COIN CHANGE PROBLEM ( DE Shaw archives)
Problem
Given a value N, if we want to make change for N cents, and we have an infinite supply of each of S = { S1, S2, .. , Sm} valued coins, how many ways can we make the change? The order of coins doesn’t matter.
For example, for N = 4 and S = {1,2,3}, there are four solutions: {1,1,1,1},{1,1,2},{2,2},{1,3}. So output should be 4. For N = 10 and S = {2, 5, 3, 6}, there are five solutions: {2,2,2,2,2}, {2,2,3,3}, {2,2,6}, {2,3,5} and {5,5}. So the output should be 5.
Time Limit: 5
Memory Limit: 256
Source Limit:
Explanation
Example 1:
Input:
n = 4 , m = 3
S[] = {1,2,3}
Output: 4
Explanation: Four Possible ways are:
{1,1,1,1},{1,1,2},{2,2},{1,3}.
Example 2:
Input:
n = 10 , m = 4
S[] ={2,5,3,6}
Output: 5
Explanation: Five Possible ways are:
{2,2,2,2,2}, {2,2,3,3}, {2,2,6}, {2,3,5} and {5,5}.
Contributers:
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