# 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

• 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;
}
}

• 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;
}
};

• 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


• 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
}