; |
| 92 | + |
| 93 | + for (int i = 1; i < nums.length; ++i) { |
| 94 | + if (nums[i] < 0) { |
| 95 | + int temp = maxProd; |
| 96 | + maxProd = minProd; |
| 97 | + minProd = temp; |
| 98 | + } |
| 99 | + |
| 100 | + maxProd = Math.max(nums[i], maxProd * nums[i]); |
| 101 | + minProd = Math.min(nums[i], minProd * nums[i]); |
| 102 | + |
| 103 | + result = Math.max(result, maxProd); |
| 104 | + } |
| 105 | + |
| 106 | + return result; |
| 107 | + } |
| 108 | +} |
| 109 | + |
| 110 | + |
| 111 | + ``` |
| 112 | + |
| 113 | + </TabItem> |
| 114 | + <TabItem value="C++" label="C++"> |
| 115 | + <SolutionAuthor name="@mahek0620"/> |
| 116 | + ```cpp |
| 117 | + #include <vector> |
| 118 | +#include <algorithm> |
| 119 | + |
| 120 | +class Solution { |
| 121 | +public: |
| 122 | + int maxProduct(vector<int>& nums) { |
| 123 | + if (nums.empty()) |
| 124 | + return 0; |
| 125 | + |
| 126 | + int max_prod = nums[0]; |
| 127 | + int min_prod = nums[0]; |
| 128 | + int result = max_prod; |
| 129 | + |
| 130 | + for (int i = 1; i < nums.size(); ++i) { |
| 131 | + if (nums[i] < 0) |
| 132 | + std::swap(max_prod, min_prod); |
| 133 | + |
| 134 | + max_prod = std::max(nums[i], max_prod * nums[i]); |
| 135 | + min_prod = std::min(nums[i], min_prod * nums[i]); |
| 136 | + |
| 137 | + result = std::max(result, max_prod); |
| 138 | + } |
| 139 | + |
| 140 | + return result; |
| 141 | + } |
| 142 | +}; |
| 143 | + |
| 144 | + |
| 145 | + ``` |
| 146 | + |
| 147 | + </TabItem> |
| 148 | +</Tabs> |
| 149 | + |
| 150 | + |
| 151 | +</TabItem> |
| 152 | + |
| 153 | +</Tabs> |
| 154 | + |
| 155 | +## References |
| 156 | + |
| 157 | +- **LeetCode Problem**: [Maximum Product Subarray](https://leetcode.com/problems/maximum-product-subarray/) |
| 158 | + |
| 159 | +- **Solution Link**: [LeetCode Solution](https://leetcode.com/problems/maximum-product-subarray/solution/) |
| 160 | + |
| 161 | +- **Authors GeeksforGeeks Profile:** [Mahek Patel](https://leetcode.com/u/mahekrpatel611/) |
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