Posts (238+)

Browse the full archive. Use topics in the sidebar to explore by tag.

September 2026

Reservoir Sampling:One Pass When You Do Not Know n Up Front

Keep the first k items, then for each later index i (1-based), replace a slot with probability k/i — a uniform sample of k from a stream of unknown length.

Algorithms

Binary Exponentiation:pow(base, exp) in Logarithmic Multiplies

Square the base and consume the exponent bit by bit — O(log exp) multiplies instead of a loop of exp products, for integers or modular pow.

Algorithms

Fisher-Yates:Shuffle in Place Without Bias

For i from n-1 down to 1, swap a[i] with a uniform index in 0..i — every permutation equally likely, which is what Collections.shuffle already runs.

Algorithms

Euclid GCD:Subtract, Then Mod, Then Extended Coefficients

Replace repeated subtraction with remainder, then back-substitute for Bézout coefficients — gcd, lcm, and a modular inverse when gcd is 1.

Algorithms

Count-Min Sketch:Approximate Frequencies When Exact Maps Do Not Fit

d × w counters and the min over hashes: over-estimate frequencies on purpose when a HashMap of every key will not fit.

Java

Pick the Collection:Nulls, Order, Threads, and the Hot Operation

A decision guide for the Java Collections series: given the hot operation, null policy, encounter order, and whether another thread looks — which JDK type to new.

Algorithms

Aho-Corasick:Many Patterns, One Pass Over the Text

Build a trie of all needles, add failure links like KMP on a forest, then scan the haystack once — every pattern that ends at the current character reports.

Algorithms

HyperLogLog:Approximate Distinct Count in Tiny Memory

Estimate cardinality with a handful of registers and a harmonic mean — plus-or-minus is the point, not a HashSet of every key.

Java

Sequenced Collections:First, Last, and Reversed Without the Ceremony

Learn how Java 21 sequenced collections provide uniform first, last, and reversed operations across lists, deques, ordered sets, and ordered maps.

Algorithms

Boyer-Moore:Skip Ahead When the Mismatch Is Near the End

Align the pattern at the window end, use a bad-character skip (and the good-suffix idea) so a late mismatch jumps the haystack instead of sliding by one.