problem 2396

Solutions/2396_같은 길이 막대기 만들기.cpp

@@ -0,0 +1,107 @@
+#include <cassert>
+#include <cctype>
+#include <climits>
+#include <cmath>
+#include <cstdio>
+#include <cstdlib>
+#include <cstring>
+#include <ctime>
+
+#include <algorithm>
+#include <array>
+#include <bitset>
+#include <deque>
+#include <functional>
+#include <iomanip>
+#include <iostream>
+#include <iterator>
+#include <limits>
+#include <list>
+#include <map>
+#include <numeric>
+#include <queue>
+#include <set>
+#include <sstream>
+#include <stack>
+#include <string>
+#include <unordered_map>
+#include <vector>
+
+using namespace std;
+
+bool skip;  // Flag for quick return from backtracking's pruning
+
+void backtracking(
+    vector<int>& count,     // Count of sticks per length
+    const int largest,      // The largest length
+    const int n,            // Number of sticks
+    const int target,       // The possible answer to be tested
+    int sum = 0,            // Sum of lengths for current partition
+    int cnt = 0,            // Count of sticks used
+    int last = 50           // The length of last stick used
+) {
+    if (sum == target && cnt == n) {
+        // Answer found, print and exit right away
+        cout << target << '\n';
+        exit(0);
+    }
+    if (sum == target) {
+        // A partition is complete, start a new partition
+        sum = 0;
+        last = largest;
+    }
+
+    // [Pruning 4] To avoid duplicate chekcing, fill the rest of partition with only equal length or smaller sticks
+    // [Pruning 5] The possible sticks to choose are of length <= `target - sum`
+    for (int len = min(last, target - sum); len >= 1; len--) {
+        if (count[len] > 0) {
+            count[len]--;
+            backtracking(count, largest, n, target, sum + len, cnt + 1, len);
+            count[len]++;
+            if (skip) {
+                // Non-promising case
+                return;
+            }
+            // [Pruning 6] Failed to make a new partition using `len`, no need to check further
+            if (sum == 0) {
+                // [Pruning 7] Failed to make the first partition, `target` can not be the answer
+                if (cnt == 0) {
+                    skip = true;
+                }
+                return;
+            }
+        }
+    }
+}
+
+int main() {
+    cin.tie(nullptr);
+    ios_base::sync_with_stdio(false);
+
+    int n;
+    cin >> n;
+
+    int len;
+    int largest = 0;        // The largest stick's length
+    int sum = 0;            // Sum of all sticks' lengths
+    vector<int> count(51);  // Count of sticks per length
+    for (int i = 0; i < n; i++) {
+        cin >> len;
+        count[len]++;
+        largest = max(largest, len);
+        sum += len;
+    }
+
+    // [Pruning 1] The smallest possible answer is the length of the largest stick
+    // [Pruning 2] If no answer is present until `sum / 2`, the answer is `sum` (all sticks together)
+    for (int test = largest; test <= sum / 2; test++) {
+        // [Pruning 3] Only divisors of `sum` are the possible answers
+        if (sum % test == 0) {
+            skip = false;
+            backtracking(count, largest, n, test);
+        }
+    }
+    cout << sum << '\n';
+
+    return 0;
+}