# MIXTURES spoj Solution - Correct, Optimal and Working

``````/*
* MIXTURES.cpp
*
*  Created on: Nov 4, 2014
*      Author: Arpit Bhayani
*/

#include <map>
#include <cmath>
#include <set>
#include <cstring>
#include <stack>
#include <vector>
#include <queue>
#include <list>
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <climits>

using namespace std;

#define si(x) scanf("%d" , &x)
#define sl(x) scanf("%ld" , &x)
#define sll(x) scanf("%lld" , &x)
#define sc(x) scanf("%c" , &x)
#define ss(x) scanf("%s" , &x)

#define pi(x) printf("%d\n" , x)
#define pl(x) printf("%ld\n" , x)
#define pll(x) printf("%lld\n" , x)
#define pc(x) printf("%c\n" , x)
#define ps(x) printf("%s\n" , x)

#define fup(i,a,b) for(int i=a;i<b;i++)
#define fdn(i,a,b) for(int i=a;i>=b;i--)

#define DEBUG 0
#define gc getchar
#define ll long long

#define SEPERATOR " : "

#define trace1(a) cout << #a << SEPERATOR << a << endl;
#define trace2(a,b) cout << #a << SEPERATOR << a << SEPERATOR << #b << SEPERATOR << b << endl;
#define trace3(a,b,c) cout << #a << SEPERATOR << a << SEPERATOR << #b << SEPERATOR << b << #c << SEPERATOR << c << endl;

void scanint(ll int &x) {
register ll int c = gc();
x = 0;
for (; (c < 48 || c > 57); c = gc())
;
for (; c > 47 && c < 58; c = gc()) {
x = (x << 1) + (x << 3) + c - 48;
}
}

int i = 0;
char ch;
while ((ch = getchar()) != '\n') {
str[i++] = ch;
}
str[i] = '\0';
return i;
}

#define ASIZE 10
int array[110];
int hash[110][110];

int sum(int a, int b) {
int sum = 0;
for (int i = a; i <= b; i++) {
sum = (sum + array[i]) % 100;
}
return sum;
}

int mcm(int i, int j) {

if (i == j) {
hash[i][j] = 0;
return 0;
}

if (hash[i][j] != -1) {
return hash[i][j];
}

int result = INT_MAX;
for (int k = i; k < j; k++) {
int temp = mcm(i, k) + mcm(k + 1, j) + sum(i, k) * sum(k + 1, j);
result = min(result, temp);
}

hash[i][j] = result;
return result;

}

int main(int argc, char * argv[]) {

int n;
while (scanf("%d", &n) != EOF) {
for (int i = 0; i < n; i++) {
si(array[i]);
}

for (int i = 0; i < 110; i++) {
for (int j = 0; j < 110; j++) {
hash[i][j] = -1;
}
}
cout << mcm(0, n - 1) << endl;

}

return 0;
}
``````