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Falling Squares — Coordinate Compress + Segment Tree
Simulate falling squares, track tallest stack height. Coordinate compress x-coordinates, use segment tree with lazy propagation for range max.
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Count of Range Sum — Merge Sort / BIT
Count subarray sums within [lower, upper]. Use prefix sums and merge sort: during merge count pairs of prefix sums with difference in range.
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Number of Longest Increasing Subsequences — DP + BIT
Count all LIS of maximum length. DP: track length and count. Segment tree on values enables O(n log n) solution.
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Shifting Letters II — Difference Array
Apply range shift operations to letters. Difference array: mark +1 at start and -1 at end+1, prefix sum gives net shift at each position.
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Range Sum Query 2D Immutable — 2D Prefix Sum
Sum of rectangle region. Precompute 2D prefix sums: prefix[i][j] = sum of all cells from (0,0) to (i-1,j-1). Inclusion-exclusion for query.
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