Space Optimization
PlaygroundsHardCompare memory footprints of original 2D DP grids vs optimized 1D DP rows.
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Memory Reduction Audit
Original 2D DP Space
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O(N * Target)
Optimized 1D DP Space
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O(Target)
Time Complexity
O(N * target) time
Space Complexity
O(target) optimized space
Conceptual Overview
Space Optimization reduces the memory footprint of dynamic programming algorithms by discarding intermediate subproblems cells that are no longer needed to compute subsequent states.
Recurrence Relation
dp[j] = dp[j] || dp[j - val] updated in reverse order j = target down to val
State Transitions
Overwrites the current cell in-place. Processing backwards ensures we query cells from the previous iteration's row state, not the current row state.
Source: CP-Algorithms dynamic programming reference