你如何从给定的N个数字中测试所有可能的加法组合,使它们加起来得到给定的最终数字?
一个简单的例子:
要添加的数字集:N ={1,5,22,15,0,…} 期望结果:12345
你如何从给定的N个数字中测试所有可能的加法组合,使它们加起来得到给定的最终数字?
一个简单的例子:
要添加的数字集:N ={1,5,22,15,0,…} 期望结果:12345
当前回答
我不喜欢上面看到的Javascript解决方案。下面是我使用部分应用、闭包和递归构建的一个:
好的,我主要关心的是,如果组合数组能满足目标要求,希望这样你就能找到剩下的组合了
这里只需要设置目标并传递组合数组。
function main() {
const target = 10
const getPermutationThatSumT = setTarget(target)
const permutation = getPermutationThatSumT([1, 4, 2, 5, 6, 7])
console.log( permutation );
}
我提出的当前实现
function setTarget(target) {
let partial = [];
return function permute(input) {
let i, removed;
for (i = 0; i < input.length; i++) {
removed = input.splice(i, 1)[0];
partial.push(removed);
const sum = partial.reduce((a, b) => a + b)
if (sum === target) return partial.slice()
if (sum < target) permute(input)
input.splice(i, 0, removed);
partial.pop();
}
return null
};
}
其他回答
建议回答:
下面是一个使用es2015生成器的解决方案:
function* subsetSum(numbers, target, partial = [], partialSum = 0) {
if(partialSum === target) yield partial
if(partialSum >= target) return
for(let i = 0; i < numbers.length; i++){
const remaining = numbers.slice(i + 1)
, n = numbers[i]
yield* subsetSum(remaining, target, [...partial, n], partialSum + n)
}
}
使用生成器实际上非常有用,因为它允许您在找到有效子集时立即暂停脚本执行。这与没有生成器(即缺乏状态)的解决方案形成对比,后者必须遍历每个数字子集
我不喜欢上面看到的Javascript解决方案。下面是我使用部分应用、闭包和递归构建的一个:
好的,我主要关心的是,如果组合数组能满足目标要求,希望这样你就能找到剩下的组合了
这里只需要设置目标并传递组合数组。
function main() {
const target = 10
const getPermutationThatSumT = setTarget(target)
const permutation = getPermutationThatSumT([1, 4, 2, 5, 6, 7])
console.log( permutation );
}
我提出的当前实现
function setTarget(target) {
let partial = [];
return function permute(input) {
let i, removed;
for (i = 0; i < input.length; i++) {
removed = input.splice(i, 1)[0];
partial.push(removed);
const sum = partial.reduce((a, b) => a + b)
if (sum === target) return partial.slice()
if (sum < target) permute(input)
input.splice(i, 0, removed);
partial.pop();
}
return null
};
}
c++版本的相同算法
#include <iostream>
#include <list>
void subset_sum_recursive(std::list<int> numbers, int target, std::list<int> partial)
{
int s = 0;
for (std::list<int>::const_iterator cit = partial.begin(); cit != partial.end(); cit++)
{
s += *cit;
}
if(s == target)
{
std::cout << "sum([";
for (std::list<int>::const_iterator cit = partial.begin(); cit != partial.end(); cit++)
{
std::cout << *cit << ",";
}
std::cout << "])=" << target << std::endl;
}
if(s >= target)
return;
int n;
for (std::list<int>::const_iterator ai = numbers.begin(); ai != numbers.end(); ai++)
{
n = *ai;
std::list<int> remaining;
for(std::list<int>::const_iterator aj = ai; aj != numbers.end(); aj++)
{
if(aj == ai)continue;
remaining.push_back(*aj);
}
std::list<int> partial_rec=partial;
partial_rec.push_back(n);
subset_sum_recursive(remaining,target,partial_rec);
}
}
void subset_sum(std::list<int> numbers,int target)
{
subset_sum_recursive(numbers,target,std::list<int>());
}
int main()
{
std::list<int> a;
a.push_back (3); a.push_back (9); a.push_back (8);
a.push_back (4);
a.push_back (5);
a.push_back (7);
a.push_back (10);
int n = 15;
//std::cin >> n;
subset_sum(a, n);
return 0;
}
Javascript版本:
function subsetSum(numbers, target, partial) { var s, n, remaining; partial = partial || []; // sum partial s = partial.reduce(function (a, b) { return a + b; }, 0); // check if the partial sum is equals to target if (s === target) { console.log("%s=%s", partial.join("+"), target) } if (s >= target) { return; // if we reach the number why bother to continue } for (var i = 0; i < numbers.length; i++) { n = numbers[i]; remaining = numbers.slice(i + 1); subsetSum(remaining, target, partial.concat([n])); } } subsetSum([3,9,8,4,5,7,10],15); // output: // 3+8+4=15 // 3+5+7=15 // 8+7=15 // 5+10=15
下面是一个更好的版本,具有更好的输出格式和c++ 11特性:
void subset_sum_rec(std::vector<int> & nums, const int & target, std::vector<int> & partialNums)
{
int currentSum = std::accumulate(partialNums.begin(), partialNums.end(), 0);
if (currentSum > target)
return;
if (currentSum == target)
{
std::cout << "sum([";
for (auto it = partialNums.begin(); it != std::prev(partialNums.end()); ++it)
cout << *it << ",";
cout << *std::prev(partialNums.end());
std::cout << "])=" << target << std::endl;
}
for (auto it = nums.begin(); it != nums.end(); ++it)
{
std::vector<int> remaining;
for (auto it2 = std::next(it); it2 != nums.end(); ++it2)
remaining.push_back(*it2);
std::vector<int> partial = partialNums;
partial.push_back(*it);
subset_sum_rec(remaining, target, partial);
}
}