Create find-the-number-of-possible-ways-for-an-event.py

Author: kamyu104

Python/find-the-number-of-possible-ways-for-an-event.py

@@ -0,0 +1,31 @@
+# Time:  precompute: O(max_n^2 + max_y * min(max_n, max_x))
+#        runtime:    O(min(n, x))
+# Space: O(max_n^2 + max_y * min(max_n, max_x))
+
+MOD = 10**9+7
+MAX_N = MAX_X = MAX_Y = 1000
+R = min(MAX_N, MAX_X)
+NCR = [[0]*(MAX_N+1) for _ in xrange(MAX_N+1)]
+DP = [[0]*(MAX_N+1) for _ in xrange(MAX_N+1)]
+NCR[0][0] = DP[0][0] = 1
+for i in xrange(1, MAX_N+1):
+    NCR[i][0] = 1
+    for j in xrange(1, i+1):
+        NCR[i][j] = (NCR[i-1][j]+NCR[i-1][j-1])%MOD
+        DP[i][j] = (DP[i-1][j]*j+DP[i-1][j-1]*j)%MOD
+
+POW = [[1]*(R+1) for _ in xrange(MAX_Y+1)]
+for i in xrange(1, MAX_Y+1):
+    for j in xrange(1, R+1):
+        POW[i][j] = (POW[i][j-1]*i)%MOD
+
+# dp, combinatorics
+class Solution(object):
+    def numberOfWays(self, n, x, y):
+        """
+        :type n: int
+        :type x: int
+        :type y: int
+        :rtype: int
+        """
+        return reduce(lambda accu, x: (accu+x)%MOD, (NCR[x][i]*DP[n][i]*POW[y][i] for i in xrange(1, min(n, x)+1)), 0)