← Back to DSA Animator
Maximum Product Subarray LC #152 Medium DP · Min/Max Track
Problem

Given an integer array nums, find a subarray with the largest product and return the product. Negative × negative = positive, so track both max and min.

Example 1
Input: [2,3,-2,4]
Output: 6
Example 2
Input: [-2,3,-4]
Output: 24
maxP=max(n, maxP*n, minP*n), minP=min(n, maxP*n, minP*n).
Try Examples
Custom:
Approach
Track maxP and minP — negative × negative = positive
maxP = max(n, maxP*n, minP*n), minP = min(n, maxP*n, minP*n). res = max(res, maxP).
Array & Candidates
Load an example to begin.
Variables
i / n
—
maxP
—
minP
—
ans
—
Step Logic
Press ▶ Play or Next Step to begin.
📊
Ready
0 / 0
Select an example and press Play.
Algorithm
1
Track maxP, minP ending at current index
2
minP*n can become max when n is negative
3
maxP = max(n, maxP*n, minP*n)
4
minP = min(n, maxP*n, minP*n), res = max(res, maxP)
Time
O(n)
Space
O(1)
Why This Works

Unlike sum, a negative product can flip to max when multiplied by another negative. Track both max and min product ending here. At each step, new max = n, old max×n, or old min×n.