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leetcode 152. Maximum Product Subarray

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.

使用动态规划求解:

  新建三个数组suffix_min[n], suffix_max[n], global_max[n]. 分别表示包含最后元素的最小乘积,包含最后元素的最大乘积,和全局最大乘积。

假设已知suffix_min[i-1], suffix_max[i-1],

那么suffix_max[i]是suffix_max[i-1] * A[i], suffix_min[i-1]*A[i], A[i]三者中的最大值,suffix_min[i]是三者中的最小值。

而global_max[i]则是global_max[i-1]和suffix_max[i]中的最大值。

 1 int maxProduct(int A[], int n)  2     { 3         if (n <= 0) 4             return n; 5         int *suffix_max = new int[n]; 6         int *suffix_min = new int[n]; 7         int *global_max = new int[n]; 8         int temp_min, temp_max, max_product; 9         10         suffix_max[0] = A[0];11         suffix_min[0] = A[0];12         global_max[0] = A[0];13         for (int i = 1; i < n; i++)14         {15             temp_min = A[i] * suffix_min[i - 1];16             temp_max = A[i] * suffix_max[i - 1];17             suffix_min[i] = min(A[i], min(temp_min, temp_max));18             suffix_max[i] = max(A[i], max(temp_min, temp_max));19             global_max[i] = max(suffix_max[i], global_max[i - 1]);20         }21         max_product = global_max[n - 1];22         delete[] suffix_max;23         delete[] suffix_min;24         delete[] global_max;25         26         return max_product;27     }

对于本题,只需要求出global_max[n]即可,实际上不需要记录全部global_max[0, ..., n -1]

 1  int maxProduct(int A[], int n)  2     { 3         if (n <= 0) 4             return n; 5         int temp_min, temp_max; 6          7         int suffix_max = A[0]; 8         int suffix_min = A[0]; 9         int global_max = A[0];10         for (int i = 1; i < n; i++)11         {12             temp_min = A[i] * suffix_min;13             temp_max = A[i] * suffix_max;14             suffix_min = min(A[i], min(temp_min, temp_max));15             suffix_max = max(A[i], max(temp_min, temp_max));16             global_max = max(suffix_max, global_max);17         }18         19         return global_max;20     }

 

leetcode 152. Maximum Product Subarray