Minimum Total Space Wasted With K Resizing Operations

Minimum Total Space Wasted With K Resizing Operations

What is this problem about?

The Minimum Total Space Wasted With K Resizing Operations problem gives you an array representing memory allocations over time, along with an integer K. You can resize the allocated memory at most K times. Between resizes, the allocated size must be at least the maximum allocation in that period, and any unused space is "wasted." Minimize total wasted space. This Minimum Total Space Wasted With K Resizing Operations coding problem is a partition DP problem.

Why is this asked in interviews?

Media.net asks this to test partition-based dynamic programming — where you split an array into at most K+1 segments and optimize each segment independently. It validates knowledge of the DP pattern for "divide array into K parts optimally." The array and dynamic programming interview pattern is cleanly demonstrated.

Algorithmic pattern used

Partition DP. Define dp[i][j] = minimum wasted space in the first i elements with j resizing operations. Precompute waste(l, r) = the wasted space in segment [l, r] = (r - l + 1) * max(arr[l..r]) - sum(arr[l..r]). For each i and j, try all possible last partition start points l: dp[i][j] = min(dp[l-1][j-1] + waste(l, i)). Use prefix max and prefix sum to compute waste(l, r) in O(1). Total time: O(n² * K).

Example explanation

Allocations: [10, 20, 10], K=1.

• 0 resizes: one segment [10,20,10]. Max=20, sum=40. Waste = 3*20-40 = 20.
• 1 resize: split into [10,20] and [10]. Waste = (220-30) + (110-10) = 10+0 = 10. Or split [10] and [20,10]: waste = 0 + (2*20-30) = 10. Minimum = 10.

Common mistakes candidates make

• Recomputing max and sum from scratch for each segment (O(n³) total) instead of using prefix arrays.
• Off-by-one in the partition DP — segments should be contiguous and non-overlapping.
• Not initializing dp[0][j] = 0 (empty prefix has no waste).
• Forgetting K resizes = K+1 segments.

Interview preparation tip

Partition DP into K parts follows a consistent template: precompute segment costs in O(1) using prefix arrays, then run DP over the number of segments allowed. This pattern appears in problems like "paint K houses," "split array largest sum," and "burst balloons." The waste(l, r) function here is the segment cost — precomputing it using prefix max and prefix sum is the critical optimization. Practice building these precomputed cost arrays separately before integrating them into DP.