Master Key Data Structures & Algorithms: Python

Explore dynamic programming and the cadence algorithm to solve continuous subarray problems with maximum sum, and apply to stock price analysis, uptime monitoring, weather data, and audio signal analysis.

Learn dynamic programming through Kadane's algorithm to find the maximum sum contiguous subarray in a sequence of integers, and contrast it with brute-force approaches.

Kadane's key ideas for finding the maximum subarray sum involve two pointers: maintaining a current sum and a final max, discarding negative sums, and starting anew at positive numbers.

Debug Kadane's algorithm by tracking current sum and maximum, starting from the first element, then iterating to update the best subarray in Python.

Apply Kadane's algorithm to find the maximum subarray sum by updating the current sum and starting a new subset when it becomes negative, tracking the best final sum.

Explore Bohr's algorithm, a voting-based method for identifying the majority value, and apply it to image processing, noise detection, and ensemble model voting in streaming data.

Identify a possible majority candidate and validate it against the data through a two-step process, distinguishing between count and actual frequency.

Explore the Boyer Moore majority vote algorithm steps, selecting a candidate with count updates, then verify the majority by counting matches, and prepare to implement the Python version.

Apply Boyer Moore's majority vote algorithm in Python, using a candidate and count in a two-phase process to validate the majority element.

Learn how dynamic programming solves problems by breaking them into smaller, similar subproblems, storing results, and reusing them to achieve optimal solutions such as Fibonacci, pathfinding, knapsack, and change-making.

Explore dynamic programming types, comparing top-down recursion with memoization to bottom-up for loops, and learn how base conditions enable efficient Fibonacci computations.

Explore the Fibonacci series, where each number depends on the previous two and starts with zero and one. Implement Fibonacci using dynamic programming with a top-down approach.

Apply memoization with recursion to compute fibonacci using a dp dictionary that stores results and avoids recomputation. Use base cases fib(0)=0 and fib(1)=1 and update dp[n] with each calculation.

Implement a top-down, memoized Fibonacci in Python using recursion and a dictionary cache. Learn base cases, subproblems n-1 and n-2, and how memoization avoids recomputation.

Learn to implement Fibonacci with DP tabulation using a non-recursive for loop that builds a dp array from 2 to n and return dp[n].

Learn a Python bottom-up dynamic programming approach using tabulation: build a dp array, iterate from two, compute each dp[i] from dp[i-1] and dp[i-2], and return dp[n].

Optimize memory in dynamic programming by using three variables—current, previous, and previous two—to compute Fibonacci values without dp arrays.

Explore how dynamic programming avoids repeated problems by storing results in memory to save cpu cycles, with top-down and bottom-up approaches and the Fibonacci example.

Learn the prefix sum technique, a pre-calculated cumulative total to quickly compute the summation of array elements up to a given index and answer range queries.

Explore how the prefix sum technique pre-calculates cumulative totals in an array with a prefix array, enabling fast summation queries and reuse of pre-calculated results.

Apply the prefix sum to compute any subarray sum by subtracting the prefix up to left-1 from the prefix up to right, enabling fast queries after a single scan.

Explore the performance of the prefix sum method, building a prefix array in O(n) and answering q queries in O(1) for a total of O(n+q) vs. O(nq).

Construct a prefix sum array from the data and use it to answer multiple range sum queries in order of n plus q.

Learn to build a prefix sum array and answer multiple queries with left and right indices, achieving order of n plus order of q total time.