题目描述补充

题目：平面上的点列表问题

给定一个包含多个点的平面列表，每个点由其在二维空间中的坐标(x, y)表示。请实现一个算法，完成以下任务之一（或两者都实现，根据面试要求）：

1. 计算最近点对距离：找到列表中任意两点之间的最短距离。
2. 检测是否存在重合点：检查列表中是否存在至少两个点坐标完全相同。

输入：一个二维数组，其中每个元素是一个包含两个整数的数组，代表一个点的x和y坐标。

输出：

• 对于最近点对距离问题，输出最短距离。
• 对于检测重合点问题，如果存在重合点，输出true，否则输出false。

示例代码

PHP 示例

function findClosestPairDistance($points) {
    if (count($points) < 2) return float('INF');

    $minDistance = PHP_INT_MAX;

    foreach ($points as $i => $p1) {
        foreach ($points as $j => $p2) {
            if ($i !== $j) {
                $distance = sqrt(pow($p1[0] - $p2[0], 2) + pow($p1[1] - $p2[1], 2));
                $minDistance = min($minDistance, $distance);
            }
        }
    }

    return $minDistance;
}

function hasDuplicatePoints($points) {
    $seen = [];
    foreach ($points as $p) {
        $key = implode(',', $p);
        if (isset($seen[$key])) return true;
        $seen[$key] = true;
    }
    return false;
}

// 示例用法
$points = [[1, 2], [3, 4], [5, 6], [1, 2]]; // 包含一个重合点
echo "Closest Pair Distance: " . findClosestPairDistance($points) . "\n";
echo "Has Duplicate Points: " . (hasDuplicatePoints($points) ? "true" : "false") . "\n";

Python 示例

import math

def find_closest_pair_distance(points):
    if len(points) < 2:
        return float('inf')
    
    min_distance = float('inf')
    
    for i in range(len(points)):
        for j in range(i + 1, len(points)):
            distance = math.sqrt((points[i][0] - points[j][0])**2 + (points[i][1] - points[j][1])**2)
            min_distance = min(min_distance, distance)
    
    return min_distance

def has_duplicate_points(points):
    seen = set()
    for point in points:
        tuple_point = tuple(point)
        if tuple_point in seen:
            return True
        seen.add(tuple_point)
    return False

# 示例用法
points = [(1, 2), (3, 4), (5, 6), (1, 2)]  # 包含一个重合点
print("Closest Pair Distance:", find_closest_pair_distance(points))
print("Has Duplicate Points:", has_duplicate_points(points))

JavaScript 示例

function findClosestPairDistance(points) {
    if (points.length < 2) return Infinity;

    let minDistance = Infinity;

    for (let i = 0; i < points.length; i++) {
        for (let j = i + 1; j < points.length; j++) {
            const distance = Math.sqrt(Math.pow(points[i][0] - points[j][0], 2) + Math.pow(points[i][1] - points[j][1], 2));
            minDistance = Math.min(minDistance, distance);
        }
    }

    return minDistance;
}

function hasDuplicatePoints(points) {
    const seen = new Set();
    for (const point of points) {
        const key = `${point[0]},${point[1]}`;
        if (seen.has(key)) return true;
        seen.add(key);
    }
    return false;
}

// 示例用法
const points = [[1, 2], [3, 4], [5, 6], [1, 2]]; // 包含一个重合点
console.log("Closest Pair Distance:", findClosestPairDistance(points));
console.log("Has Duplicate Points:", hasDuplicatePoints(points));

在以上示例中，我们分别用PHP、Python和JavaScript实现了计算最近点对距离和检测是否存在重合点的功能。这些代码可以直接在相应的环境中运行以验证其功能。