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
Thank you.. ephemient
我已经将上述逻辑从python转换为php..
<?php
$data = array(array(2,3,5,10,15),array(4,6,23,15,12),array(23,34,12,1,5));
$maxsum = 25;
print_r(bestsum($data,$maxsum)); //function call
function bestsum($data,$maxsum)
{
$res = array_fill(0, $maxsum + 1, '0');
$res[0] = array(); //base case
foreach($data as $group)
{
$new_res = $res; //copy res
foreach($group as $ele)
{
for($i=0;$i<($maxsum-$ele+1);$i++)
{
if($res[$i] != 0)
{
$ele_index = $i+$ele;
$new_res[$ele_index] = $res[$i];
$new_res[$ele_index][] = $ele;
}
}
}
$res = $new_res;
}
for($i=$maxsum;$i>0;$i--)
{
if($res[$i]!=0)
{
return $res[$i];
break;
}
}
return array();
}
?>
其他回答
func sum(array : [Int]) -> Int{
var sum = 0
array.forEach { (item) in
sum = item + sum
}
return sum
}
func susetNumbers(array :[Int], target : Int, subsetArray: [Int],result : inout [[Int]]) -> [[Int]]{
let s = sum(array: subsetArray)
if(s == target){
print("sum\(subsetArray) = \(target)")
result.append(subsetArray)
}
for i in 0..<array.count{
let n = array[i]
let remaning = Array(array[(i+1)..<array.count])
susetNumbers(array: remaning, target: target, subsetArray: subsetArray + [n], result: &result)
}
return result
}
var resultArray = [[Int]]()
let newA = susetNumbers(array: [1,2,3,4,5], target: 5, subsetArray: [],result:&resultArray)
print(resultArray)
这个问题的一个迭代c++堆栈解决方案。与其他迭代解决方案不同的是,它不会对中间序列进行不必要的复制。
#include <vector>
#include <iostream>
// Given a positive integer, return all possible combinations of
// positive integers that sum up to it.
std::vector<std::vector<int>> print_all_sum(int target){
std::vector<std::vector<int>> output;
std::vector<int> stack;
int curr_min = 1;
int sum = 0;
while (curr_min < target) {
sum += curr_min;
if (sum >= target) {
if (sum == target) {
output.push_back(stack); // make a copy
output.back().push_back(curr_min);
}
sum -= curr_min + stack.back();
curr_min = stack.back() + 1;
stack.pop_back();
} else {
stack.push_back(curr_min);
}
}
return output;
}
int main()
{
auto vvi = print_all_sum(6);
for (auto const& v: vvi) {
for(auto const& i: v) {
std::cout << i;
}
std::cout << "\n";
}
return 0;
}
输出print_all_sum (6):
111111
11112
1113
1122
114
123
15
222
24
33
c#版本的@msalvadores代码的答案
void Main()
{
int[] numbers = {3,9,8,4,5,7,10};
int target = 15;
sum_up(new List<int>(numbers.ToList()),target);
}
static void sum_up_recursive(List<int> numbers, int target, List<int> part)
{
int s = 0;
foreach (int x in part)
{
s += x;
}
if (s == target)
{
Console.WriteLine("sum(" + string.Join(",", part.Select(n => n.ToString()).ToArray()) + ")=" + target);
}
if (s >= target)
{
return;
}
for (int i = 0;i < numbers.Count;i++)
{
var remaining = new List<int>();
int n = numbers[i];
for (int j = i + 1; j < numbers.Count;j++)
{
remaining.Add(numbers[j]);
}
var part_rec = new List<int>(part);
part_rec.Add(n);
sum_up_recursive(remaining,target,part_rec);
}
}
static void sum_up(List<int> numbers, int target)
{
sum_up_recursive(numbers,target,new List<int>());
}
Perl版本(前导答案):
use strict;
sub subset_sum {
my ($numbers, $target, $result, $sum) = @_;
print 'sum('.join(',', @$result).") = $target\n" if $sum == $target;
return if $sum >= $target;
subset_sum([@$numbers[$_ + 1 .. $#$numbers]], $target,
[@{$result||[]}, $numbers->[$_]], $sum + $numbers->[$_])
for (0 .. $#$numbers);
}
subset_sum([3,9,8,4,5,7,10,6], 15);
结果:
sum(3,8,4) = 15
sum(3,5,7) = 15
sum(9,6) = 15
sum(8,7) = 15
sum(4,5,6) = 15
sum(5,10) = 15
Javascript版本:
const subsetSum = (numbers, target, partial = [], sum = 0) => { If (sum < target) 数字。forEach((num, i) => subsetSum(数字。Slice (i + 1), target, partial.concat([num]), sum + num)); Else if (sum == target) console.log(的总和(% s) = % s, partial.join(),目标); } subsetSum([3、9、8、4、5、7、10、6],15);
Javascript一行实际返回结果(而不是打印它):
const subsetSum = (n, t, p = [], s = 0, r = []) = > (s < t ? n.forEach ((l i) = > subsetSum (n.slice (i + 1), t,[……p、l], s + l r)): s = = t ? r.push (p): 0, r); console.log (subsetSum([3、9、8、4、5、7、10、6],15));
我最喜欢的是带有回调的一行语句:
const subsetSum = (n, t,辛西娅·布雷齐尔,p =黑铝,s = 0) = > s & lt; t ? n.forEach ((l, i) = > subsetSum (n.slice (i + 1)、t、辛西娅·布雷齐尔,黑... p, l铝,s + l)): s = = t ?辛西娅·布雷齐尔(p): 0; 子集([3,9,8,4,5,7,10,6],15,console.log);
这类似于硬币更换问题
public class CoinCount
{
public static void main(String[] args)
{
int[] coins={1,4,6,2,3,5};
int count=0;
for (int i=0;i<coins.length;i++)
{
count=count+Count(9,coins,i,0);
}
System.out.println(count);
}
public static int Count(int Sum,int[] coins,int index,int curSum)
{
int count=0;
if (index>=coins.length)
return 0;
int sumNow=curSum+coins[index];
if (sumNow>Sum)
return 0;
if (sumNow==Sum)
return 1;
for (int i= index+1;i<coins.length;i++)
count+=Count(Sum,coins,i,sumNow);
return count;
}
}