elements-of-programming-interviews/Drawing_skylines.cpp at master · koth/elements-of-programming-interviews · GitHub

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// Copyright (c) 2013 Elements of Programming Interviews. All rights reserved.

#include <algorithm>
#include <cassert>
#include <iostream>
#include <random>
#include <vector>

using std::cout;
using std::default_random_engine;
using std::endl;
using std::random_device;
using std::uniform_int_distribution;
using std::vector;

struct Skyline;
void merge_intersect_skylines(vector<Skyline>* merged, Skyline* a, int* a_idx,
                              Skyline* b, int* b_idx);
vector<Skyline> merge_skylines(vector<Skyline>* L, vector<Skyline>* R);
vector<Skyline> drawing_skylines_helper(const vector<Skyline>& skylines,
                                        int start, int end);

// @include
struct Skyline {
  int left, right, height;
};

vector<Skyline> drawing_skylines(vector<Skyline> skylines) {
  return drawing_skylines_helper(skylines, 0, skylines.size());
}

vector<Skyline> drawing_skylines_helper(const vector<Skyline>& skylines,
                                        int start, int end) {
  if (end - start <= 1) {  // 0 or 1 skyline, just copy it.
    return {skylines.cbegin() + start, skylines.cbegin() + end};
  }
  int mid = start + ((end - start) >> 1);
  auto L = drawing_skylines_helper(skylines, start, mid);
  auto R = drawing_skylines_helper(skylines, mid, end);
  return merge_skylines(&L, &R);
}

vector<Skyline> merge_skylines(vector<Skyline>* L, vector<Skyline>* R) {
  int i = 0, j = 0;
  vector<Skyline> merged;

  while (i < L->size() && j < R->size()) {
    if ((*L)[i].right < (*R)[j].left) {
      merged.emplace_back((*L)[i++]);
    } else if ((*R)[j].right < (*L)[i].left) {
      merged.emplace_back((*R)[j++]);
    } else if ((*L)[i].left <= (*R)[j].left) {
      merge_intersect_skylines(&merged, &(*L)[i], &i, &(*R)[j], &j);
    } else {  // L[i].left > R[j].left.
      merge_intersect_skylines(&merged, &(*R)[j], &j, &(*L)[i], &i);
    }
  }

  copy(L->cbegin() + i, L->cend(), back_inserter(merged));
  copy(R->cbegin() + j, R->cend(), back_inserter(merged));
  return merged;
}

void merge_intersect_skylines(vector<Skyline>* merged, Skyline* a, int* a_idx,
                              Skyline* b, int* b_idx) {
  if (a->right <= b->right) {
    if (a->height > b->height) {
      if (b->right != a->right) {
        merged->emplace_back(*a), ++*a_idx;
        b->left = a->right;
      } else {
        ++*b_idx;
      }
    } else if (a->height == b->height) {
      b->left = a->left, ++*a_idx;
    } else {  // a->height < b->height.
      if (a->left != b->left) {
        merged->emplace_back(Skyline{a->left, b->left, a->height});
      }
      ++*a_idx;
    }
  } else {  // a->right > b->right.
    if (a->height >= b->height) {
      ++*b_idx;
    } else {
      if (a->left != b->left) {
        merged->emplace_back(Skyline{a->left, b->left, a->height});
      }
      a->left = b->right;
      merged->emplace_back(*b), ++*b_idx;
    }
  }
}
// @exclude

int main(int argc, char* argv[]) {
  default_random_engine gen((random_device())());
  // Random test 2000 times.
  for (int times = 0; times < 2000; ++times) {
    int n;
    if (argc == 2) {
      n = atoi(argv[1]);
    } else {
      uniform_int_distribution<int> dis(1, 5000);
      n = dis(gen);
    }
    vector<Skyline> A;
    for (int i = 0; i < n; ++i) {
      uniform_int_distribution<int> left_dis(0, 999);
      int left = left_dis(gen);
      uniform_int_distribution<int> right_dis(left, left + 200);
      int right = right_dis(gen);
      uniform_int_distribution<int> height_dis(0, 99);
      int height = height_dis(gen);
      A.emplace_back(Skyline{left, right, height});
    }
    vector<Skyline> ans = drawing_skylines(A);
    cout << "n = " << n << endl;
    // just check there is no overlap.
    for (int i = 0; i < ans.size(); ++i) {
      assert(ans[i].left <= ans[i].right);
      if (i > 0) {
        assert(ans[i - 1].right <= ans[i].left);
        assert(ans[i - 1].right != ans[i].left ||
               ans[i - 1].height != ans[i].height);
      }
    }
  }
  return 0;
}