算法2013110702

题设：以1、2、5、10元为基本单位，求将任意X元分解的所有组合。

解法：利用递归与动态规划。

# make changes for value with units [0, pos]def makeChanges(value, units, pos, cache):assert value >= 0assert len(units) >= 1assert pos >= 0aKey = (value, pos)if (cache.has_key(aKey)):return cache[aKey]if pos == 0:if value%units[0] == 0:result = [[value/units[0]]]else:result = []else:result = []subValue = valuei = 0while True:subResult = makeChanges(subValue, units, pos-1, cache)for subItem in subResult:subItem.append(i)result.append(subItem)subValue -= units[pos]i += 1if subValue < 0:breakcache[aKey] = resultreturn result# get changes for value with unitsdef getChanges(value, units):assert value >= 0assert len(units) >= 1return makeChanges(value, units, len(units)-1, {})units = [1, 2, 5, 10]value = 20print getChanges(value, units)

附：在线代码测试http://ideone.com/v0nIAZ