有重復數字的組合問題

Description:

描述：

This is a standard interview problem to make some combination of the numbers whose sum equals to a given number using backtracking.

這是一個標準的面試問題，它使用回溯功能將總和等于給定數字的數字進行某種組合。

Problem statement:

問題陳述：

Given a set of positive numbers and a number, your task is to find out the combinations of the numbers from the set whose summation equals to the given number. You can use the numbers repeatedly to make the combination.

給定一組正數和一個數字，您的任務是從集合中找出總和等于給定數字的數字組合。 您可以重復使用數字進行組合。

Input:Test case TT no. of N values and corresponding N positive numbers and the Number.E.g.332 3 51232 7 51441 2 3 45Constrains:1 <= T <= 5001 <= N <= 201 <= A[i] <= 91 <= Number<= 50Output:Print all the combination which summation equals to the given number.

Example

例

Input:N=3Set[ ]=2 3 5Number=12Output:2 2 2 2 2 22 2 2 3 32 2 3 52 5 53 3 3 3

Explanation with example:

舉例說明：

Let there is a set S of positive numbers N and a positive number.

設一組正數N和一個正數S。

For pre-requisite, we are recommending you to go to our article combinational sum problem.

對于先決條件，我們建議您轉到我們的文章組合總和問題 。

Making some combinations repeatedly using a number in such a way that the summation of that combination results that given number is a problem of combination and we will solve this problem using backtracking approach.

重復使用數字進行一些組合，使得該組合的總和導致給定數字是組合的問題，我們將使用回溯方法解決該問題。

Let, f(i) = function to insert the is^th number into the combinational subset

In this case we will consider two cases to solve the problem,

在這種情況下，我們將考慮兩種情況來解決該問題，

We will consider i^th element into the part of our combination subset until the sum greater the given number (f(i)).

我們將考慮^第 i ^個元素進入組合子集的一部分，直到總和大于給定數( f(i) )。

We will not consider ith element into the part of our combination subset (not f(i)).

我們不會在組合子集的一部分( 不是f(i) )中考慮第ith個元素。

And every time we will check the current sum with the number. Each of the time we will count the number of occurrence and the also the combinations.

并且每次我們將用數字檢查當前總和。 每次，我們將計算發生的次數以及組合。

Let,f(i) = function to insert the i^th number into the combinational subset

For the input:

對于輸入：

S[] = {2, 3, 5}Number = 12

Here from every (not f(2)) there will be two edges (f(3)) and (not f(3)) again from (not f(3)) there will be ( f(5)) and (not f(5)). Here in this case we will discard that edges which have a current sum greater than the given number and make a count to those numbers which are equal to the given number.

在每個(非f(2))中將有兩個邊(f(3))和(非f(3))從(非f(3))再有(f(5))和(非f(5)) 。 在這種情況下，我們將丟棄當前總和大于給定數字的那些邊，并對等于給定數字的那些數字進行計數。

C++ implementation:

C ++實現：

#include <bits/stdc++.h> using namespace std;void combination(int* arr, int n, int num, int pos, int curr_sum, vector<vector<int> >& v, vector<int> vi, set<vector<int> >& s) {if (num < curr_sum)return;if (num == curr_sum && s.find(vi) == s.end()) {s.insert(vi);v.push_back(vi);return;}//go for the next elements for combinationfor (int i = pos; i < n; i++) {if (curr_sum + arr[i] <= num) {vi.push_back(arr[i]);combination(arr, n, num, i, curr_sum + arr[i], v, vi, s);vi.pop_back();}} }//print the vector void print(vector<vector<int> > v) {for (int i = 0; i < v.size(); i++) {for (int j = 0; j < v[i].size(); j++) {cout << v[i][j] << " ";}cout << endl;} }void combinational_sum(int* arr, int n, int num) {vector<vector<int> > v;vector<int> vi;int pos = 0;int curr_sum = 0;set<vector<int> > s;combination(arr, n, num, pos, curr_sum, v, vi, s);print(v); }int main() {int t;cout << "Test Case : ";cin >> t;while (t--) {int n, num;cout << "Enter the value of N : ";cin >> n;int arr[n];cout << "Enter the values : ";for (int i = 0; i < n; i++) {cin >> arr[i];}sort(arr, arr + n);cout << "Enter the number : ";cin >> num;combinational_sum(arr, n, num);}return 0; }

Output

輸出量

Test Case : 3 Enter the value of N : 3 Enter the values : 2 3 5 Enter the number : 12 2 2 2 2 2 2 2 2 2 3 3 2 2 3 5 2 5 5 3 3 3 3 Enter the value of N : 3 Enter the values : 2 7 5 Enter the number : 14 2 2 2 2 2 2 2 2 2 5 5 2 5 7 7 7 Enter the value of N : 4 Enter the values : 1 2 3 4 Enter the number : 5 1 1 1 1 1 1 1 1 2 1 1 3 1 2 2 1 4 2 3

翻譯自: https://www.includehelp.com/icp/combinational-sum-problem-with-repetition-of-digits.aspx

有重復數字的組合問題

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