tasks a-s

Task/Pascals-triangle-Puzzle/Python/pascals-triangle-puzzle-1.py

@@ -0,0 +1,122 @@
+# Pyramid solver
+#            [151]
+#         [   ] [   ]
+#      [ 40] [   ] [   ]
+#   [   ] [   ] [   ] [   ]
+#[ X ] [ 11] [ Y ] [ 4 ] [ Z ]
+#  X -Y + Z = 0
+
+def combine( snl, snr ):
+
+	cl = {}
+	if isinstance(snl, int):
+		cl['1'] = snl
+	elif isinstance(snl, string):
+		cl[snl] = 1
+	else:
+		cl.update( snl)
+
+	if isinstance(snr, int):
+		n = cl.get('1', 0)
+		cl['1'] = n + snr
+	elif isinstance(snr, string):
+		n = cl.get(snr, 0)
+		cl[snr] = n + 1
+	else:
+		for k,v in snr.items():
+			n = cl.get(k, 0)
+			cl[k] = n+v
+	return cl
+
+
+def constrain(nsum, vn ):
+	nn = {}
+	nn.update(vn)
+	n = nn.get('1', 0)
+	nn['1'] = n - nsum
+	return nn
+
+def makeMatrix( constraints ):
+	vmap = set()
+	for c in constraints:
+		vmap.update( c.keys())
+	vmap.remove('1')
+	nvars = len(vmap)
+	vmap = sorted(vmap)		# sort here so output is in sorted order
+	mtx = []
+	for c in constraints:
+		row = []
+		for vv in vmap:
+			row.append(float(c.get(vv, 0)))
+		row.append(-float(c.get('1',0)))
+		mtx.append(row)
+	
+	if len(constraints) == nvars:
+		print 'System appears solvable'
+	elif len(constraints) < nvars:
+		print 'System is not solvable - needs more constraints.'
+	return mtx, vmap
+
+
+def SolvePyramid( vl, cnstr ):
+
+	vl.reverse()
+	constraints = [cnstr]
+	lvls = len(vl)
+	for lvln in range(1,lvls):
+		lvd = vl[lvln]
+		for k in range(lvls - lvln):
+			sn = lvd[k]
+			ll = vl[lvln-1]
+			vn = combine(ll[k], ll[k+1])
+			if sn is None:
+				lvd[k] = vn
+			else:
+				constraints.append(constrain( sn, vn ))
+
+	print 'Constraint Equations:'
+	for cstr in constraints:
+		fset = ('%d*%s'%(v,k) for k,v in cstr.items() )
+		print ' + '.join(fset), ' = 0'
+
+	mtx,vmap = makeMatrix(constraints)
+
+	MtxSolve(mtx)
+
+	d = len(vmap)
+	for j in range(d):
+		print vmap[j],'=', mtx[j][d]
+
+
+def MtxSolve(mtx):
+	# Simple Matrix solver...
+
+	mDim = len(mtx)			# dimension---
+	for j in range(mDim):
+		rw0= mtx[j]
+		f = 1.0/rw0[j]
+		for k in range(j, mDim+1):
+			rw0[k] *= f
+		
+		for l in range(1+j,mDim):
+			rwl = mtx[l]
+			f = -rwl[j]
+			for k in range(j, mDim+1):
+				rwl[k] += f * rw0[k]
+
+	# backsolve part ---
+	for j1 in range(1,mDim):
+		j = mDim - j1
+		rw0= mtx[j]
+		for l in range(0, j):
+			rwl = mtx[l]
+			f = -rwl[j]
+			rwl[j]    += f * rw0[j]
+			rwl[mDim] += f * rw0[mDim]
+
+	return mtx
+
+
+p = [ [151], [None,None], [40,None,None], [None,None,None,None], ['X', 11, 'Y', 4, 'Z'] ]
+addlConstraint = { 'X':1, 'Y':-1, 'Z':1, '1':0 }
+SolvePyramid( p, addlConstraint)

Task/Pascals-triangle-Puzzle/Python/pascals-triangle-puzzle-2.py

@@ -0,0 +1,19 @@
+from csp import Problem
+
+p = Problem()
+pvars = "R2 R3 R5 R6 R7 R8 R9 R10 X Y Z".split()
+# 0-151 is the possible finite range of the variables
+p.addvars(pvars, xrange(152))
+p.addrule("R7 == X + 11")
+p.addrule("R8 == Y + 11")
+p.addrule("R9 == Y + 4")
+p.addrule("R10 == Z + 4")
+p.addrule("R7 + R8 == 40")
+p.addrule("R5 == R8 + R9")
+p.addrule("R6 == R9 + R10")
+p.addrule("R2 == 40 + R5")
+p.addrule("R3 == R5 + R6")
+p.addrule("R2 + R3 == 151")
+p.addrule("Y == X + Z")
+for sol in p.xsolutions():
+    print [sol[k] for k in "XYZ"]

Task/Pascals-triangle-Puzzle/Python/pascals-triangle-puzzle-3.py

@@ -0,0 +1 @@
+[5, 13, 8]