我正在尝试使用递归来完成n层嵌套的for循环。例如，如果n = 3，则会有3个“级别”。
for(z=0;z<6;z++){
for(y=0;y<6;y++){
for(x=0;x<6;x++){
if (z+y+x==f){
//do something
}
}
}
}
等等。
我似乎无法想出如何将if循环放置在最后的for循环中，以及如何从if语句中访问前面for循环的变量。我知道关于变量嵌套循环的问题已经被问了很多次，我已经查看了所有的答案。但是没有一个能帮助我。
有人能够提供一种使用递归轻松实现此目的的方法吗？请记住，我仍然是C++的初学者，请指点我正确的方向。
用例如下：
编写一个程序来输入骰子数m。该程序将输出可能情况的总数，每个可能n的可能情况以及具有最高概率的n。注意：只读取一个输入m。 n由程序计算
例如，如果用户输入m = 2，则程序应输出
可能情况的总数为36。
可能性有：
2 1
3 2
4 3
.
.
.
12 1
为了提高效率，我避免使用递归。此外，它不使用任何特定的C++语法 - 它也可以在C上良好运行。
我们正在尝试创建N个嵌套的"for"循环。 而不是使用
for(int i = 0; i<max; i++)
for (int j = 0; j<max; j++)
...
我将使用一个数组来替换i、j等变量：i[0]、i[1]，...，i[n-1]。
以下是我的解决方案：
const int n = /*Insert N here: how many loops do you need?*/;
int i[n+1]; // if "n" is not known before hand, then this array will need to be created dynamically.
//Note: there is an extra element at the end of the array, in order to keep track of whether to exit the array.
for (int a=0; a<n+1; a++) {
i[a]=0;
}
int MAX = 79; //That's just an example, if all of the loops are identical: e.g. "for(int i=0; i<79; i++)". If the value of MAX changes for each loop, then make MAX an array instead: (new) int MAX [n]; MAX[0]=10; MAX[1]=20;...;MAX[n-1]=whatever.
int p = 0; //Used to increment all of the indicies correctly, at the end of each loop.
while (i[n]==0) {//Remember, you're only using indicies i[0], ..., i[n-1]. The (n+1)th index, i[n], is just to check whether to the nested loop stuff has finished.
//DO STUFF HERE. Pretend you're inside your nested for loops. The more usual i,j,k,... have been replaced here with i[0], i[1], ..., i[n-1].
//Now, after you've done your stuff, we need to increment all of the indicies correctly.
i[0]++;
// p = 0;//Commented out, because it's replaced by a more efficient alternative below.
while(i[p]==MAX) {//(or "MAX[p]" if each "for" loop is different. Note that from an English point of view, this is more like "if(i[p]==MAX". (Initially i[0]) If this is true, then i[p] is reset to 0, and i[p+1] is incremented.
i[p]=0;
i[++p]++; //increase p by 1, and increase the next (p+1)th index
if(i[p]!=MAX)
p=0;//Alternatively, "p=0" can be inserted above (currently commented-out). This one's more efficient though, since it only resets p when it actually needs to be reset!
}
}
就是这样，希望注释可以清楚地说明它的意图。我认为它应该相当高效——几乎和真正的嵌套for循环一样高效。大部分开销只在开始时发生一次，因此使用递归函数等比其更加高效。
具有多个循环的递归算法的基本结构如下：
void recursiveLoops(vector<int>& indexes, const vector<int>& endPerIndex, int currentIndex) {
if (currentIndex == indexes.size()) {
// This is where the real logic goes.
// indexes[i] contain the value of the i-th index.
} else {
for (indexes[pos] = 0 ; indexes[pos] != endPerIndex[pos] ; indexes[pos]++) {
// Recurse for the next level
recursiveLoops(indexes, endPerIndex, pos+1);
}
}
}
从顶层调用recursiveLoops的设置需要两个向量 - 一个用于索引，另一个用于每个级别的迭代次数。下面的示例设置了三个嵌套循环，在每个级别上迭代5、6和9次：
vector<int> indexes(3, 0);
vector<int> endPerIndex;
endPerIndex.push_back(5);
endPerIndex.push_back(6);
endPerIndex.push_back(9);
recursiveLoops(indexes, endPerIndex, 0);
这里是一个简单的C++示例。首先，我创建了一个包含每个维度范围的向量，称为maxes。如果所有索引的总和为2，则打印“did something”。在这个示例中，我循环z从0到1，y从0到2，x从0到3。
你当然可以让它更整洁。
以下是：
#include <iostream>
#include <vector>
using namespace std;
int f(){
return 2 ;
}
void inner(int depth,vector<int> & numbers,vector<int> & maxes){
if (depth>0){
for(int i=0;i<maxes[depth-1];i++){
numbers[depth-1]=i;
inner(depth-1, numbers,maxes) ;
}
}else{
// calculate sum of x,y,z:
cout << "values are ";
for(int i=0;i<numbers.size();i++){
cout <<numbers[i]<<" ";
}
int thesum(0);
for(int i=0;i<numbers.size();i++){
thesum+=numbers[i];
}
if (thesum==f()){
cout << "did something! ";
}
cout<<endl;
}
}
void donest(){
vector<int> numbers;
numbers.resize(3);
vector<int> maxes;
maxes.push_back(4);
maxes.push_back(3);
maxes.push_back(2);
inner(numbers.size(),numbers,maxes);
}
int main(){
donest();
}
结果：
values are 0 0 0
values are 1 0 0
values are 2 0 0 did something!
values are 3 0 0
values are 0 1 0
values are 1 1 0 did something!
values are 2 1 0
values are 3 1 0
values are 0 2 0 did something!
values are 1 2 0
values are 2 2 0
values are 3 2 0
values are 0 0 1
values are 1 0 1 did something!
values are 2 0 1
values are 3 0 1
values are 0 1 1 did something!
values are 1 1 1
values are 2 1 1
values are 3 1 1
values are 0 2 1
values are 1 2 1
values are 2 2 1
values are 3 2 1
只需为每个递归函数计算深度，并计数到f即可。
void myRecursiveFunc(int depth){
if(depth == f)
//do something
return;
else{
myRecursiveFunc(depth + 1);
}
}
如果你真的想要，你可以使用三个不同的函数来处理 x、y 和 z。
你可以这样写，但是...我不建议。这段代码令人困惑，而且没有任何好处。如果你之所以想这么写是因为你的实际使用情况有很多嵌套循环，那么请考虑不要那样做，因为这是一个设计上的严重问题。
void nested_loop(const int levels, const int comparator, const int level = 0, const int accumulator = 0)
{
if (level < levels) {
for (int i = 0; i < 6; i++) {
nested_loop(levels, comparator, level + 1, accumulator + i);
}
}
else {
if (accumulator == comparator) { // your if (z+y+x==f)
//do something
}
}
}
int main() {
const int levels = 3;
const int f = 42;
nested_loop(levels, f);
}
你对为什么需要这样做非常模糊。作为一个入门解决方案，可能的解决方法是将每个for循环替换为递归函数。
void recursiveX(int zVal, int yVal, int xVal)
{
if(zVal+yVal+xVal == f)...
if(xVal != 0)
recursiveX(zVal, yVal, xVal -1);
}
void recursiveY(int zVal, int yVal)
{
recursiveX(zVal, yVal, 6);
if(yVal != 0)
recursiveY(zVal, yVal-1);
}
void recursiveZ(int val)
{
recursiveY(val, 6);
if(val != 0)
recursiveZ(val-1);
}
...
recursiveZ(6);
int n_loops{3}; //number of nested for loops
int loops_idx[n_loops]; //like i,j,k but in an array
for (int i = 0; i < n_loops; i++)
loops_idx[i]=0;
int max_idx[n_loops]{3,2,4}; // like in for(; i < counter ;), but the counters in an array
bool is_finished = false;
int debug_n_of_execution{0};
while (!is_finished)
{
for (; loops_idx[0]<max_idx[0]; loops_idx[0]++)
{
/*
some code with loops_idx array as i,j,k...
*/
++debug_n_of_execution;
for (int i = 0; i < n_loops; i++)
std::cout<<loops_idx[i]<<" ";
std::cout << "\n";
}
--loops_idx[0]; //to cancel last increment
//Here it will increment the last loop_idx which isn't equal to max_idx[i]-1
//eg. after first above for loop loops_idx will be (max-1, 0, 0)
//So it will be after this loop (0, 1, 0) and start from the beginning...
for (int i = 0; i < n_loops+1; i++) //+1 to know if all loops are finished
{
if (i == n_loops)
{is_finished= true; break;}
if(loops_idx[i]==max_idx[i]-1)
continue;
++loops_idx[i];
for (int j = 0; j < i; j++) //make any previous loop = 0
loops_idx[j]=0;
break;
}
}
//just to check
int debug_perfect_n_of_execution{max_idx[0]};
for (int i = 1; i < n_loops; i++)
debug_perfect_n_of_execution*= max_idx[i];
std::cout<<"Number of execution: "<<debug_n_of_execution<<" = "<<debug_perfect_n_of_execution;
assert(debug_n_of_execution==debug_perfect_n_of_execution);
std::cout << "\nTests Finished";
这里是结果：
0 0 0
1 0 0
2 0 0
0 1 0
1 1 0
2 1 0
0 0 1
1 0 1
2 0 1
0 1 1
1 1 1
2 1 1
0 0 2
1 0 2
2 0 2
0 1 2
1 1 2
2 1 2
0 0 3
1 0 3
2 0 3
0 1 3
1 1 3
2 1 3
Number of execution: 24 = 24
Tests Finished
x[3][2] = {{0, 10}, {5, 20}, {2, 60}};y[3] = {0, 5, 2};#include <stdio.h>
int main(){
// bruteforce
int level = 10;
int start[10] = {0, 0, 0, 0};
int x[10][2] = {{0, 5}, {0, 5}, {0, 5}, {0, 5}};
for (int i = 1;i < level; ++i){
x[i][1] = x[i][1] + 1;
}
while(3>2){
// Your code here
//
printf("%d %d %d %d\n", x[0][0], x[1][0], x[2][0], x[3][0]);
// variable loop code
// ==== Not To Modify ====
int a = 0;
int b = 0;
for(int i = 0;i < level; ++i){
if (x[i][0] >= x[i][1])
{
if(i != level-1){
x[i][0] = start[i];
x[i+1][0] = x[i+1][0] + 1;
}else{
a = 1;
}
b = 1;
}else{
if(b == 0){
x[0][0] = x[0][0] + 1;
b = 1;
}
}
}
if(a == 1){
break;
}
}
return 0;
}