[Leetcode] Problem Series of Jump Game

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By Long Luo

This article is the solution Leetcode Jump Game Problems Series .

55. Jump Game

55. Jump Game

Brute Force

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public boolean canJump(int[] nums) {
    int len = nums.length;
    boolean[] visited = new boolean[len];
    visited[0] = true;
    for (int i = 0; i < len; i++) {
        int steps = nums[i];
        if (visited[i] && steps > 0) {
            for (int j = 1; j <= steps && i + j < len; j++) {
                visited[i + j] = true;
            }
        }
    }

    return visited[len - 1];
}

Analysis

  • Time Complexity: \(O(n^2)\)
  • Space Complexity: \(O(n)\)

Greedy

Jump to the farest postion.

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public boolean canJump(int[] nums) {
    int len = nums.length;
    int maxIdx = 0;
    for (int i = 0; i < len; i++) {
        int steps = nums[i];
        if (maxIdx >= i) {
            maxIdx = Math.max(maxIdx, i + steps);
            if (maxIdx >= len - 1) {
                return true;
            }
        }
    }

    return false;
}

Analysis

  • Time Complexity: \(O(n)\)
  • Space Complexity: \(O(1)\)

45. Jump Game II

45. Jump Game II

DP

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public static int jump_dp(int[] nums) {
    int len = nums.length;
    if (len <= 1) {
        return 0;
    }

    int[] dp = new int[len];
    Arrays.fill(dp, Integer.MAX_VALUE);
    dp[0] = 0;
    int minStep = Integer.MAX_VALUE;
    for (int i = 0; i < len; i++) {
        int num = nums[i];
        for (int j = 1; j <= num && i + j < len; j++) {
            dp[i + j] = Math.min(dp[i + j], dp[i] + 1);
            if (i + j >= len - 1) {
                minStep = Math.min(minStep, dp[i] + 1);
                return minStep;
            }
        }
    }

    return minStep;
}

Analysis

  • Time Complexity: \(O(n^2)\)
  • Space Complexity: \(O(n)\)

Greedy

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public int jump(int[] nums) {
    int maxPosition = 0;
    int end = 0;
    int steps = 0;
    for (int i = 0; i < nums.length - 1; i++) {
        maxPosition = Math.max(maxPosition, i + nums[i]);
        if (i == end) {
            end = maxPosition;
            steps++;
        }
    }

    return steps;
}

Think reverse, from destination to origin position.

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public int jump(int[] nums) {
    int ans = 0;
    int position = nums.length - 1;
    while (position > 0) {
        for (int i = 0; i < position; i++) {
            if (i + nums[i] >= position) {
                ans++;
                position = i;
                break;
            }
        }
    }

    return ans;
}

Analysis

  • Time Complexity: \(O(n)\)
  • Space Complexity: \(O(1)\)

1306. Jump Game III

1306. Jump Game III

BFS

BFS Solution:

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public boolean canReach_bfs_opt(int[] arr, int start) {
    if (arr[start] == 0) {
        return true;
    }

    int len = arr.length;
    boolean[] visited = new boolean[len];
    Queue<Integer> queue = new LinkedList<>();
    queue.offer(start);
    visited[start] = true;

    while (!queue.isEmpty()) {
        int curPos = queue.poll();
        if (arr[curPos] == 0) {
            return true;
        }

        int right = curPos + arr[curPos];
        if (right >= 0 && right < len && !visited[right]) {
            visited[right] = true;
            queue.offer(right);
        }

        int left = curPos - arr[curPos];
        if (left >= 0 && left < len && !visited[left]) {
            visited[left] = true;
            queue.offer(left);
        }
    }

    return false;
}

Analysis

  • Time Complexity: \(O(n)\)
  • Space Complexity: \(O(n)\)

DFS

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public boolean canReach_dfs(int[] arr, int start) {
    int len = arr.length;
    boolean[] vis = new boolean[len];
    return dfs(arr, vis, start);
}

public boolean dfs(int[] arr, boolean[] vis, int start) {
    if (start < 0 || start >= arr.length || vis[start]) {
        return false;
    }

    vis[start] = true;
    if (arr[start] == 0) {
        return true;
    }

    return dfs(arr, vis, start - arr[start]) || dfs(arr, vis, start + arr[start]);
}

Analysis

  • Time Complexity: \(O(n)\)
  • Space Complexity: \(O(n)\)

1345. Jump Game IV

1345. Jump Game IV

BFS

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Analysis

  • Time Complexity: \(O(n)\)
  • Space Complexity: \(O(n)\)

1340. Jump Game V

1340. Jump Game V

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Analysis

  • Time Complexity: \(O(n)\)
  • Space Complexity: \(O(n)\)

1696. Jump Game VI

1696. Jump Game VI

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public static boolean canJump(int[] nums) {
    int len = nums.length;
    int maxIdx = 0;
    for (int i = 0; i < len; i++) {
        int steps = nums[i];
        if (maxIdx >= i) {
            maxIdx = Math.max(maxIdx, i + steps);
            if (maxIdx >= len - 1) {
                return true;
            }
        }
    }

    return false;
}

Analysis

  • Time Complexity: \(O(n)\)
  • Space Complexity: \(O(n)\)

1871. Jump Game VII

1871. Jump Game VII

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Analysis

  • Time Complexity: \(O(n)\)
  • Space Complexity: \(O(n)\)

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