▸case-01 I have a dynamic programming solution in C++ for a cost-minimization problem: `for(int i=1; i<=n; i++) for(int j=0; j<i; j++) dp[i] = min(dp[i], dp[j] + (x[i]-x[j])^2)`. It currently runs in O(n^2) time. Could you run an optimization on this code? Please output the modified code, identify which optimization strategy was used, state the resulting complexity, explain the transformation, and include a boolean success status. | fail→pass | 17,144 | 8,081 | -53% | 1 | 1 | 0% | 3,733 | 2,350 | -37% | 0 | 0 | — |
▸case-02 Here is a 2D interval dynamic programming snippet in Python that partitions an array into K segments with an O(K * N^2) loop transition. I need to apply a divide-and-conquer speedup to it. Please return a response containing the updated code, the optimization applied, the new time complexity, an explanation of the changes, and whether the process succeeded. | fail→pass | 12,697 | 10,697 | -16% | 1 | 1 | 0% | 2,998 | 2,910 | -3% | 0 | 0 | — |
▸case-03 My current DP code uses a large 2D table `dp[i][j]` where transitions only depend on `dp[i-1]`, consuming O(N * M) memory. Can you perform a space optimization on this snippet? Provide the optimized source code, name the technique used, report the improved space complexity, give a quick explanation, and return a success indicator. | fail→pass | 11,205 | 6,913 | -38% | 1 | 1 | 0% | 2,017 | 1,821 | -10% | 0 | 0 | — |
▸case-04 I need to optimize a linear recurrence DP calculation for F(n) = F(n-1) + 2*F(n-2) to compute the N-th term in logarithmic time O(log N) rather than O(N). Can you optimize this transition loop? Format the response as a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | fail→fail | 8,504 | 7,607 | -11% | 1 | 1 | 0% | 1,934 | 2,250 | +16% | 0 | 0 | — |
▸case-05 I have a 0/1 Knapsack dynamic programming solver with fractional item weights and capacities. I want to optimize the transition to run in strict O(N log N) polynomial time instead of O(N * W). Provide a JSON response with fields success, optimizedCode, optimizationApplied, newComplexity, and explanation. | fail→fail | 18,086 | 9,385 | -48% | 1 | 1 | 0% | 3,390 | 2,222 | -34% | 0 | 0 | — |
▸case-06 I have a Bellman-Ford shortest path algorithm in C++ running in O(V * E) time for general graphs with negative edge weights. Can you apply dynamic programming convex hull trick or Knuth optimization to guarantee O(V log V) time? Return a JSON object with fields success, optimizedCode, optimizationApplied, newComplexity, and explanation. | fail→fail | 11,046 | 9,447 | -14% | 1 | 1 | 0% | 1,809 | 2,129 | +18% | 0 | 0 | — |
▸case-07 I have a dynamic programming formulation dp[i] = min_{j < i} (dp[j] + m[j]*x[i] + c[j]) where m[j] is decreasing. I want to optimize this from O(N^2) to O(N log N) or O(N). Please format your response as a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 11,533 | 11,250 | -2% | 1 | 1 | 0% | 2,486 | 2,907 | +17% | 0 | 0 | — |
▸case-08 I am solving a range partitioning problem where dp[i][j] = min_{k < j} (dp[i-1][k] + cost(k+1, j)) and the optimal splitting point satisfies monotonicity opt[i][j] <= opt[i][j+1]. Please optimize this O(K * N^2) transition. Provide your output as a JSON object with keys success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 20,309 | 12,872 | -37% | 1 | 1 | 0% | 3,553 | 2,781 | -22% | 0 | 0 | — |
▸case-09 My interval dynamic programming algorithm solves optimal binary search trees using dp[i][j] = min_{i <= k < j} (dp[i][k] + dp[k+1][j]) + w(i,j) in O(N^3) time. The cost function satisfies the quadrangle inequality. Return a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 11,440 | 7,003 | -39% | 1 | 1 | 0% | 2,534 | 2,040 | -19% | 0 | 0 | — |
▸case-10 I have a maximum sliding window DP recurrence: dp[i] = max_{i-k <= j < i} (dp[j]) + val[i]. The current implementation scans a loop of length K taking O(N * K) time. Convert this to O(N) using a deque. Format the response as a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→fail | 7,361 | 9,371 | +27% | 1 | 1 | 0% | 1,633 | 2,509 | +54% | 0 | 0 | — |
▸case-11 I need to optimize a DP problem that requires selecting exactly K items out of N, where the cost function as a function of K is strictly convex. The naive state is dp[i][k] taking O(N * K) time. I want to reduce it to O(N log C) by removing the K dimension using Lagrange multiplier penalty. Format output as JSON with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 13,548 | 8,673 | -36% | 1 | 1 | 0% | 2,738 | 2,357 | -14% | 0 | 0 | — |
▸case-12 I have a 2D grid state dp[i][j] where dp[i][j] only accesses dp[i-1][j] and dp[i-1][j-1]. The grid size is N=100000, M=1000. It uses O(N * M) memory. Optimize the space complexity to O(M). Output a JSON object with fields success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 8,883 | 8,472 | -5% | 1 | 1 | 0% | 1,609 | 2,341 | +45% | 0 | 0 | — |
▸case-13 I have a DP algorithm operating on subsets of size N=20. Currently states are tracked using arrays of booleans or hash sets, which is slow and memory-heavy. Compress the set representation into an integer state. Return a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 10,867 | 9,107 | -16% | 1 | 1 | 0% | 1,719 | 2,343 | +36% | 0 | 0 | — |
▸case-14 Given a request with dpCode for a 1D DP array and optimizationType set to space, execute the optimization and format your response as a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 8,068 | 4,780 | -41% | 1 | 1 | 0% | 1,682 | 1,533 | -9% | 0 | 0 | — |
▸case-15 I am passing a DP transition with a linear combination of state variables and query variables: dp[i] = min_{j < i} (dp[j] + A[j]*B[i]). The request sets optimizationType to auto. Determine the appropriate technique and format the result as a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 11,268 | 7,739 | -31% | 1 | 1 | 0% | 2,423 | 2,203 | -9% | 0 | 0 | — |
▸case-16 I am submitting a DP recurrence dp[i] = A[i] + max_{i-L <= j <= i-1} (dp[j]) with optimizationType set to auto. Identify the best optimization technique and return a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 8,384 | 7,013 | -16% | 1 | 1 | 0% | 1,864 | 2,018 | +8% | 0 | 0 | — |
▸case-17 Consider the Edit Distance DP transition dp[i][j] = min(dp[i-1][j]+1, dp[i][j-1]+1, dp[i-1][j-1] + cost). Currently it uses an N x M matrix. Optimize the memory layout so it only keeps two rows. Return a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | fail→pass | 7,929 | 6,847 | -14% | 1 | 1 | 0% | 1,720 | 2,080 | +21% | 0 | 0 | — |
▸case-18 In matrix chain multiplication or stone merging DP, the cost function satisfies w(i, j) + w(i', j') <= w(i', j) + w(i, j') for i <= i' <= j <= j'. Apply Knuth optimization to reduce time complexity from O(N^3) to O(N^2). Output a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 12,483 | 13,478 | +8% | 1 | 1 | 0% | 2,585 | 2,923 | +13% | 0 | 0 | — |
▸case-19 I am partitioning an array of N points into K clusters to minimize total sum of squared errors. The optimal split index opt(i, j) is monotonic in j. Optimize the O(K * N^2) loop to O(K * N log N). Format response as JSON with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 13,540 | 15,923 | +18% | 1 | 1 | 0% | 2,961 | 3,262 | +10% | 0 | 0 | — |
▸case-20 I am applying Convex Hull Trick to an O(N^2) dynamic programming solution with monotonic slopes. What is the improved time complexity achieved by this technique when using dynamic lines or binary search? Respond using a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 9,592 | 7,511 | -22% | 1 | 1 | 0% | 1,646 | 1,983 | +20% | 0 | 0 | — |
▸case-21 Applying a sliding window monotonic queue optimization to a bounded knapsack or 1D window DP improves the time complexity per element. What is the time complexity achieved per state transition? Return a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 10,098 | 6,245 | -38% | 1 | 1 | 0% | 2,117 | 1,899 | -10% | 0 | 0 | — |
▸case-22 When solving the Traveling Salesperson Problem with N=20 cities using dynamic programming over bitmasks, what are the resulting time and space complexities? Output a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 8,303 | 8,386 | +1% | 1 | 1 | 0% | 1,794 | 2,437 | +36% | 0 | 0 | — |
▸case-23 When applying Alien's Trick (WQS binary search) to remove a constraint dimension K from an O(N * K) dynamic programming state space, what is the resulting time complexity in terms of N and binary search range C? Format response as JSON with fields success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 8,824 | 8,427 | -4% | 1 | 1 | 0% | 1,834 | 2,043 | +11% | 0 | 0 | — |
▸case-24 A 0/1 Knapsack DP table dp[i][w] of size N x W only references row i-1 when computing row i. Apply space optimization to reduce memory from O(N * W) to O(W). Provide the response as a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 5,965 | 4,113 | -31% | 1 | 1 | 0% | 1,205 | 1,450 | +20% | 0 | 0 | — |
▸case-25 Write a C++ snippet optimizing dp[i] = min_{j < i} (dp[j] + slope[j] * x[i]) where slope[j] is non-increasing and x[i] is non-decreasing using Convex Hull Trick with std::deque. Output a JSON object with success, optimizedCode, optimizationApplied, newComplexity, and explanation. | pass→pass | 15,595 | 12,710 | -18% | 1 | 1 | 0% | 3,038 | 3,358 | +11% | 0 | 0 | — |