矩阵乘法计算量估算， 华为笔试题

Posted 2020-12-16 lixyuan

思路：构造一颗二叉树，递归计算左右子树的计算量， 再加上左子树矩阵*右子树矩阵的计算量。

坑：测试数据存在右括号多于左括号数量的情况，需要特殊处理一下。

import java.util.*;
public class Main {
    public class Node {
        Node left, right;
        int row, col;//val
        public Node(int x, int y) {
            row = x;
            col = y;
            left = null; 
            right = null;
        }
    }
    public Node creatTree(char[] s, int[][] a, int start, int end) {
        if(start > end || start < 0 || start >= s.length || end < 0 || end >= s.length)
            return null;
        if(start == end) {
            int idx = s[start] - ‘A‘;
            return new Node(a[idx][0], a[idx][1]);
        }
        int l = start + 1, r = end - 1;
        int cnt = 1, mid = l;
        if(s[l] == ‘(‘) {
            while(cnt != 0) {
                mid++; 
                if(s[mid] == ‘(‘) cnt ++;
                if(s[mid] == ‘)‘) cnt --;
            }
        }
        Node root = new Node(-1,-1);
        root.left = creatTree(s, a, l, mid);
        root.right = creatTree(s, a, mid+1, r);
        return root;
    }
    public int[] dfs(Node root) {
        if(root == null) return new int[] {-1,-1, 0};
        if(root.left == null && root.right == null) {
            int[] res = new int[] {root.row, root.col, 0};
            //System.out.println(Arrays.toString(res));
            return res;
        }
        int[] l = dfs(root.left);
        int[] r = dfs(root.right);
        int[] res = new int[] {l[0], r[1], l[2] + r[2] + l[0]*l[1]*r[1]};
        return res;
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        Main mn = new Main();
        while(sc.hasNext()) {
            int n = sc.nextInt();
            int[][] a = new int[n][2];
            for(int i=0; i < n; i++) {
                a[i][0] = sc.nextInt();
                a[i][1] = sc.nextInt();
            }
            char[] s = sc.next().toCharArray();
            int cnt = 0;//判断左括号数量是否等于右括号数量
            for(int i=0; i < s.length; i++) {
                if(s[i] == ‘(‘) cnt ++;
                if(s[i] == ‘)‘) cnt --;
            }
            Node tree = null;
            if(cnt != 0) {
                tree = mn.creatTree(s, a, 0, s.length-2); // 去除多余的一个右括号
            } else {
                tree = mn.creatTree(s, a, 0, s.length-1);
            }
            int[] res = mn.dfs(tree);
            System.out.println(res[2]);
        }
    }
}
/*
1. 构造二叉树，节点信息包括:row(行数),col(列数)
2. 计算子树乘法次数，再加上左子树矩阵*右子树矩阵的计算量。
*/