CSES - Coin Combinations I
Author: Michael Cao
In this problem, we are asked the number of ways to achieve some value, , using coins of distinct values where the order of coins does not matter. This is known as the "Unordered Coin Change" problem, which you can read about in CPH Chapter 7 under "Counting the Number of Solutions".
Main Idea
To solve this problem, let equal the number of ways to achieve the sum of values, . Then, for some weight , let's try to use each coin. For , we'll transition from for all , where defines the value of the -th coin.
So, the transitions are:
Warning!
Remember to take your answer mod , as instructed in the problem statement.
Example Code
C++
#include <bits/stdc++.h>using namespace std;using ll = long long;using vi = vector<int>;#define pb push_back#define rsz resize#define all(x) begin(x), end(x)#define sz(x) (int)(x).size()using pi = pair<int, int>;#define f first
Java
Note
An otherwise working solution that uses dp[i] %= m;
instead of
if (dp[i] > M) dp[i] -= M;
may time out on CSES, but would work on USACO,
which gives double time for Java (see line 32 of the solution).
import java.io.*;import java.util.*;public class CountingCoins1 {static BufferedReader r = new BufferedReader(new InputStreamReader(System.in));static PrintWriter pw = new PrintWriter(System.out);public static void main(String[] args) throws IOException {StringTokenizer st = new StringTokenizer(r.readLine());int n = Integer.parseInt(st.nextToken());
Python
This section is not complete.
We don't currently have a Python solution for this problem. Please switch to another language to view the solution code.
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