c_cpp 计算网格上从左上角单元格到右下角单元格的最小成本路径

Posted 2021-05-14

// $ g++ mincost.cpp --std=c++11
#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>

#undef RECURSION
#undef MEMOIZATION
#undef DYNAMIC_PROGRAMMING
#undef RUN

#define RECURSION 1
#define MEMOIZATION 2
#define DYNAMIC_PROGRAMMING 3
// #define RUN RECURSION
// #define RUN MEMOIZATION
#define RUN DYNAMIC_PROGRAMMING

#if RUN == RECURSION

int
MinCost(std::vector<std::vector<int>>& cost,
        unsigned int row, unsigned int col)
{
  assert(row < cost.size() && col < cost[row].size());

  if (row == 0 && col == 0) {
    return cost[row][col];
  } else if (row == 0) {
    return cost[row][col] + MinCost(cost, row, col-1);
  } else if (col == 0) {
    return cost[row][col] + MinCost(cost, row-1, col);
  }
  return cost[row][col] + std::min(MinCost(cost, row, col-1),
                                   MinCost(cost, row-1, col));
}

int
MinCost(std::vector<std::vector<int>>& cost)
{
  assert(cost.size());
  unsigned int rightmost = cost.size()-1;
  assert(cost[rightmost].size());
  unsigned int bottommost = cost[rightmost].size() - 1;
  return MinCost(cost, rightmost, bottommost);
}

#elif RUN == MEMOIZATION

int
MinCost(std::vector<std::vector<int>>& cost,
        unsigned int row, unsigned int col,
        std::vector<std::vector<int>>& memo)
{
  assert(row < cost.size() && col < cost[row].size() &&
         memo.size() == cost.size() && memo[row].size() == cost[row].size());

  if (!memo[row][col]) {
    if (row == 0 && col == 0) {
      memo[row][col] = cost[row][col];
    } else if (row == 0) {
      memo[row][col] = cost[row][col] + MinCost(cost, row, col-1, memo);
    } else if (col == 0) {
      memo[row][col] = cost[row][col] + MinCost(cost, row-1, col, memo);
    } else {
      memo[row][col] = cost[row][col] +
                       std::min(MinCost(cost, row, col-1, memo),
                                MinCost(cost, row-1, col, memo));
    }
  }

  return memo[row][col];
}

int
MinCost(std::vector<std::vector<int>>& cost)
{
  assert(cost.size());
  unsigned int rightmost = cost.size()-1;
  assert(cost[rightmost].size());
  unsigned int bottommost = cost[rightmost].size() - 1;

  std::vector<std::vector<int>>
    memo (cost.size(), std::vector<int>(cost[rightmost].size(), 0));

  return MinCost(cost, rightmost, bottommost, memo);
}

#else // RUN == DYNAMIC_PROGRAMMING

int
MinCost(std::vector<std::vector<int>>& cost)
{
  assert(cost.size() && cost[0].size());

  unsigned int rightmost = cost.size()-1;
  unsigned int bottommost = cost[rightmost].size() - 1;

  unsigned int sum = 0;
  unsigned int x = 0, y = 0; // Starting cell.

  // Find the minimal cost path from top-left cell to the bottom-right cell.
  while (true) {
    sum += cost[x][y];
    if (x == rightmost && y == bottommost) {
      break;
    } else if (x == rightmost) {
      ++y;

    } else if (y == bottommost) {
      ++x;
    } else {
      if (cost[x+1][y] < cost[x][y+1]) {
        ++x;
      } else {
        ++y;
      }
    }
  }

  return sum;
}

#endif

int main()
{
  // Calculate the minimal cost path from the top-left cell
  // to the bottom-right cell on a grid.
  std::vector<std::vector<int>> cost {
    { 1, 3, 5, 8 },
    { 4, 2, 1, 7 },
    { 4, 3, 2, 3 }
  };

  std::cout << MinCost(cost) << std::endl;

  return 0;
}