使用背包变体的最佳MLB阵容

Question

我正在编写一个程序,使用背包解决方案找到最佳的MLB阵容.为此,我传递了玩家数据,其中包含玩家计算的价值和工资.作为一个背包问题,工资将是我的"重量".

我的问题是无法选择球员,而是选择最佳阵容.我选择投手,中锋,一垒手,二垒手,三垒手,短暂停站和三名外野手.我能成功地做到这一点.我希望我的"体重"为36,000,但我目前只选择一个总共21,000的阵容.

这是我的背包代码:

CalculateLineUp.prototype.findOptimalLineUp = function(data, capacity) {
  var items = data.data;
  var idxItem   = 0,
      idxCapSpace = 0,
      idxPosition = 0,
      oldMax    = 0,
      newMax    = 0,
      numItems  = items.length,
      weightMatrix  = new Array(numItems+1),
      keepMatrix    = new Array(numItems+1),
      positionArray = new Array("P", "C", "1B", "2B", "3B", "SS", "OF", "OF", "OF"),
      solutionSet   = [];

  // Setup matrices
  for(idxItem = 0; idxItem < numItems + 1; idxItem++){
    weightMatrix[idxItem] = new Array(capacity+1);
    keepMatrix[idxItem]   = new Array(capacity+1);
  }

  // Build weightMatrix from [0][0] -> [numItems-1][capacity-1]
  for (idxItem = 0; idxItem <= numItems; idxItem++){
    for (idxCapSpace = 0; idxCapSpace <= capacity; idxCapSpace++){  

          // Fill top row and left column with zeros
          if (idxItem === 0 || idxCapSpace === 0){
            weightMatrix[idxItem][idxCapSpace] = 0;
          }

          // If item will fit, decide if there's greater value in keeping it,
          // or leaving it
          else if (items[idxItem-1]["Salary"] <= idxCapSpace){
            newMax = items[idxItem-1]["Value"] + weightMatrix[idxItem-1][idxCapSpace-items[idxItem-1]["Salary"]];
            oldMax = weightMatrix[idxItem-1][idxCapSpace];

            // Update the matrices
            if(newMax > oldMax ){ 
              weightMatrix[idxItem][idxCapSpace]  = newMax;
              keepMatrix[idxItem][idxCapSpace]    = 1;

            }
            else{
              weightMatrix[idxItem][idxCapSpace]  = oldMax; 
              keepMatrix[idxItem][idxCapSpace]    = 0;
            }
          }

          //Else, item can't fit; value and weight are the same as before
           //else
             //weightMatrix[idxItem][idxCapSpace] = weightMatrix[idxItem-1][idxCapSpace];
    }
  }

  // Traverse through keepMatrix ([numItems][capacity] -> [1][?])
  // to create solutionSet
  idxCapSpace = capacity;
  idxItem   = numItems;
  for(idxItem; idxItem < capacity; idxItem--){
    if(keepMatrix[idxItem][idxCapSpace] === 1 && !this.filledAllPositions(items[idxItem - 1]["Position"])){
      solutionSet.push(items[idxItem - 1]);
      idxCapSpace = idxCapSpace - items[idxItem - 1]["Salary"];
    }
  }
  return {"maxValue": weightMatrix[numItems][capacity], "set": solutionSet};
};

我是一个公然的错误,我只是没有看到,还是我的逻辑完全脱离了？

Answer 1

您正在检查解决方案集吗？接受位置的逻辑不包含在背包逻辑中，这意味着解决方案集是背包解决方案之上的过滤器。您确实得到了正确的背包解决方案，但是因为在解决方案之上，您正在检查位置是否已被填充，所以从解决方案集中消除了一些项目（争夺相同位置的项目）和总重量减少了。