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March 31, 2013 08:32
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Given a list of N coins, their values being in an array A[], return the minimum number of coins required to sum to S (you can use as many coins you want). If it's not possible to sum to S, return -1
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#include <cmath> | |
#include <vector> | |
#include <iostream> | |
using namespace std; | |
// greedy | |
int minCoins_greedy(vector<int> a, int sum) { | |
sort(a.begin(), a.end(), greater<int>()); // sorted in descending order | |
a.erase(unique(a.begin(), a.end()), a.end()); // remove duplicates | |
int ret; | |
for (int i = 0; i < a.size(); i++) { | |
int remains = sum - a[i]; | |
//cout << sum << " - " << a[i] << " = " << remains << endl; | |
if (remains > 0) { | |
ret = minCoins_greedy(a, remains); | |
//cout << "ret: " << ret << endl; | |
if (ret > 0) { | |
cout << a[i] << " + "; | |
return ++ret; | |
} | |
} else if (remains == 0) { | |
cout << a[i] << " + "; | |
return 1; | |
} | |
} | |
return -1; | |
} | |
// dynamic programming | |
#define MIN(a, b) ((a) == -1) ? (b) : min((a),(b)); | |
int minCoins(vector<int> S, int sum) { | |
int setSize = S.size(); | |
int count[setSize+1][sum+1]; | |
// For sum = 0, do not need any coins | |
for (int i = 0; i < setSize+1; i++) | |
count[i][0] = 0; | |
// For empty set, it is impossible to sum to >0 | |
// use -1 represents fail | |
for (int j = 1; j < sum+1; j++) | |
count[0][j] = -1; | |
/* | |
* cost func: | |
* c(n, m) = min( c(n-1, m) , c(n, m-M[n]) + 1 ) | |
* ^^^^^^^^^ ^^^^^^^^^^^^^^^^ | |
* don't take take M[n] | |
*/ | |
for (int i = 1; i < setSize+1; i++) { | |
for (int j = 1; j < sum+1; j++) { | |
if ((j - S[i-1]) >= 0) { | |
count[i][j] = MIN(count[i-1][j], count[i][j-S[i-1]] + 1); | |
} | |
else | |
count[i][j] = count[i-1][j]; | |
} | |
} | |
// uncomment this code to print table | |
for (int i = 0; i <= setSize; i++) | |
{ | |
for (int j = 0; j <= sum; j++) | |
printf ("%4d", count[i][j]); | |
printf("\n"); | |
} | |
return count[setSize][sum]; | |
} | |
int main() { | |
// Input to a sorted vector | |
int size, sum; | |
cout << "input 'size' and 'sum'" << endl; | |
cout << "ex: 4 63" << endl; | |
cin >> size >> sum; | |
cout << "input coins" << endl; | |
cout << "ex: 1 10 30 40" << endl; | |
int* arr; | |
arr = new int[size]; | |
for (int i = 0; i < size; i++) { | |
int c; | |
cin >> c; | |
arr[i] = c; | |
} | |
vector<int> vecArr(arr, arr+size); | |
// Output | |
int out = minCoins(vecArr, sum); | |
//int out = minCoins_greedy(vecArr, sum); | |
cout << endl; | |
if (out > 0) | |
cout << "Minimum " << out << " coins needed" << endl; | |
else | |
cout << "Impossible" << endl; | |
delete[] arr; | |
return 0; | |
} |
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