Day 27: try dp

Author: thatguyintech

day27/countingBinomialCoefficient.py

@@ -1,48 +1,97 @@
-def countingBinomialCoefficient(num, prime):
-    prevRow = []
-    count = 0
-   
-    for rowNum in xrange(num+1):
-        row = [1] * (rowNum+1)
-       
-        for i in xrange(len(prevRow)-1):
-            row[i+1] = prevRow[i] + prevRow[i+1]
-
-        for j in xrange(len(row)):
-            if row[j] % prime != 0:
-                count += 1
-        prevRow = row
-
-    return count
-
-def testCountingBinomialCoefficient():
+class BinomialCoefficient(object):
+    def __init__(self):
+        self.coefficients = {}
+        self.notDivisible = {}
+
+    # returns the binomial expansion coefficient for TOTAL choose SUBGROUP
+    # aka C(total, subgroup)
+    def getBinomialCoefficient(self, total, subgroup):
+        if (total, subgroup) in self.coefficients:
+            return self.coefficients[(total, subgroup)]
+
+        if total == subgroup or subgroup == 0:
+            self.coefficients[(total, subgroup)] = 1
+            return 1
+
+        return self.getBinomialCoefficient(total-1, subgroup) + self.getBinomialCoefficient(total-1, subgroup-1)
+
+    # returns the number of coefficients in Pascal's triangle up to
+    # the NUMth row of the triangle that are not divisible by PRIME
+    def binomialCoefficientsNotDivisibleByPrime(self, num, prime):
+        if num == 0:
+            self.notDivisible[prime] = {0: 1}
+            return 1
+
+        if prime in self.notDivisible and num in self.notDivisible[prime]:
+            return self.notDivisible[prime][num]
+
+        notDivisibleThisRow = len([i for i in xrange(num+1) if self.getBinomialCoefficient(num, i) % prime != 0])
+
+        self.notDivisible[prime][num] = self.binomialCoefficientsNotDivisibleByPrime(num-1, prime) + notDivisibleThisRow
+        return self.notDivisible[prime][num]
+
+def testGetBinomialCoefficient(binomialCalculator):
+    b = binomialCalculator
+
+    assert b.getBinomialCoefficient(0, 0) == 1
+
+    assert b.getBinomialCoefficient(1, 0) == 1
+    assert b.getBinomialCoefficient(1, 1) == 1
+
+    assert b.getBinomialCoefficient(2, 0) == 1
+    assert b.getBinomialCoefficient(2, 1) == 2
+    assert b.getBinomialCoefficient(2, 2) == 1
+
+    assert b.getBinomialCoefficient(3, 0) == 1
+    assert b.getBinomialCoefficient(3, 1) == 3
+    assert b.getBinomialCoefficient(3, 2) == 3
+    assert b.getBinomialCoefficient(3, 3) == 1
+
+    assert b.getBinomialCoefficient(4, 0) == 1
+    assert b.getBinomialCoefficient(4, 1) == 4
+    assert b.getBinomialCoefficient(4, 2) == 6
+    assert b.getBinomialCoefficient(4, 3) == 4
+    assert b.getBinomialCoefficient(4, 4) == 1
+
+    assert b.getBinomialCoefficient(5, 0) == 1
+    assert b.getBinomialCoefficient(5, 1) == 5
+    assert b.getBinomialCoefficient(5, 2) == 10
+    assert b.getBinomialCoefficient(5, 3) == 10
+    assert b.getBinomialCoefficient(5, 4) == 5
+    assert b.getBinomialCoefficient(5, 5) == 1
+
+def testCountBinomialCoefficientsNotDivisibleByPrime(binomialCalculator):
+    b = binomialCalculator
+
     # prime = 2
-    assert countingBinomialCoefficient(0, 2) == 1
-    assert countingBinomialCoefficient(1, 2) == 3
-    assert countingBinomialCoefficient(2, 2) == 5
-    assert countingBinomialCoefficient(3, 2) == 9
-    assert countingBinomialCoefficient(4, 2) == 11
-    assert countingBinomialCoefficient(5, 2) == 15
+    assert b.binomialCoefficientsNotDivisibleByPrime(0, 2) == 1
+    assert b.binomialCoefficientsNotDivisibleByPrime(1, 2) == 3
+    assert b.binomialCoefficientsNotDivisibleByPrime(2, 2) == 5
+    assert b.binomialCoefficientsNotDivisibleByPrime(3, 2) == 9
+    assert b.binomialCoefficientsNotDivisibleByPrime(4, 2) == 11
+    assert b.binomialCoefficientsNotDivisibleByPrime(5, 2) == 15
 
     # prime = 5
-    assert countingBinomialCoefficient(0, 5) == 1
-    assert countingBinomialCoefficient(1, 5) == 3
-    assert countingBinomialCoefficient(2, 5) == 6
-    assert countingBinomialCoefficient(3, 5) == 10
-    assert countingBinomialCoefficient(4, 5) == 15
-    assert countingBinomialCoefficient(5, 5) == 17
-    assert countingBinomialCoefficient(6, 5) == 21
+    assert b.binomialCoefficientsNotDivisibleByPrime(0, 5) == 1
+    assert b.binomialCoefficientsNotDivisibleByPrime(1, 5) == 3
+    assert b.binomialCoefficientsNotDivisibleByPrime(2, 5) == 6
+    assert b.binomialCoefficientsNotDivisibleByPrime(3, 5) == 10
+    assert b.binomialCoefficientsNotDivisibleByPrime(4, 5) == 15
+    assert b.binomialCoefficientsNotDivisibleByPrime(5, 5) == 17
+    assert b.binomialCoefficientsNotDivisibleByPrime(6, 5) == 21
 
     # prime = 7
-    assert countingBinomialCoefficient(5, 7) == 21 
+    assert b.binomialCoefficientsNotDivisibleByPrime(5, 7) == 21 
 
-    # BIG DATA (these don't finish running with the brute force implementation)
-    # assert countingBinomialCoefficient(999999999, 7) == 2129970655314432
-    # assert countingBinomialCoefficient(879799878, 17) == 6026990181372288
-    # assert countingBinomialCoefficient(879799878, 19) == 8480245105257600
+    # BIG DATA
+    assert b.binomialCoefficientsNotDivisibleByPrime(999999999, 7)  == 2129970655314432
+    assert b.binomialCoefficientsNotDivisibleByPrime(879799878, 17) == 6026990181372288
+    assert b.binomialCoefficientsNotDivisibleByPrime(879799878, 19) == 8480245105257600
 
 def main():
-    testCountingBinomialCoefficient()
+    b = BinomialCoefficient()
+    testGetBinomialCoefficient(b)
+    testCountBinomialCoefficientsNotDivisibleByPrime(b)
 
 if __name__ == "__main__":
     main()