Check Whether Bounded Jumps Reach the Final Index

### Problem Start at index zero of binary string `s`, whose first character is zero. From i you may jump to a zero-valued position j satisfying `i+minJump <= j <= min(i+maxJump,s.length-1)`. Return whether the final index is reachable. ```cpp class Solution { public: bool canReach(string s, int minJump, int maxJump); }; ``` ### Examples **Example 1:** ```text s = "00100", minJump = 2, maxJump = 3 Output: false Explanation: Index 2 is blocked. Index 3 is reachable but cannot jump the single step to index 4. ``` **Example 2:** ```text s = "010010", minJump = 2, maxJump = 3 Output: true Explanation: Jump 0 -> 3 -> 5. ``` ### Constraints - `2 <= s.length <= 10^5`. - Characters are 0 or 1, and `s[0] == 0`. - `1 <= minJump <= maxJump < s.length`. ### Clarifying Questions Only landing positions must contain zero; positions jumped over can contain either digit. The last character need not be zero. ```hint Inspect the structure Which landing positions are legal, and does the input promise that the final character is zero? ``` ### Reasoning checkpoints - Require every landing to contain zero and every jump length to stay within the inclusive bounds. - Prove both reachability and unreachability claims without restricting cells jumped over. ### Optional extensions How could prefix sums of reachability replace the sliding predecessor count?