Create Marbles.cpp

Marbles.cpp

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+#include <bits/stdc++.h>
+using namespace std;
+#define ll long long
+
+ll x, y, d;
+void extendedEuclid(ll a, ll b) {
+    if(b==0) { x=1; y=0; d=a; return;}
+    extendedEuclid(b, a%b);
+    ll y1 = x-(a/b)*y;
+    x = y;
+    y = y1;
+}
+
+int main() {
+    ll v,n1,n2,c1,c2;
+    while(scanf("%lld",&v),v){
+        scanf("%lld %lld %lld %lld",&c1,&n1,&c2,&n2);
+        extendedEuclid(n1,n2);
+        if (v%d != 0) {
+            printf("failed\n");
+        } else {
+            // to get to ax + by = v
+            x *= v/d;
+            y *= v/d;
+            // two equations of Linear Diophantine
+            /* x = x0 + (b/d)n, y = y0 − (a/d)n, where n is an integer */
+
+            // derivation of n based on the fact that x and y has to be positive
+            // x0 + (b/d)n >= 0, solve for n: we get n >= -x0*d/b
+            // y0 - (a/d)n >= 0, solve for n: we get n <= y0*a/b
+            // putting together x0*d/b <= n <= y0*d/b
+            n2 /= d, n1 /= d; // divide first to prevent overflow
+            ll lowerbound=ceil(-(double)x/n2);
+            ll upperbound=floor((double)y/n1);
+            if(lowerbound<=upperbound) {
+                // compare cost
+                ll res1 = c1*(x+n2*lowerbound) + c2*(y-n1*lowerbound);
+                ll res2 = c1*(x+n2*upperbound) + c2*(y-n1*upperbound);
+                if (res1 < res2) {
+                    printf("%lld %lld\n",(x+n2*lowerbound), (y-n1*lowerbound));
+                } else {
+                    printf("%lld %lld\n",(x+n2*upperbound), (y-n1*upperbound));
+                }
+            } else
+                printf("failed\n");
+        }
+    }
+}