LeetCode Day 23: Stable Binary Arrays I

Day 23/30 – LeetCode streak Problem: Find All Possible Stable Binary Arrays I A binary array of length 'zero + one' is stable if it uses exactly 'zero' zeros and 'one' ones, and no run of identical bits is longer than 'limit'. Core idea DP state:  * 'dp[z][o][0]' = ways to build a stable array with 'z' zeros and 'o' ones, ending in '0'.  * 'dp[z][o][1]' = ways to build a stable array with 'z' zeros and 'o' ones, ending in '1'. * To end in '0' at '(z, o)', you must come from some '(z − k, o, 1)' and append a run of 'k' zeros, where '1 ≤ k ≤ limit' and 'k ≤ z'. * Similarly, to end in '1' at '(z, o)', come from '(z, o − k, 0)' and append 'k' ones. * These transitions are range sums over previous states. Instead of recomputing the full sum each time, use a sliding window idea so each state is computed in 'O(1)'. Transitions (sliding window view) For 'z ≥ 1' and 'o ≥ 1': * Ending with '0': sum of states where we append up to 'limit' zeros after a sequence ending in '1'. * Ending with '1': sum of states where we append up to 'limit' ones after a sequence ending in '0'. Day 23 takeaway: This problem is a solid example of combining DP on counts of zeros and ones with run-length constraints, and optimizing naive range-sum transitions using a sliding window — a pattern that appears in many sequence-counting DP problems. #leetcode #dsa #java #dynamicprogramming #consistency

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