Maximum Product Subarray


Problem Statement :


Given an integer array nums, find a 
subarray
 that has the largest product, and return the product.

The test cases are generated so that the answer will fit in a 32-bit integer.

 

Example 1:

Input: nums = [2,3,-2,4]
Output: 6
Explanation: [2,3] has the largest product 6.
Example 2:

Input: nums = [-2,0,-1]
Output: 0
Explanation: The result cannot be 2, because [-2,-1] is not a subarray.
 

Constraints:

1 <= nums.length <= 2 * 104
-10 <= nums[i] <= 10
The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.



Solution :



title-img


                            Solution in C :

#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define MIN(a, b) ((a) < (b) ? (a) : (b))

int maxProduct(int* nums, int N)
{
    int *pos = calloc(N, sizeof(int));
    int *neg = calloc(N, sizeof(int));

    int i, best = INT_MIN;

    if (N == 1)
        return nums[0];
    
    for (i = 0; i < N; i++) {
        int n = nums[i];
        if (i == 0) {
            if (n < 0) {
                neg[0] = n;
                pos[0] = 0;
            } else {
                neg[0] = 0;
                pos[0] = n;
            }
        } else {
            if (n < 0) {
                neg[i] = MIN(pos[i - 1] * n, n);
                pos[i] = neg[i - 1] * n;
            } else {
                neg[i] = neg[i - 1] * n;
                pos[i] = MAX(pos[i - 1] * n, n);
            }
        }
        best = MAX(best, pos[i]);
    }
    
    return best;
}
                        


                        Solution in C++ :

class Solution {
public:
    int maxProduct(vector<int>& nums) {
        int n = nums.size();

        int maxProduct = INT_MIN;

        //applying Kadane's algo from Left to Right
        
        int currProd_Left_to_Right = 1;

        for(int i=0; i<n; i++){
            currProd_Left_to_Right*=nums[i];

            maxProduct = max(maxProduct, currProd_Left_to_Right);
            
             if(currProd_Left_to_Right == 0){
                currProd_Left_to_Right = 1;
            }

        }

        //applying Kadane's algo from Right to Left

        int currProd_Right_to_Left = 1;

        for(int i=n-1; i>=0; i--){
            currProd_Right_to_Left*=nums[i];
            
            maxProduct = max(maxProduct, currProd_Right_to_Left);
            
            if(currProd_Right_to_Left == 0){
                currProd_Right_to_Left = 1;
            }

        }

        return maxProduct;
    }
};
                    


                        Solution in Java :

class Solution {
    public int maxProduct(int[] nums) {
            
        int n = nums.length;

        int maxProduct = Integer.MIN_VALUE;

        //applying Kadane's algo from Left to Right
        
        int currProd_Left_to_Right = 1;

        for(int i=0; i<n; i++){
            currProd_Left_to_Right*=nums[i];

            maxProduct = Math.max(maxProduct, currProd_Left_to_Right);
            
             if(currProd_Left_to_Right == 0){
                currProd_Left_to_Right = 1;
            }

        }

        //applying Kadane's algo from Right to Left

        int currProd_Right_to_Left = 1;

        for(int i=n-1; i>=0; i--){
            currProd_Right_to_Left*=nums[i];
            
            maxProduct = Math.max(maxProduct, currProd_Right_to_Left);
            
            if(currProd_Right_to_Left == 0){
                currProd_Right_to_Left = 1;
            }

        }

        return maxProduct;
    }
}
                    


                        Solution in Python : 
                            
class Solution:
    def maxProduct(self, nums: List[int]) -> int:
        n = len(nums)

        maxProduct = float('-inf')

        #applying Kadane's algo from Left to Right
        
        currProd_Left_to_Right = 1

        for i in range(0,n):
            currProd_Left_to_Right*=nums[i]

            maxProduct = max(maxProduct, currProd_Left_to_Right)
            
            if currProd_Left_to_Right == 0:
                currProd_Left_to_Right = 1
            

        

        #applying Kadane's algo from Right to Left

        currProd_Right_to_Left = 1

        for i in range(n-1,-1,-1):
            currProd_Right_to_Left*=nums[i]
            
            maxProduct = max(maxProduct, currProd_Right_to_Left)
            
            if currProd_Right_to_Left == 0:
                currProd_Right_to_Left = 1
            

    
        return maxProduct
                    


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