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10.05. Sparse Array Search

Description

Given a sorted array of strings that is interspersed with empty strings, write a method to find the location of a given string.

Example1:


 Input: words = ["at", "", "", "", "ball", "", "", "car", "", "","dad", "", ""], s = "ta"

 Output: -1

 Explanation: Return -1 if s is not in words.

Example2:


 Input: words = ["at", "", "", "", "ball", "", "", "car", "", "","dad", "", ""], s = "ball"

 Output: 4

Note:

  1. 1 <= words.length <= 1000000

Solutions

We design a function $dfs(i, j)$ to find the target string in the array $nums[i, j]$. If found, return the index of the target string, otherwise return $-1$. So the answer is $dfs(0, n-1)$.

The implementation of the function $dfs(i, j)$ is as follows:

  1. If $i > j$, return $-1$.
  2. Otherwise, we take the middle position $mid = (i + j) / 2$, then recursively call $dfs(i, mid-1)$. If the return value is not $-1$, it means that the target string is found in the left half, return it directly. Otherwise, if $words[mid] = s$, it means that the target string is found, return it directly. Otherwise, recursively call $dfs(mid+1, j)$ and return.

In the worst case, the time complexity is $O(n \times m)$, and the space complexity is $O(n)$. Where $n$ and $m$ are the length of the string array and the length of the string $s$, respectively.

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class Solution:
    def findString(self, words: List[str], s: str) -> int:
        def dfs(i: int, j: int) -> int:
            if i > j:
                return -1
            mid = (i + j) >> 1
            l = dfs(i, mid - 1)
            if l != -1:
                return l
            if words[mid] == s:
                return mid
            return dfs(mid + 1, j)

        return dfs(0, len(words) - 1)

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class Solution {
    public int findString(String[] words, String s) {
        return dfs(words, s, 0, words.length - 1);
    }

    private int dfs(String[] words, String s, int i, int j) {
        if (i > j) {
            return -1;
        }
        int mid = (i + j) >> 1;
        int l = dfs(words, s, i, mid - 1);
        if (l != -1) {
            return l;
        }
        if (words[mid].equals(s)) {
            return mid;
        }
        return dfs(words, s, mid + 1, j);
    }
}

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class Solution {
public:
    int findString(vector<string>& words, string s) {
        function<int(int, int)> dfs = [&](int i, int j) {
            if (i > j) {
                return -1;
            }
            int mid = (i + j) >> 1;
            int l = dfs(i, mid - 1);
            if (l != -1) {
                return l;
            }
            if (words[mid] == s) {
                return mid;
            }
            return dfs(mid + 1, j);
        };
        return dfs(0, words.size() - 1);
    }
};

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func findString(words []string, s string) int {
    var dfs func(i, j int) int
    dfs = func(i, j int) int {
        if i > j {
            return -1
        }
        mid := (i + j) >> 1
        if l := dfs(i, mid-1); l != -1 {
            return l
        }
        if words[mid] == s {
            return mid
        }
        return dfs(mid+1, j)
    }
    return dfs(0, len(words)-1)
}

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function findString(words: string[], s: string): number {
    const dfs = (i: number, j: number): number => {
        if (i > j) {
            return -1;
        }
        const mid = (i + j) >> 1;
        const l = dfs(i, mid - 1);
        if (l !== -1) {
            return l;
        }
        if (words[mid] === s) {
            return mid;
        }
        return dfs(mid + 1, j);
    };
    return dfs(0, words.length - 1);
}

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class Solution {
    func findString(_ words: [String], _ s: String) -> Int {
        return dfs(words, s, 0, words.count - 1)
    }

    private func dfs(_ words: [String], _ s: String, _ i: Int, _ j: Int) -> Int {
        if i > j {
            return -1
        }
        let mid = (i + j) >> 1
        let left = dfs(words, s, i, mid - 1)
        if left != -1 {
            return left
        }
        if words[mid] == s {
            return mid
        }
        return dfs(words, s, mid + 1, j)
    }
}

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