There are some spherical balloons taped onto a flat wall that represents the XY-plane. The balloons are represented as a 2D integer array points where points[i] = [xstart, xend] denotes a balloon whose horizontal diameter stretches between xstart and xend. You do not know the exact y-coordinates of the balloons.
Arrows can be shot up directly vertically (in the positive y-direction) from different points along the x-axis. A balloon with xstart and xend is burst by an arrow shot at x if xstart <= x <= xend. There is no limit to the number of arrows that can be shot. A shot arrow keeps traveling up infinitely, bursting any balloons in its path.
Given the array points, return the minimum number of arrows that must be shot to burst all balloons.
Input:
points = [[10,16],[2,8],[1,6],[7,12]]
Output:
2
Explanation: The balloons can be burst by 2 arrows:
- Shoot an arrow at x = 6, bursting the balloons [2,8] and [1,6].
- Shoot an arrow at x = 11, bursting the balloons [10,16] and [7,12].
Example 2:
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Input:
points = [[1,2],[3,4],[5,6],[7,8]]
Output:
4
Explanation: One arrow needs to be shot for each balloon for a total of 4 arrows.
Example 3:
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Input:
points = [[1,2],[2,3],[3,4],[4,5]]
Output:
2
Explanation: The balloons can be burst by 2 arrows:
- Shoot an arrow at x = 2, bursting the balloons [1,2] and [2,3].
- Shoot an arrow at x = 4, bursting the balloons [3,4] and [4,5].
The key idea is to always shoot the next arrow at the earliest possible position that bursts the most balloons. By sorting balloons by their end coordinate, we can always shoot an arrow at the end of the current balloon, ensuring we burst as many overlapping balloons as possible with each arrow.
classSolution {
public:int findMinArrowShots(vector<vector<int>>& points) {
sort(points.begin(), points.end(), [](const vector<int>& a, const vector<int>& b) {
return a[1] < b[1];
});
int ans =0;
longlong last = LLONG_MIN;
for (constauto& p : points) {
int a = p[0], b = p[1];
if (a > last) {
ans++;
last = b;
}
}
return ans;
}
};
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publicclassSolution {
publicint FindMinArrowShots(int[][] points) {
Array.Sort(points, (a, b) => a[1] < b[1] ? -1 : a[1] > b[1] ? 1 : 0);
int ans = 0;
long last = long.MinValue;
foreach (var point in points) {
if (point[0] > last) {
++ans;
last = point[1];
}
}
return ans;
}
}
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funcfindMinArrowShots(points [][]int) (ansint) {
sort.Slice(points, func(i, jint) bool { returnpoints[i][1] < points[j][1] })
last:=-(1<<60)
for_, p:=rangepoints {
a, b:=p[0], p[1]
ifa > last {
ans++last = b }
}
return}
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classSolution {
publicintfindMinArrowShots(int[][] points) {
Arrays.sort(points, Comparator.comparingInt(a -> a[1]));
int ans = 0;
long last = Long.MIN_VALUE;
for (int[] p : points) {
int a = p[0], b = p[1];
if (a > last) {
ans++;
last = b;
}
}
return ans;
}
}
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classSolution:
deffindMinArrowShots(self, points: list[list[int]]) -> int:
points.sort(key=lambda x: x[1])
ans =0 last = float('-inf')
for a, b in points:
if a > last:
ans +=1 last = b
return ans
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functionfindMinArrowShots(points: number[][]):number {
points.sort((a, b) =>a[1] -b[1]);
letans=0;
letlast=-Infinity;
for (const [a, b] ofpoints) {
if (last<a) {
ans++;
last=b;
}
}
returnans;
}