Greedy algorithm for finding minimum numbers of stops

Question

Mr X is traveling by car on an expressway. Suppose there are several gas (petrol) stations on the way: at distances 0 = d0 < d1 < d2 < ... < dn from the starting point d0.

Mr X’scar, when full, can travel a distance D >= max{di+1 - di} . Mr X wants to minimize the number of stops he makes to fill gas.

Devise an greedy algorithm that return min numbers of stops needed.

Please add what you have tried. This isn't a code writing service. — Grice, Oct 23 '14 at 17:46
A greedy algorithm in this case would start at d0 then travel to di < d0 + D. In other words, the last station he would reach before he run out of gas. And then repeat from that station. — Adam Burry, Oct 23 '14 at 17:55
@AdamBurry Please don't encourage these people by helping them. They need to do their own homework, not fill the site with crap questions. — Oblivious Sage, Oct 23 '14 at 17:57

Adam Burry · Accepted Answer · 2014-10-24T03:52:05.773

This is the sort of thing it is asking for.

GCC 4.8.3: g++ -Wall -Wextra -std=c++0x -g main.cpp

#include <algorithm>
#include <iostream>
#include <stdexcept>
#include <vector>

int count_stops(int D, const std::vector<int>& d) {
  if (d.size() < 2) { throw std::logic_error("Vector too small."); }

  auto p = std::begin(d);
  auto count = 0;

  while (p != --std::end(d)) {
    // Greedy: go as far as I can on this tank of gas.
    auto n = --std::find_if(p, std::end(d), [=](int x) {
      return *p + D < x; });
    // The specification says we do not need to worry about this...
    if (p == n) { throw std::logic_error("D too small."); }
    p = n;
    ++count; }

  return count; }


int main(int, char* []) {
  auto D = 16;
  auto d = std::vector<int> { 0, 5, 15, 30, 32, 33, 37, 49, 53, 59, 61 };

  std::cout << "stops: " << count_stops(D, d) << "\n";
  return 0; }

This problem is problem 17.2-4 from Cormen, Leiserson, and Rivest, "Introduction to Algorithms", 1990. There is a detailed solution here: http://people.cis.ksu.edu/~subbu/Papers/Minimum%20Stops.pdf — Adam Burry, Oct 27 '14 at 12:46

Greedy algorithm for finding minimum numbers of stops

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