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Jump Game VII - Problem

Jump Game VII is an exciting path-finding challenge! You're given a binary string s where '0' represents safe ground and '1' represents dangerous terrain. Starting at index 0 (which is always '0'), you need to reach the last index of the string.

However, there are jump constraints: from any position i, you can only jump to position j if:
• The jump distance is between minJump and maxJump (inclusive)
• The destination s[j] is '0' (safe ground)

Goal: Return true if you can reach the final index, false otherwise.

Example: s = "011010", minJump = 2, maxJump = 3
From index 0 → can jump to indices 2,3 → from index 3 → can jump to index 5 ✅

Input & Output

example_1.py — Basic Jump

$ Input: s = "011010", minJump = 2, maxJump = 3

› Output: true

💡 Note: Starting at index 0, we can jump to index 2 or 3 (both are '0'). From index 3, we can jump to index 5 (which is '0' and the last index). Path: 0 → 3 → 5.

example_2.py — Impossible Jump

$ Input: s = "01101110", minJump = 2, maxJump = 3

› Output: false

💡 Note: From index 0, we can reach indices 2 and 3. From index 2, we can reach indices 4 and 5, but both are '1'. From index 3, we can reach indices 5 and 6, but both are '1'. No path exists to reach index 7.

example_3.py — Edge Case

$ Input: s = "0", minJump = 1, maxJump = 1

› Output: true

💡 Note: The string has only one character, and we start at index 0, which is already the last index. Therefore, we can reach the end.

Constraints

1 ≤ s.length ≤ 10⁵
s[i] is either '0' or '1'
s[0] == '0'
1 ≤ minJump ≤ maxJump < s.length

Visualization

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Understanding the Visualization

Survey the River

Identify safe stones ('0') and dangerous stones ('1')

Track Jump Range

Maintain awareness of positions we can reach with current jump limits

Make Optimal Jumps

Use sliding window to efficiently determine next reachable positions

Reach the Goal

Successfully cross if we can reach the final stone

Key Takeaway

🎯 Key Insight: The sliding window technique transforms an O(n²) problem into O(n) by efficiently maintaining a count of reachable positions within the valid jumping range, avoiding redundant position checks.

Asked in

G Google 32 a Amazon 28 f Meta 24 ⊞ Microsoft 18

The optimal approach uses a sliding window technique with prefix sum to efficiently track reachable positions within the valid jumping range. Instead of checking each previous position individually (O(n²)), we maintain a count of reachable positions in our current window, achieving O(n) time complexity.

Common Approaches

Approach	Time	Space	Notes
✓ Sliding Window with Prefix Sum (Optimal)	O(n)	O(1)	Use sliding window to efficiently track reachable positions within jumping range
Dynamic Programming	O(n²)	O(n)	Use DP to track reachable positions and build solution bottom-up

Sliding Window with Prefix Sum (Optimal) — Algorithm Steps

Use a sliding window to track reachable positions in range [i-maxJump, i-minJump]
Maintain a count of reachable positions in the current window
For each position, check if count > 0 to determine reachability
Update the window by adding/removing positions as we progress

Visualization

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Step-by-Step Walkthrough

Initialize window

Start with empty sliding window for reachable positions

Slide window forward

For each position, add newly reachable positions and remove old ones

Check window count

If window has any reachable position, current position is reachable

Update efficiently

O(1) window updates instead of O(maxJump) position checks

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>

bool canReach(char* s, int minJump, int maxJump) {
    int n = strlen(s);
    if (s[n-1] == '1') return false;
    
    int reachableCount = 0;
    bool* dp = (bool*)calloc(n, sizeof(bool));
    dp[0] = true;
    
    for (int i = 1; i < n; i++) {
        // Add position that just came into range
        if (i >= minJump && dp[i - minJump]) {
            reachableCount++;
        }
        
        // Remove position that just went out of range
        if (i > maxJump && dp[i - maxJump - 1]) {
            reachableCount--;
        }
        
        // Current position is reachable if there's any reachable position in window
        dp[i] = s[i] == '0' && reachableCount > 0;
    }
    
    bool result = dp[n-1];
    free(dp);
    return result;
}

int main() {
    char s[100001];
    int minJump, maxJump;
    scanf("%s %d %d", s, &minJump, &maxJump);
    
    printf("%s\n", canReach(s, minJump, maxJump) ? "true" : "false");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through the string with O(1) operations per position

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables to track the sliding window

✓ Linear Space

67.2K Views

Medium Frequency

~25 min Avg. Time

1.8K Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Sliding Window with Prefix Sum (Optimal) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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