1989. Maximum Number of People That Can Be Caught in Tag

Description

You are playing a game of tag with your friends. In tag, people are divided into two teams: people who are "it", and people who are not "it". The people who are "it" want to catch as many people as possible who are not "it".

You are given a 0-indexed integer array team containing only zeros (denoting people who are not "it") and ones (denoting people who are "it"), and an integer dist. A person who is "it" at index i can catch any one person whose index is in the range [i - dist, i + dist] (inclusive) and is not "it".

Return the maximum number of people that the people who are "it" can catch.

 

Example 1:

Input: team = [0,1,0,1,0], dist = 3
Output: 2
Explanation:
The person who is "it" at index 1 can catch people in the range [i-dist, i+dist] = [1-3, 1+3] = [-2, 4].
They can catch the person who is not "it" at index 2.
The person who is "it" at index 3 can catch people in the range [i-dist, i+dist] = [3-3, 3+3] = [0, 6].
They can catch the person who is not "it" at index 0.
The person who is not "it" at index 4 will not be caught because the people at indices 1 and 3 are already catching one person.

Example 2:

Input: team = [1], dist = 1
Output: 0
Explanation:
There are no people who are not "it" to catch.

Example 3:

Input: team = [0], dist = 1
Output: 0
Explanation:
There are no people who are "it" to catch people.

 

Constraints:

  • 1 <= team.length <= 105
  • 0 <= team[i] <= 1
  • 1 <= dist <= team.length

Solutions

Solution 1

Python Code
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class Solution:
    def catchMaximumAmountofPeople(self, team: List[int], dist: int) -> int:
        ans = j = 0
        n = len(team)
        for i, x in enumerate(team):
            if x:
                while j < n and (team[j] or i - j > dist):
                    j += 1
                if j < n and abs(i - j) <= dist:
                    ans += 1
                    j += 1
        return ans

Java Code
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class Solution {
    public int catchMaximumAmountofPeople(int[] team, int dist) {
        int ans = 0;
        int n = team.length;
        for (int i = 0, j = 0; i < n; ++i) {
            if (team[i] == 1) {
                while (j < n && (team[j] == 1 || i - j > dist)) {
                    ++j;
                }
                if (j < n && Math.abs(i - j) <= dist) {
                    ++ans;
                    ++j;
                }
            }
        }
        return ans;
    }
}

C++ Code
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class Solution {
public:
    int catchMaximumAmountofPeople(vector<int>& team, int dist) {
        int ans = 0;
        int n = team.size();
        for (int i = 0, j = 0; i < n; ++i) {
            if (team[i]) {
                while (j < n && (team[j] || i - j > dist)) {
                    ++j;
                }
                if (j < n && abs(i - j) <= dist) {
                    ++ans;
                    ++j;
                }
            }
        }
        return ans;
    }
};

Go Code
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func catchMaximumAmountofPeople(team []int, dist int) (ans int) {
	n := len(team)
	for i, j := 0, 0; i < n; i++ {
		if team[i] == 1 {
			for j < n && (team[j] == 1 || i-j > dist) {
				j++
			}
			if j < n && abs(i-j) <= dist {
				ans++
				j++
			}
		}
	}
	return
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}