Lecture 122: Number of Dice Rolls with Target Sum

Lectures/Lecture_122/Lecture_Codes/README.md

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+# Lecture Codes
+
+|  **Problem**  |  **Solution**  |  **Level**  |
+|:--------------|:--------------:|:-----------:|
+|  [Dice throw](https://www.geeksforgeeks.org/problems/dice-throw5349/1)  |  [Solution1](), [Solution2](), [Solution3](), [Solution4]()  |  Medium  |

Lectures/Lecture_122/Lecture_Codes/dice_throw_1.cpp

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+// Recursion [TLE]
+
+class Solution {
+    public:
+    long long solve(int dice, int faces, int target) {
+        // base cases
+        if (target < 0) {
+            return 0;
+        }
+
+        if (dice == 0 && target != 0) {
+            return 0;
+        }
+
+        if (target == 0 && dice != 0) {
+            return 0;
+        }
+
+        if (dice == 0 && target == 0) {
+            return 1;
+        }
+
+        // calculating all possible ways for find target sum
+        int ans = 0;
+
+        for (int i=1; i<=faces; i++) {
+            ans += solve(dice-1, faces, target-i);
+        }
+
+        return ans;
+
+    }
+
+    long long noOfWays(int m, int n, int x) {
+        // code here
+        return solve(n, m, x);
+    }
+};

Lectures/Lecture_122/Lecture_Codes/dice_throw_2.cpp

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+// Recursion + Memoization
+
+class Solution {
+    public:
+    long long solve(int dice, int faces, int target, vector<vector<long long>> &dp) {
+        // base cases
+        if (target < 0) {
+            return 0;
+        }
+
+        if (dice == 0 && target != 0) {
+            return 0;
+        }
+
+        if (target == 0 && dice != 0) {
+            return 0;
+        }
+
+        if (dice == 0 && target == 0) {
+            return 1;
+        }
+
+        if (dp[dice][target] != -1) {
+            return dp[dice][target];
+        }
+
+        // calculating all possible ways for find target sum
+        long long ans = 0;
+
+        for (int i=1; i<=faces; i++) {
+            ans += solve(dice-1, faces, target-i, dp);
+        }
+
+        return dp[dice][target] = ans;
+
+    }
+
+    long long noOfWays(int m, int n, int x) {
+        // code here
+        vector<vector<long long>> dp(n+1, vector<long long>(x+1, -1));
+        return solve(n, m, x, dp);
+    }
+};

Lectures/Lecture_122/Lecture_Codes/dice_throw_3.cpp

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+// Tabulation Method
+
+class Solution {
+    public:
+    long long solve(int d, int f, int t) {
+        vector<vector<long long>> dp(d+1, vector<long long>(t+1, 0));
+
+        dp[0][0] = 1;
+
+        for (int dice=1; dice<=d; dice++) {
+            for (int target=1; target<=t; target++) {
+                // calculating all possible ways for find target sum
+                long long ans = 0;
+
+                for (int i=1; i<=f; i++) {
+                    if (target-i >= 0) {
+                        ans += dp[dice-1][target-i];
+                    }
+                }
+
+                dp[dice][target] = ans;
+            }
+        }
+
+        return dp[d][t];
+
+    }
+
+    long long noOfWays(int m, int n, int x) {
+        // code here
+        return solve(n, m, x);
+    }
+};

Lectures/Lecture_122/Lecture_Codes/dice_throw_4.cpp

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+// Space Optimization
+
+class Solution {
+    public:
+    long long solve(int d, int f, int t) {
+        vector<long long> prev(t+1, 0);
+        vector<long long> curr(t+1, 0);
+
+        prev[0] = 1;
+
+        for (int dice=1; dice<=d; dice++) {
+            for (int target=1; target<=t; target++) {
+                // calculating all possible ways for find target sum
+                long long ans = 0;
+
+                for (int i=1; i<=f; i++) {
+                    if (target-i >= 0) {
+                        ans += prev[target-i];
+                    }
+                }
+
+                curr[target] = ans;
+            }
+            prev = curr;
+        }
+
+        return prev[t];
+
+    }
+
+    long long noOfWays(int m, int n, int x) {
+        // code here
+        return solve(n, m, x);
+    }
+};