The Coin Change Problem

Problem Statement

How many different ways can you make change for an amount, given a list of coins? In this problem, your code will need to efficiently compute the answer.

Problem Statement

Write a program that, given two arguments to STDIN

• a list of coins c1, c2, c3, ..
• and an amount n

Prints out how many different ways you can make change from the coins to STDOUT.

The problem can be formally stated:

Given a value N, if we want to make change for N cents, and we have infinite supply of each of C = { C1, C2, .. , Cm} valued coins, how many ways can we make the change? The order of coins doesn’t matter.

Example 1:

For N = 4 and C = {1,2,3} there are four solutions: {1,1,1,1},{1,1,2},{2,2},{1,3}

So given the input

1, 2, 3 4

your program should output:

4

用动态规划实现，三个循环搞定  dp[j][k]表示大小为 k 的数分成 j 部分之和

for(int i=0;i<A.size();i++)
   for(int j=1;j<=m;j++)
	for(int k=A[i];k<=N;k++) dp[j][k]+=dp[j-1][k-A[i]];