搬砖问题枚举搜索可视化 - C语言程序设计基础

方案A · 三重循环全部枚举 (穷举所有组合)

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for (men = 0; men <= n; men++) {
  for (women = 0; women <= n; women++) {
    for (children = 0; children <= n; children++) {
      if (men + women + children == n &&
          6*men + 4*women + children == 2*n) { ... }
    } } }

men (男: 3块) 0 外层循环

women (女: 2块) 0 中层循环

children (小: 半块) 0 内层穷举

人数式: 0+0+0 = 0 (目标: 30) 不符

搬砖式: 6(0)+4(0)+0 = 0 (目标: 60) 不符

序号	men	women	children	人数和	砖式和	判定

等待开始 · 预计 (n+1)³ 次尝试

方案B · 二重循环 + 计算 children (代数化简剪枝)

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for (men = 0; men <= n / 3; men++) {  // 缩小范围
  for (women = 0; women <= n / 2; women++) {
    children = n - men - women;  // 直接代数计算
    if (children >= 0 &&
        6*men + 4*women + children == 2*n) { ... }
  } }

men (0 ~ n/3) 0 外层枚举

women (0 ~ n/2) 0 内层枚举

children (计算值得出) 30 无需第三重循环

代数算式: children = 30 - 0 - 0 = 30 (天然保和) ≥0有效

搬砖式: 6(0)+4(0)+30 = 30 (目标: 60) 不符

序号	men	women	children	搬砖和	目标 2n	判定

等待开始 · 预计 (n/3+1)×(n/2+1) 次尝试