public StolenItems FindKnackSnapMaxValueWithItems(int capacity, int[] weights, int[] values, int n)
{
//base case
if (n == values.Length || capacity == 0)
{
StolenItems item = new StolenItems();
item.Max = 0;
item.Items = string.Empty;
return(item);
}
if (weights[n] > capacity)
{
//if the current n weight is greater than the capacity, skip n and go for next
return(FindKnackSnapMaxValueWithItems(capacity, weights, values, n + 1));
}
//Get the max value excluding the current for the weight of capacity
StolenItems excludeitem = FindKnackSnapMaxValueWithItems(capacity, weights, values, n + 1);
//Get the max value including the current for the weight of capacity
//since we are includeitem = new StolenItems();
StolenItems includeitem = new StolenItems();
includeitem = FindKnackSnapMaxValueWithItems(capacity - weights[n], weights, values, n + 1);
includeitem.Max = values[n] + includeitem.Max;
StolenItems currentitem = new StolenItems();
//return the max of the including or excluding
if (excludeitem.Max > includeitem.Max)
{
currentitem.Items = excludeitem.Items;
currentitem.Max = excludeitem.Max;
}
else
{
currentitem.Items = includeitem.Items + " , " + values[n];
currentitem.Max = includeitem.Max;
}
return(currentitem);
}
//Logic of this Dynamic Program
//We iterate for each unit of the weight againt each item
//As usual put the first row and column as zero (if there is no weight we can't put any item or if there is no item, there is no value)
//If the item cannot be put into the bag of the weight(w), then put zero
//if the item can fit into bag then take two values
//value1 - one the cell about it cell[row -1, col]
//and value2 - value of the item + (if there are any weight left, then find the left unit for this item and get the value from the row above row m[row -1, [weightleft]
//set max of value1 and value2
//continue till last
//last bottom right will be the answer and that is the maxvalue for using all weight and for all items
//create an another array to keep track of all the matches- this will be used to backtrack the items
//with the backtrack array you can check whether each item is added. It a item is added subtract it's weight and check the next item for the remaining weight
//https://www.youtube.com/watch?v=EH6h7WA7sDw
public StolenItems FindKnackSnapMaxValueWithItemsUsingDP(int[] weight, int[] values, int capacity)
{
//Declare an array with one index greater than given
//Let's m the x-axia as weight and y axis as value
int noofitems = weight.Length;
int[,] maxarray = new int[noofitems + 1, capacity + 1];
int[,] backtrack = new int[noofitems + 1, capacity + 1];
// Build table K[][] in bottom up manner
//noofitem = value.Length...not index
//iterate for ech item
for (int i = 0; i <= noofitems; i++)
{
//each unit of weight
for (int j = 0; j <= capacity; j++)
{
if (i == 0 || j == 0)
{
maxarray[i, j] = 0;
}
//check the item can fit into the bag of capacity j
//int[] weight is index based and we are iterating via length based
else if (weight[i - 1] <= j)
{
//it can fit into the bag
int value1 = maxarray[i - 1, j];
int value2 = values[i - 1] + maxarray[i - 1, (j - weight[i - 1])];
maxarray[i, j] = Math.Max(value1, value2);
//logic for backtrack array..
//if the item is placed in the bag then mark 1 else 0 ( by default it is zero)
if (maxarray[i, j] == value2) //which means this is placed in the bag
{
backtrack[i, j] = 1;
}
}
else
{
//cannot fit
maxarray[i, j] = 0;
}
}
}
StolenItems items = new StolenItems();
items.Max = maxarray[noofitems, capacity];
//We need to find the items
//keep track of remaining capacity in the bag
int w = capacity;
bool[] itemsused = new bool[noofitems];
//check whether each item can be added from last item
//i = 3,2,1
for (int i = noofitems; i > 0; i--)
{
if (backtrack[i, w] == 1)
{
//we are keeping this item in the bag
itemsused[i - 1] = true;
//substract actual weight of the item
// w = w - 1;
w = w - weight[i - 1];
}
else
{
itemsused[i - 1] = false;
}
}
StringBuilder sb = new StringBuilder();
for (int k = 0; k < itemsused.Length; k++)
{
if (itemsused[k])
{
sb.Append(values[k]).Append(",");
}
}
//test this logic use this logic in real world
StringBuilder sb2 = new StringBuilder();
//values will be 0,1,2
int runningcapacity = capacity;
for (int j = 0; j < values.Length; j++)
{
//backtrack array has one extra item so the corresponding value will be j + 1
if (backtrack[j + 1, runningcapacity] == 1)
{
sb2.Append(values[j]).Append(",");
runningcapacity = runningcapacity - weight[j];
}
}
//check sb is equal to sb2
bool test = sb2.Equals(sb);
items.Items = sb.ToString();
return(items);
}