Merge pull request prabhupant#280 from imehar/master

Added a question in dynamic programming

Author: prabhupant

algorithms/dynamic_programming/dice.py

@@ -0,0 +1,24 @@
+'''
+Given n dices each with m faces, numbered from 1 to m,
+find the number of ways to get a given sum X.
+X is the summation of values on each face when all the dice are thrown.
+
+'''
+
+dp = [[-1 for i in range(x+1)] for j in range(n+1)]
+
+
+def num_of_ways(m, n, x):
+    if x == 0 and n == 0:
+        return 1
+    if x < 0 or n == 0:
+        return 0
+    if dp[n][x] != -1:
+        return dp[n][x]
+
+    ans = 0
+    for i in range(1, m + 1):
+        ans += num_of_ways(m, n - 1, x - i)
+
+    dp[n][x] = ans
+    return ans