1155. Number of Dice Rolls With Target Sum (Dynamic Programming - Tabulation)

Author: cheehwatang

solutions/1155. Number of Dice Rolls With Target Sum/NumberOfDiceRollsWithTargetSum_Tabulation.java

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+package com.cheehwatang.leetcode;
+
+// Time Complexity  : O(n * k * target),
+// where 'n', 'k' and 'target' are the variables used by the method.
+// For each dice, 'n', we check each values of 'target' to add the number of faces 'k' that can sum to 'target',
+// in a 3 layer nested for-loops.
+//
+// Space Complexity : O(n * target),
+// where 'n' and 'target' are the variables used by the method.
+// We use a matrix of 'n' rows with 'target' columns for tabulation.
+
+public class NumberOfDiceRollsWithTargetSum_Tabulation {
+
+    // Approach:
+    // A dynamic programming problem where there are overlapping subproblem,
+    // for which each roll has possible 1 to k number face-up.
+    // Here, the iterative and tabulation method is used.
+    // By reducing the target by the face-up number each roll (hence n - 1),
+    // the successful sequence of rolls is achieved when n = 0 and target = 0, which forms the base case for the table.
+
+    public int numRollsToTarget(int n, int k, int target) {
+        // As the array is 0-indexed, we need + 1 length to accommodate 'n' and 'target' respectively.
+        int[][] table = new int[n + 1][target + 1];
+        // The seed/base case for successful sequence in the table.
+        table[0][0] = 1;
+        // Iterate through the table to get the result for all possibilities.
+        int modulus = (int) (1e9 + 7);
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < target; j++) {
+                // Skip if the position in the array is 0, meaning nothing to add to the j + 1 to k positions.
+                if (table[i][j] == 0) continue;
+                for (int face = 1; face <= k; face++) {
+                    if (face + j <= target) {
+                        table[i + 1][j + face] = (table[i + 1][j + face] + table[i][j]) % modulus;
+                    }
+                }
+            }
+        }
+        return table[n][target];
+    }
+}