数学趣题——寻找假币

递归分治二分查找法

   1: #include "stdio.h"

   2:  

   3: int getFalseCoin(int coin[], int low, int high)

   4: {

   5:     int i, sum1 = 0, sum2 = 0, sum3 = 0;

   6:  

   7:     if(low + 1 == high)

   8:     {

   9:         if(coin[low] < coin[high]) return low + 1;

  10:         else return high + 1;

  11:     }

  12:  

  13:     if((high - low + 1) % 2 == 0)                    /*n是偶数*/

  14:     {

  15:         for(i = low; i <= low + (high - low) / 2; i++)

  16:             sum1 = sum1 + coin[i];               /*前半段和*/

  17:  

  18:         for(i = low + (high - low) / 2 + 1; i <= high; i++)

  19:             sum2 = sum2 + coin[i];               /*后半段和*/

  20:  

  21:         if(sum1 < sum2) return getFalseCoin(coin, low, low + (high - low) / 2);

  22:  

  23:         if(sum1 > sum2) return getFalseCoin(coin, low + (high - low) / 2 + 1, high);

  24:     }

  25:  

  26:     if((high - low + 1) % 2 != 0)

  27:     {

  28:         for(i = low; i <= low + (high - low) / 2 - 1; i++)

  29:             sum1 = sum1 + coin[i];               /*前半段和*/

  30:  

  31:         for(i = low + (high - low) / 2 + 1; i <= high; i++)

  32:             sum2 = sum2 + coin[i];               /*后半段和*/

  33:  

  34:         sum3 = coin[low+(high-low)/2];

  35:  

  36:         if(sum1 < sum2)

  37:             return getFalseCoin(coin, low, low + (high - low) / 2 - 1);

  38:  

  39:         if(sum1 > sum2)

  40:             return getFalseCoin(coin, low + (high - low) / 2 + 1, high);

  41:  

  42:         if(sum1 + sum3 == sum2 + sum3) return low + (high - low) / 2 + 1;

  43:     }

  44:  

  45: }

  46:  

  47: int main()

  48: {

  49:     int coin[30] = {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2};

  50:     printf("The %dth coin is false\n", getFalseCoin(coin, 0, 29));

  51:     return 0;

  52: }