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🔷All∑Math⚙️Algo🗂️DS📚Theory

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⚙️AlgorithmIntermediate

Double Counting

Double counting is the strategy of counting the same quantity in two different ways to derive an equality or an efficient algorithm.

#double counting#contribution technique#handshake lemma+12
⚙️AlgorithmIntermediate

Contribution Technique

The contribution technique flips perspective: compute how much each element contributes to the total, then sum these contributions.

#contribution technique
Advanced
Filtering by:
#linearity of expectation
#monotonic stack
#sum of subarray minimums
+12
∑MathIntermediate

Linearity of Expectation Applications

Linearity of expectation says the expected value of a sum equals the sum of expected values, even if the variables are dependent.

#linearity of expectation#indicator variables#expected inversions+12
∑MathIntermediate

Expected Value

Expected value is the long-run average outcome of a random variable if you could repeat the experiment many times.

#expected value#linearity of expectation#indicator variables+12
⚙️AlgorithmAdvanced

DP with Expected Value

Dynamic programming with expected value solves problems where each state transitions randomly and we seek the expected cost, time, or steps to reach a goal.

#expected value dp#linearity of expectation#indicator variables+11