Careercup | Chapter 7

7.4 Write methods to implement the multiply, subtract, and divide operations for integers. Use only the add operator.

比较简单。但是要封装得好。

7.5 Given two squares on a two-dimensional plane, find a line that would cut these two squares in half. Assume that the top and the bottom sides of the square run parallel to the x-axis.

怎样写得简洁。要解决：

1. 怎么把多种情况综全考虑？

这类题就是先把special case想法，再写算法。

7.6 Given a two-dimensional graph with points on it, find a line which passes the most number of points.

见此。当时没考虑精度的问题。

 int findMaxLine(vector<int> &points) {
     int max = ;
     int dup = ;
     map<int, int> counts;
     double epison = 0.0001;

     for (int i = ; i < points.size(); ++i) {
         counts.clear();
         dup = ;
         int m = ;
         for (int j = i + ; j < points.size(); ++j) {
             if (points[i].x == points[j].x && points[i].y == points[j].y) {
                 dup++;
             } else if (points[i].x == points[j].x) {
                 counts[]++;
                 if (counts[] > m) m = counts[];
             } else {
                 double k = (points[i].y - points[j].y) * 1.0 / (points[i].x - points[j].x);
                 counts[(int)(k/epison)]++;
                 if (counts[int)(k/epison)] > m) m = counts[int)(k/epison)];
             }
         }
         if (m + dup > max) max = m + dup;
     }
     return max;
 }

7.7 Design an algorithm to find the kth number such that the only prime factors are 3, 5, and 7.

 int findKthMagicNumber(int k) {
     vector<queue<int> > queues();
     queues[].push();

     for (int i = ; i < k; ++i) {
         int minIndex = , minNumber;
         for (int j = ; j < ; ++j) {
             if (!queues[j].empty() && queues[j].front() < queues[minIndex].front()) minIndex = j;
         }
         minNumber = queues[minIndex].front();
         for (int j = minIndex; j < ; ++j) {
             queues[j].push(minNumber * nums[j]);
         }
         queues[minIndex].pop();
     }
     return minNumber;
 }