First Missing Positive Algorithm
The First Missing Positive Algorithm is an advanced programming technique that deals with finding the smallest missing positive integer in an unsorted integer array. This problem can be quite challenging, especially when considering edge cases and efficiency. The primary goal of this algorithm is to achieve a linear runtime complexity without using additional space, making it an in-place algorithm. The algorithm must be designed in such a way that it can handle a wide variety of inputs, including arrays with negative numbers, duplicates, and large gaps between positive integers.
To implement the First Missing Positive Algorithm, one popular approach is to use a variation of the bucket sort technique. First, iterate through the array and place each positive integer in its corresponding position (i.e., move the number 'k' to the index 'k-1') while ignoring negative numbers and numbers larger than the array's size. After this step, the array should have all the positive integers in their correct positions, with negative numbers and larger numbers filling the remaining spaces. Next, iterate through the modified array to find the first missing positive integer by checking if the number at each index matches the index plus one. If a mismatch is found, return the index plus one as the smallest missing positive integer. If no mismatch is found, the smallest missing positive integer is the array's size plus one. This process ensures that the algorithm has a linear runtime complexity and uses no additional space, making it highly efficient and suitable for solving complex programming problems.
class Solution {
public:
int firstMissingPositive(int A[], int n) {
int i = 0;
while (i < n) {
if (0 < A[i] && A[i] <= n && A[i] != A[A[i]-1]) {
swap(A[i], A[A[i]-1]);
} else {
i++;
}
}
for (int i = 0; i < n; i++) {
if (A[i] != i + 1) {
return i + 1;
}
}
return n + 1;
}
};
