Add Knapsack

Author: marttp

kotlin/Dynamic Programming/Knapsack.kt

@@ -0,0 +1,22 @@
+fun knapsack(cap: Int, weights: List<Int>, values: List<Int>): Int {
+    val n = values.size
+    // Base case: Set the first column and last row to 0 by
+    // initializing the entire DP table to 0.
+    val dp = Array(n + 1) { IntArray(cap + 1) }
+    // Populate the DP table.
+    for (i in n - 1 downTo 0) {
+        for (c in 1..cap) {
+            // If the item 'i' fits in the current knapsack capacity,
+            // the maximum value at 'dp[i][c]' is the largest of either:
+            // 1. The maximum value if we include item 'i'.
+            // 2. The maximum value if we exclude item 'i'.
+            if (weights[i] <= c) {
+                dp[i][c] = Math.max(values[i] + dp[i + 1][c - weights[i]], dp[i + 1][c])
+            } else {
+                // If it doesn't fit, we have to exclude it.
+                dp[i][c] = dp[i + 1][c]
+            }
+        }
+    }
+    return dp[0][cap]
+}

kotlin/Dynamic Programming/KnapsackOptimized.kt

@@ -0,0 +1,27 @@
+fun knapsackOptimized(cap: Int, weights: List<Int>, values: List<Int>): Int {
+    val n = values.size
+    // Initialize 'prevRow' as the DP values of the row below the
+    // current row.
+    var prevRow = IntArray(cap + 1)
+    for (i in n - 1 downTo 0) {
+        // Set the first cell of the 'currRow' to 0 to set the base
+        // case for this row. This is done by initializing the entire
+        // row to 0.
+        val currRow = IntArray(cap + 1)
+        for (c in 1..cap) {
+            // If item 'i' fits in the current knapsack capacity, the
+            // maximum value at 'currRow[c]' is the largest of either:
+            // 1. The maximum value if we include item 'i'.
+            // 2. The maximum value if we exclude item 'i'.
+            if (weights[i] <= c) {
+                currRow[c] = Math.max(values[i] + prevRow[c - weights[i]], prevRow[c])
+            } else {
+                // If it doesn't fit, we have to exclude it.
+                currRow[c] = prevRow[c]
+            }
+        }
+        // Set 'prevRow' to 'currRow' values for the next iteration.
+        prevRow = currRow
+    }
+    return prevRow[cap]
+}