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题目描述

有N条线段，长度分别为a[1]-a[n]。

现要求你计算这N条线段最多可以组合成几个直角三角形。

每条线段只能使用一次，每个三角形包含三条线段。

输入描述

第一行输入一个正整数T（1<＝T<＝100），表示有T组测试数据.

对于每组测试数据，接下来有T行，

每行第一个正整数N，表示线段个数（3<＝N<＝20），接着是N个正整数，表示每条线段长度，（0<a[i]<100）。

输出描述

对于每组测试数据输出一行，每行包括一个整数，表示最多能组合的直角三角形个数

示例：

Python算法源码

from itertools import combinations

#用于存储每个状态的信息
class TriangleState:
    def __init__(self, index, count, used):
        self.index = index
        self.count = count
        self.used = used

#用于执行非递归深度优先搜索
def iterative_dfs(lengths):
    max_triangles = 0
    used_segments = [False] * len(lengths)
    stack = [TriangleState(0, 0, used_segments)]

    # 遍历状态栈
    while stack:
        current_state = stack.pop()
        current_index = current_state.index
        current_count = current_state.count
        used_segments = current_state.used

        max_triangles = max(max_triangles, current_count)

        # 遍历线段数组，从current_index开始
        x = current_index
        while x < len(lengths) - 2:
            y = x + 1
            while y < len(lengths) - 1:
                z = y + 1
                while z < len(lengths):
                    if used_segments[x] or used_segments[y] or used_segments[z]:
                        z += 1
                        continue

                    # 检查当前三条线段是否满足勾股定理
                    if lengths[x] ** 2 + lengths[y] ** 2 == lengths[z] ** 2:
                        new_used_segments = used_segments.copy()
                        new_used_segments[x] = True
                        new_used_segments[y] = True
                        new_used_segments[z] = True
                        stack.append(TriangleState(x + 1, current_count + 1, new_used_segments))
                    z += 1
                y += 1
            x += 1

    return max_triangles

# 用于读取测试数据组数并返回
def read_test_cases():
    return int(input())

# 用于读取每组测试数据并返回
def read_input_data(test_cases):
    input_data = []
    for _ in range(test_cases):
        input_data.append(list(map(int, input().split()))[1:])
    return input_data

# 用于处理每组测试数据并输出结果
def process_test_cases(input_data):
    for testCase in input_data:
        # 对线段长度进行升序排序
        testCase.sort()
        # 调用iterative_dfs函数并输出结果
        print(iterative_dfs(testCase))

# 读取测试数据组数
num_test_cases = read_test_cases()

# 读取每组测试数据
test_data = read_input_data(num_test_cases)

# 处理每组测试数据并输出结果
process_test_cases(test_data)

c算法源码

#include <stdio.h>
#include <stdbool.h>

// 结构体用于存储状态信息
typedef struct {
    int index;      // 当前索引
    int count;      // 已找到的直角三角形数量
    bool *used;     // 已使用的线段
} State;

// 非递归深度优先搜索函数
int non_recursive_dfs(int *lengths, int length_count) {
    int max_triangles = 0;
    bool *used_segments = malloc(length_count * sizeof(bool));
    State *stack = malloc(length_count * sizeof(State));
    int stack_top = -1;

    // 初始化used_segments数组
    for (int i = 0; i < length_count; i++)
        used_segments[i] = false;

    // 将初始状态压入栈中
    stack[++stack_top] = (State){0, 0, used_segments};

    // 遍历栈
    while (stack_top >= 0) {
        State current_state = stack[stack_top--];
        int current_index = current_state.index;
        int current_count = current_state.count;
        used_segments = current_state.used;

        max_triangles = (max_triangles > current_count) ? max_triangles : current_count;

        // 遍历长度数组，从current_index开始
        for (int i = current_index; i < length_count - 2; i++) {
            for (int j = i + 1; j < length_count - 1; j++) {
                for (int k = j + 1; k < length_count; k++) {
                    if (used_segments[i] || used_segments[j] || used_segments[k])
                        continue;

                    // 检查当前三条线段是否满足勾股定理
                    if (lengths[i] * lengths[i] + lengths[j] * lengths[j] == lengths[k] * lengths[k]) {
                        bool *new_used_segments = malloc(length_count * sizeof(bool));
                        for (int l = 0; l < length_count; l++)
                            new_used_segments[l] = used_segments[l];
                        new_used_segments[i] = true;
                        new_used_segments[j] = true;
                        new_used_segments[k] = true;

                        // 将新状态压入栈中
                        stack[++stack_top] = (State){i + 1, current_count + 1, new_used_segments};
                    }
                }
            }
        }
        free(current_state.used);
    }
    free(stack);

    return max_triangles;
}

int main() {
    int test_cases;
    scanf("%d", &test_cases);

    // 读取和处理每个测试用例
    for (int i = 0; i < test_cases; i++) {
        int length_count;
        scanf("%d", &length_count);
        int lengths[length_count];

        // 读取当前测试用例的线段长度
        for (int j = 0; j < length_count; j++)
            scanf("%d", &lengths[j]);

        // 将线段长度升序排序
        for (int j = 0; j < length_count - 1; j++) {
            for (int k = 0; k < length_count - j - 1; k++) {
                if (lengths[k] > lengths[k + 1]) {
                    int temp = lengths[k];
                    lengths[k] = lengths[k + 1];
                    lengths[k + 1] = temp;
                }
            }
        }

        // 调用non_recursive_dfs函数并输出结果
        printf("%d\n", non_recursive_dfs(lengths, length_count));
    }

    return 0;
}

java算法源码

import java.util.Scanner;

// 用于存储状态信息的类
class State {
    int index;          // 当前索引
    int count;          // 已找到的直角三角形数量
    boolean[] used;     // 已使用的线段

    // 构造函数
    State(int index, int count, boolean[] used) {
        this.index = index;
        this.count = count;
        this.used = used.clone(); // 使用克隆避免浅拷贝问题
    }
}

public class Main {

    // 非递归深度优先搜索函数
    static int nonRecursiveDFS(int[] lengths) {
        int maxTriangles = 0;
        int lengthCount = lengths.length;
        boolean[] usedSegments = new boolean[lengthCount];
        State[] stack = new State[lengthCount];
        int stackTop = -1;

        // 将初始状态压入栈中
        stack[++stackTop] = new State(0, 0, usedSegments.clone());

        // 遍历栈
        while (stackTop >= 0) {
            State currentState = stack[stackTop--];
            int currentIndex = currentState.index;
            int currentCount = currentState.count;
            boolean[] currentUsedSegments = currentState.used;

            maxTriangles = Math.max(maxTriangles, currentCount);

            // 遍历长度数组，从currentIndex开始
            for (int i = currentIndex; i < lengthCount - 2; i++) {
                for (int j = i + 1; j < lengthCount - 1; j++) {
                    for (int k = j + 1; k < lengthCount; k++) {
                        if (currentUsedSegments[i] || currentUsedSegments[j] || currentUsedSegments[k])
                            continue;

                        // 检查当前三条线段是否满足勾股定理
                        if (lengths[i] * lengths[i] + lengths[j] * lengths[j] == lengths[k] * lengths[k]) {
                            boolean[] newUsedSegments = currentUsedSegments.clone();
                            newUsedSegments[i] = true;
                            newUsedSegments[j] = true;
                            newUsedSegments[k] = true;

                            // 将新状态压入栈中
                            stack[++stackTop] = new State(i + 1, currentCount + 1, newUsedSegments);
                        }
                    }
                }
            }
        }

        return maxTriangles;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int testCases = scanner.nextInt();

        // 读取和处理每个测试用例
        for (int t = 0; t < testCases; t++) {
            int lengthCount = scanner.nextInt();
            int[] lengths = new int[lengthCount];

            // 读取当前测试用例的线段长度
            for (int i = 0; i < lengthCount; i++)
                lengths[i] = scanner.nextInt();

            // 将线段长度升序排序
            for (int i = 0; i < lengthCount - 1; i++) {
                for (int j = 0; j < lengthCount - i - 1; j++) {
                    if (lengths[j] > lengths[j + 1]) {
                        int temp = lengths[j];
                        lengths[j] = lengths[j + 1];
                        lengths[j + 1] = temp;
                    }
                }
            }

            // 调用nonRecursiveDFS函数并输出结果
            System.out.println(nonRecursiveDFS(lengths));
        }
    }
}