Solved problem 10705 - The Fun Number System from UVA

Author: AliOsm

UVA/10705 - The Fun Number System.cpp

@@ -0,0 +1,81 @@
+/*
+  Idea:
+    - Recursion with pruning.
+    - We can try to put 0 or 1 in each place in the binary representation
+      of the number, but we need to check that if we put 1 and we can not
+      reach the number `n` in the future we can skip this branch.
+*/
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int const N = 65;
+char s[N];
+int t, k, sol[N];
+long long n;
+long long pos[N], neg[N], cpos[N], cneg[N];
+
+bool rec(int idx, long long num) {
+  if(idx == k) {
+    if(n == num) {
+      for(int i = 0; i < k; ++i)
+        printf("%d", sol[i]);
+      puts("");
+      return true;
+    }
+
+    return false;
+  }
+
+  sol[idx] = 1;
+  if(s[idx] == 'p') {
+    if(num + pos[idx] - (cneg[k] - cneg[idx]) > n) {
+      sol[idx] = 0;
+      if(rec(idx + 1, num))
+        return true;
+    } else {
+      if(rec(idx + 1, num + pos[idx]))
+        return true;
+    }
+  } else {
+    if(num - neg[idx] + (cpos[k] - cpos[idx]) < n) {
+      sol[idx] = 0;
+      if(rec(idx + 1, num))
+        return true;
+    } else {
+      if(rec(idx + 1, num - neg[idx]))
+        return true;
+    }
+  }
+
+  return false;
+}
+
+int main() {
+  scanf("%d", &t);
+  while(t-- != 0) {
+    for(int i = 0; i < k; ++i)
+      pos[i] = neg[i] = 0;
+
+    scanf("%d", &k);
+    scanf("%s", s);
+    scanf("%lld", &n);
+
+    for(int i = 0; i < k; ++i)
+      if(s[i] == 'p')
+        pos[i] = (1llu << ((k - 1) - i));
+      else
+        neg[i] = (1llu << ((k - 1) - i));
+
+    for(int i = 1; i <= k; ++i) {
+      cpos[i] = pos[i - 1] + cpos[i - 1];
+      cneg[i] = neg[i - 1] + cneg[i - 1];
+    }
+
+    if(!rec(0, 0))
+      puts("Impossible");
+  }
+  
+  return 0;
+}

UVA/README.md

@@ -113,6 +113,7 @@
 - [10608 - Friends](https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1549)
 - [10611 - The Playboy Chimp](https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1552)
 - [10673 - Play with Floor and Ceil](https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1614)
+- [10705 - The Fun Number System](https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1646)
 - [10717 - Mint](https://uva.onlinejudge.org/index.php?option=onlinejudge&page=show_problem&problem=1658)
 - [10721 - Bar Codes](https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1662)
 - [10731 - Test](https://uva.onlinejudge.org/index.php?option=onlinejudge&Itemid=99999999&page=show_problem&problem=1672)