325. Maximum Size Subarray Sum Equals k 🔒

Description

Given an integer array nums and an integer k, return the maximum length of a subarray that sums to k. If there is not one, return 0 instead.

 

Example 1:

Input: nums = [1,-1,5,-2,3], k = 3
Output: 4
Explanation: The subarray [1, -1, 5, -2] sums to 3 and is the longest.

Example 2:

Input: nums = [-2,-1,2,1], k = 1
Output: 2
Explanation: The subarray [-1, 2] sums to 1 and is the longest.

 

Constraints:

• 1 <= nums.length <= 2 * 105
• -104 <= nums[i] <= 104
• -109 <= k <= 109

Solutions

Solution 1: Hash Table + Prefix Sum

We can use a hash table \(\textit{d}\) to record the first occurrence index of each prefix sum in the array \(\textit{nums}\), initializing \(\textit{d}[0] = -1\). Additionally, we define a variable \(\textit{s}\) to keep track of the current prefix sum.

Next, we iterate through the array \(\textit{nums}\). For the current number \(\textit{nums}[i]\), we update the prefix sum \(\textit{s} = \textit{s} + \textit{nums}[i]\). If \(\textit{s} - k\) exists in the hash table \(\textit{d}\), let \(\textit{j} = \textit{d}[\textit{s} - k]\), then the length of the subarray that ends at \(\textit{nums}[i]\) and satisfies the condition is \(i - j\). We use a variable \(\textit{ans}\) to maintain the length of the longest subarray that satisfies the condition. After that, if \(\textit{s}\) does not exist in the hash table, we record \(\textit{s}\) and its corresponding index \(i\) by setting \(\textit{d}[\textit{s}] = i\). Otherwise, we do not update \(\textit{d}[\textit{s}]\). It is important to note that there may be multiple positions \(i\) with the same value of \(\textit{s}\), so we only record the smallest \(i\) to ensure the subarray length is the longest.

After the iteration ends, we return \(\textit{ans}\).

The time complexity is \(O(n)\), and the space complexity is \(O(n)\), where \(n\) is the length of the array \(\textit{nums}\).

Python3JavaC++GoTypeScriptRustJavaScriptC#

class Solution:
    def maxSubArrayLen(self, nums: List[int], k: int) -> int:
        d = {0: -1}
        ans = s = 0
        for i, x in enumerate(nums):
            s += x
            if s - k in d:
                ans = max(ans, i - d[s - k])
            if s not in d:
                d[s] = i
        return ans

class Solution {
    public int maxSubArrayLen(int[] nums, int k) {
        Map<Long, Integer> d = new HashMap<>();
        d.put(0L, -1);
        int ans = 0;
        long s = 0;
        for (int i = 0; i < nums.length; ++i) {
            s += nums[i];
            ans = Math.max(ans, i - d.getOrDefault(s - k, i));
            d.putIfAbsent(s, i);
        }
        return ans;
    }
}

class Solution {
public:
    int maxSubArrayLen(vector<int>& nums, int k) {
        unordered_map<long long, int> d{{0, -1}};
        int ans = 0;
        long long s = 0;
        for (int i = 0; i < nums.size(); ++i) {
            s += nums[i];
            if (d.count(s - k)) {
                ans = max(ans, i - d[s - k]);
            }
            if (!d.count(s)) {
                d[s] = i;
            }
        }
        return ans;
    }
};

func maxSubArrayLen(nums []int, k int) (ans int) {
    d := map[int]int{0: -1}
    s := 0
    for i, x := range nums {
        s += x
        if j, ok := d[s-k]; ok && ans < i-j {
            ans = i - j
        }
        if _, ok := d[s]; !ok {
            d[s] = i
        }
    }
    return
}

function maxSubArrayLen(nums: number[], k: number): number {
    const d: Map<number, number> = new Map();
    d.set(0, -1);
    let ans = 0;
    let s = 0;
    for (let i = 0; i < nums.length; ++i) {
        s += nums[i];
        if (d.has(s - k)) {
            ans = Math.max(ans, i - d.get(s - k)!);
        }
        if (!d.has(s)) {
            d.set(s, i);
        }
    }
    return ans;
}

use std::collections::HashMap;

impl Solution {
    pub fn max_sub_array_len(nums: Vec<i32>, k: i32) -> i32 {
        let mut d = HashMap::new();
        d.insert(0, -1);
        let mut ans = 0;
        let mut s = 0;

        for (i, &x) in nums.iter().enumerate() {
            s += x;
            if let Some(&j) = d.get(&(s - k)) {
                ans = ans.max((i as i32) - j);
            }
            d.entry(s).or_insert(i as i32);
        }

        ans
    }
}

/**
 * @param {number[]} nums
 * @param {number} k
 * @return {number}
 */
var maxSubArrayLen = function (nums, k) {
    const d = new Map();
    d.set(0, -1);
    let ans = 0;
    let s = 0;
    for (let i = 0; i < nums.length; ++i) {
        s += nums[i];
        if (d.has(s - k)) {
            ans = Math.max(ans, i - d.get(s - k));
        }
        if (!d.has(s)) {
            d.set(s, i);
        }
    }
    return ans;
};

public class Solution {
    public int MaxSubArrayLen(int[] nums, int k) {
        var d = new Dictionary<int, int>();
        d[0] = -1;
        int ans = 0;
        int s = 0;
        for (int i = 0; i < nums.Length; i++) {
            s += nums[i];
            if (d.ContainsKey(s - k)) {
                ans = Math.Max(ans, i - d[s - k]);
            }
            if (!d.ContainsKey(s)) {
                d[s] = i;
            }
        }
        return ans;
    }
}

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