Data update

Task/Knapsack-problem-Continuous/Fortran/knapsack-problem-continuous-2.f

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+! Fractional knapsack: butcher's shop problem.
+! Items may be cut; greedy optimum is achieved by sorting on value/weight
+! ratio descending, then filling the knapsack in that order.
+program butcher
+    use iso_fortran_env, only: real64
+    implicit none
+
+    integer, parameter :: NITEMS = 9
+    real(real64), parameter :: CAPACITY = 15.0_real64
+
+    character(len=10), parameter :: name(NITEMS) = [ &
+        "beef      ", "pork      ", "ham       ", "greaves   ", &
+        "flitch    ", "brawn     ", "welt      ", "salami    ", &
+        "sausage   " ]
+
+    real(real64), parameter :: weight(NITEMS) = &
+        [ 3.8_real64, 5.4_real64, 3.6_real64, 2.4_real64, 4.0_real64, &
+          2.5_real64, 3.7_real64, 3.0_real64, 5.9_real64 ]
+
+    real(real64), parameter :: price(NITEMS) = &
+        [ 36.0_real64, 43.0_real64, 90.0_real64, 45.0_real64, 30.0_real64, &
+          56.0_real64, 67.0_real64, 95.0_real64, 98.0_real64 ]
+
+    real(real64) :: ratio(NITEMS), fraction(NITEMS)
+    real(real64) :: remaining, total_value, taken
+    integer      :: order(NITEMS), i, j, tmp
+
+    ! Compute value-per-kg ratios
+    do i = 1, NITEMS
+        ratio(i) = price(i) / weight(i)
+    end do
+
+    ! Sort indices by ratio descending (insertion sort)
+    order = [(i, i = 1, NITEMS)]
+    do i = 2, NITEMS
+        j = i
+        do while (j > 1 .and. ratio(order(j)) > ratio(order(j-1)))
+            tmp = order(j); order(j) = order(j-1); order(j-1) = tmp
+            j = j - 1
+        end do
+    end do
+
+    ! Greedy fill
+    fraction    = 0.0_real64
+    remaining   = CAPACITY
+    total_value = 0.0_real64
+
+    do i = 1, NITEMS
+        if (remaining <= 0.0_real64) exit
+        j = order(i)
+        taken = min(weight(j), remaining)
+        fraction(j) = taken / weight(j)
+        total_value = total_value + fraction(j) * price(j)
+        remaining   = remaining - taken
+    end do
+
+    ! Report
+    write(*, '(a)') "Fractional knapsack -- butcher's shop (capacity 15 kg)"
+    write(*, '(a)') repeat('-', 57)
+    write(*, '(a10, 2x, a10, 2x, a10, 2x, a10, 2x, a10)') &
+        "Item", "Weight kg", "Price", "Taken kg", "Value"
+    write(*, '(a)') repeat('-', 57)
+
+    do i = 1, NITEMS
+        j = order(i)
+        if (fraction(j) > 0.0_real64) then
+            write(*, '(a10, 2x, f9.1, 2x, f9.2, 2x, f9.4, 2x, f9.2)') &
+                trim(name(j)), weight(j), price(j), &
+                fraction(j) * weight(j), fraction(j) * price(j)
+        end if
+    end do
+
+    write(*, '(a)') repeat('-', 57)
+    write(*, '(a10, 2x, f9.4, 2x, 10x, 2x, 10x, 2x, f9.2)') &
+        "Total", CAPACITY - remaining, total_value
+
+end program butcher