Formatted question description: https://leetcode.ca/all/525.html

# 525. Contiguous Array (Medium)

Given a binary array, find the maximum length of a contiguous subarray with equal number of 0 and 1.

Example 1:

Input: [0,1]
Output: 2
Explanation: [0, 1] is the longest contiguous subarray with equal number of 0 and 1.


Example 2:

Input: [0,1,0]
Output: 2
Explanation: [0, 1] (or [1, 0]) is a longest contiguous subarray with equal number of 0 and 1.


Note: The length of the given binary array will not exceed 50,000.

## Solution 1.

Let dp[i + 1] := the max length of contiguous array ending at index i.

Given start = i - dp[i], nums from nums[start] to nums[i - 1] forms a contiguous array.

If nums[start - 1] != nums[i], dp[i + 1] can be constructed using dp[i] + 2 + dp[start - 1]. The DP array saves computation in this case, but if nums[start - 1] == nums[i] I have to do linear search.

The search direction should be rightward. Assume nums[start - 1] = nums[i] = 1, If there are two zeroes can help form a longer contiguous array at the left of nums[start - 1], it’s contradicts with the fact that nums[start] ... nums[i - 1] is the longest contiguous array ending at i - 1 since nums[start - 2] ... nums[i - 1] is contiguous and even longer.

        v     v
... 0 0 1 ... 1


When search rightward from start, use int diff = 0 to denote the difference between 0 and 1. If nums[start] == nums[i], increment diff; otherwise decrement diff. When diff == 1, breaks the iteration because it means one more number same as nums[i] are popped.

// OJ: https://leetcode.com/problems/contiguous-array
// Time: O(N^2)
// Space: O(N)
class Solution {
public:
int findMaxLength(vector<int>& nums) {
vector<int> dp(nums.size() + 1, 0);
int ans = 0;
for (int i = 0; i < nums.size(); ++i) {
int start = i - dp[i];
if (start > 0 && nums[start - 1] != nums[i]) {
dp[i + 1] = dp[i] + 2 + dp[start - 1];
} else {
for (int diff = 0; start <= i && diff != 1; ++start) {
if (nums[start] == nums[i]) diff++;
else diff--;
}
dp[i + 1] = i - start + 1;
}
ans = max(ans, dp[i + 1]);
}
return ans;
}
};


## Solution 2.

Replace all 0s with -1s, and now the question becomes finding the longest contiguous array that sums up to 0.

Use unordered_map<int, int> m to store the mapping between the running sum and the index of its first occurrence. m initially holds { 0, -1 } which means a pseudo running sum 0 at index -1.

For each running sum,

• if it’s the first occurrence, store the mapping - m[sum] = i
• otherwise, update ans with max(ans, i - m[sum]).
// OJ: https://leetcode.com/problems/contiguous-array
// Time: O(N)
// Space: O(N)
// Ref: https://discuss.leetcode.com/topic/79906/easy-java-o-n-solution-presum-hashmap/
class Solution {
public:
int findMaxLength(vector<int>& nums) {
unordered_map<int, int> m{ {0, -1} };
int N = nums.size(), sum = 0, ans = 0;
for (int i = 0; i < N; ++i) {
sum += nums[i] ? 1 : -1;
if (m.count(sum)) ans = max(ans, i - m[sum]);
else m[sum] = i;
}
return ans;
}
};


Java

• class Solution {
public int findMaxLength(int[] nums) {
if (nums == null || nums.length == 0)
return 0;
int length = nums.length;
Map<Integer, Integer> map = new HashMap<Integer, Integer>();
int maxLength = 0;
int counter = 0;
for (int i = 0; i < length; i++) {
int num = nums[i] == 1 ? 1 : -1;
counter += num;
if (counter == 0)
maxLength = i + 1;
else {
if (map.containsKey(counter)) {
int prevIndex = map.get(counter);
int curLength = i - prevIndex;
maxLength = Math.max(maxLength, curLength);
}
}
if (!map.containsKey(counter))
map.put(counter, i);
}
return maxLength;
}
}

• // OJ: https://leetcode.com/problems/contiguous-array
// Time: O(N)
// Space: O(N)
// Ref: https://discuss.leetcode.com/topic/79906/easy-java-o-n-solution-presum-hashmap/
class Solution {
public:
int findMaxLength(vector<int>& A) {
unordered_map<int, int> m{ {0,-1} };
int ans = 0;
for (int i = 0, sum = 0; i < A.size(); ++i) {
sum += A[i] ? 1 : -1;
if (m.count(sum)) ans = max(ans, i - m[sum]);
else m[sum] = i;
}
return ans;
}
};

• class Solution(object):
def findMaxLength(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
d = {0: -1}
count = ans = 0
delta = {1: -1, 0: 1}
for i in range(len(nums)):
count += delta.get(nums[i], 0)
if count in d:
ans = max(ans, i - d[count])
else:
d[count] = i
return ans