查找可以在树中折断的边数,以使结果两棵树的按位或在C ++中相等
概念
对于具有m个节点且与每个节点关联的数目的给定树,我们可以破坏任何树边缘,这将导致形成2棵新树。在这里,我们必须以这种方式计算边的数量,以使在破坏该边后构造的两棵树中存在的节点的按位“或”相等。应该注意的是,每个节点的值≤10^6。
输入项
values[]={1, 3, 1, 3} 1 / | \ 2 3 4
输出结果
2
在这里,可以断开1和2之间的边,结果两棵树的按位或为3。
同样,也可以断开1和4之间的边缘。
方法
在这里,上述问题可以通过实现简单的DFS(深度优先搜索)来解决。因为节点的值≤10^6,所以可以实现22个二进制位。结果,节点值的按位或也可以用22个二进制位表示。在此,该方法是确定在子树的所有值中设置每个位的次数。对于每个边,我们将验证从0到21的每个比特,设置了该特定比特的数字在两个结果树中均为零,或者在两个结果树中均大于零,并且已经观察到条件如果对所有位都满足,则将边沿计入结果。
示例
// C++ implementation of the approach #include<bits/stdc++.h> using namespace std; int m1[1000],x1[22]; // Uses array to store the number of times each bit // is set in all the values of a subtree int a1[1000][22]; vector<vector<int>> g; int ans1 = 0; // Shows function to perform simple DFS void dfs(int u1, int p1){ for (int i=0;i<g[u1].size();i++) { int v1 = g[u1][i]; if (v1 != p1) { dfs(v1, u1); // Determining the number of times each bit is set // in all the values of a subtree rooted at v for (int i = 0; i < 22; i++) a1[u1][i] += a1[v1][i]; } } // Verifying for each bit whether the numbers // with that particular bit as set are // either zero in both the resulting trees or // greater than zero in both the resulting trees int pp1 = 0; for (int i = 0; i < 22; i++) { if (!((a1[u1][i] > 0 && x1[i] - a1[u1][i] > 0) || (a1[u1][i] == 0 && x1[i] == 0))) { pp1 = 1; break; } } if (pp1 == 0) ans1++; } // Driver code int main(){ // Number of nodes int n1 = 4; // int n1 = 5; // Uses ArrayList to store the tree g.resize(n1+1); // Uses array to store the value of nodes m1[1] = 1; m1[2] = 3; m1[3] = 1; m1[4] = 3; /* m1[1] = 2; m1[2] = 3; m1[3] = 32; m1[4] = 43; m1[5] = 8;*/ //Uses array to store the number of times each bit // is set in all the values in complete tree for (int i = 1; i <= n1; i++) { int y1 = m1[i]; int k1 = 0; // Determining the set bits in the value of node i while (y1 != 0) { int p1 = y1 % 2; if (p1 == 1) { x1[k1]++; a1[i][k1]++; } y1 = y1 / 2; k1++; } } // push_back edges g[1].push_back(2); g[2].push_back(1); g[1].push_back(3); g[3].push_back(1); g[1].push_back(4); g[4].push_back(1); //g[1].push_back(5); //g[5].push_back(1); dfs(1, 0); cout<<(ans1); }
输出结果
2