Computes minimum cost for converting one string into another

Author: daniel-s-ingram

strings/min-cost-string-conversion.py

@@ -0,0 +1,124 @@
+from __future__ import print_function
+
+try:
+	xrange			#Python 2
+except NameError:
+	xrange = range	#Python 3
+
+def compute_transform_tables(X, Y, cC, cR, cD, cI):
+'''
+Algorithm for calculating the most cost-efficient sequence for converting one string into another.
+The only allowed operations are
+---Copy character with cost cC
+---Replace character with cost cR
+---Delete character with cost cD
+---Insert character with cost cI
+'''
+	X = list(X)
+	Y = list(Y)
+	m = len(X)
+	n = len(Y)
+
+	costs = [[0 for _ in xrange(n+1)] for _ in xrange(m+1)]
+	ops = [[0 for _ in xrange(n+1)] for _ in xrange(m+1)]
+
+	for i in xrange(1, m+1):
+		costs[i][0] = i*cD
+		ops[i][0] = 'D%c' % X[i-1]
+
+	for i in xrange(1, n+1):
+		costs[0][i] = i*cI
+		ops[0][i] = 'I%c' % Y[i-1]
+
+	for i in xrange(1, m+1):
+		for j in xrange(1, n+1):
+			if X[i-1] == Y[j-1]:
+				costs[i][j] = costs[i-1][j-1] + cC
+				ops[i][j] = 'C%c' % X[i-1]
+			else:
+				costs[i][j] = costs[i-1][j-1] + cR
+				ops[i][j] = 'R%c' % X[i-1] + str(Y[j-1])
+
+			if costs[i-1][j] + cD < costs[i][j]:
+				costs[i][j] = costs[i-1][j] + cD
+				ops[i][j] = 'D%c' % X[i-1]
+
+			if costs[i][j-1] + cI < costs[i][j]:
+				costs[i][j] = costs[i][j-1] + cI
+				ops[i][j] = 'I%c' % Y[j-1]
+
+	return costs, ops
+
+def assemble_transformation(ops, i, j):
+	if i == 0 and j == 0:
+		seq = []
+		return seq
+	else:
+		if ops[i][j][0] == 'C' or ops[i][j][0] == 'R':
+			seq = assemble_transformation(ops, i-1, j-1)
+			seq.append(ops[i][j])
+			return seq
+		elif ops[i][j][0] == 'D':
+			seq = assemble_transformation(ops, i-1, j)
+			seq.append(ops[i][j])
+			return seq
+		else:
+			seq = assemble_transformation(ops, i, j-1)
+			seq.append(ops[i][j])
+			return seq
+
+if __name__ == '__main__':
+	from time import sleep
+	_, operations = compute_transform_tables('Python', 'Algorithms', -1, 1, 2, 2)
+
+	m = len(operations)
+	n = len(operations[0])
+	sequence = assemble_transformation(operations, m-1, n-1)
+	
+	file = open('min_cost.txt', 'w')
+
+	string = list('Python')
+	i = 0
+	cost = 0
+	for op in sequence:
+		print ''.join(string)
+		if op[0] == 'C':
+			file.write('%-16s' % 'Copy %c' % op[1])
+			file.write('\t\t\t' + ''.join(string))
+			file.write('\r\n')
+			
+			i += 1
+			cost -= 1
+		elif op[0] == 'R':
+			string[i] = op[2]
+
+			file.write('%-16s' % ('Replace %c' % op[1] + ' with ' + str(op[2])))
+			file.write('\t\t' + ''.join(string))
+			file.write('\r\n')
+			
+			i += 1
+			cost += 1
+		elif op[0] == 'D':
+			string.pop(i)
+
+			file.write('%-16s' % 'Delete %c' % op[1])
+			file.write('\t\t\t' + ''.join(string))
+			file.write('\r\n')
+			
+			i += 1
+			cost += 2
+		else:
+			string.insert(i, op[1])
+
+			file.write('%-16s' % 'Insert %c' % op[1])
+			file.write('\t\t\t' + ''.join(string))
+			file.write('\r\n')
+			
+			i += 1
+			cost += 2
+
+	print ''.join(string)
+	print 'Cost: ', cost
+	
+	file.write('\r\nMinimum cost: ' + str(cost))
+	file.close()