205. 区间最小数

描述

给定一个整数数组（下标由 0 到 n-1，其中 n 表示数组的规模），以及一个查询列表。每一个查询列表有两个整数 [start, end]。 对于每个查询，计算出数组中从下标 start 到 end 之间的数的最小值，并返回在结果列表中。

注意事项

在做此题前，建议先完成以下三道题 线段树的构造， 线段树的查询 及 线段树的修改。

样例

对于数组 [1,2,7,8,5]， 查询 [(1,2),(0,4),(2,4)]，返回 [2,1,5]

挑战

每次查询在O(logN)的时间内完成

代码

1. 无需考虑拆分区间

/**
 * Definition of Interval:
 * public class Interval {
 *     int start, end;
 *     Interval(int start, int end) {
 *         this.start = start;
 *         this.end = end;
 *     }
 * }
 */

public class Solution {
    /*
     * @param A: An integer array
     * @param queries: An query list
     * @return: The result list
     */
     
    class SegmentTreeNode {
        public int start;
        public int end;
        public int min;
        SegmentTreeNode left;
        SegmentTreeNode right;
        public SegmentTreeNode(int start, int end, int min) {
            this.start = start;
            this.end = end;
            this.min = min;
            this.left = null;
            this.right = null;
        }
    }

    public SegmentTreeNode build(int start, int end, int[] A) {
        if (start > end) {
            return null;
        }
    
        if (start == end) {
            return new SegmentTreeNode(start, end, A[start]);
        }
    
        SegmentTreeNode root = new SegmentTreeNode(start, end, A[0]);
        int mid = start + (end - start) / 2;
        root.left = build(start, mid, A);
        root.right = build(mid + 1, end, A);
    
        root.min = Math.min(root.left.min, root.right.min);
        return root;
    }

    public int query(SegmentTreeNode root, int start, int end) {
        if (start <= root.start && end >= root.end) {
            return root.min;
        }
    
        int mid = root.start + (root.end - root.start) / 2;
        int ans = Integer.MAX_VALUE;
        if (start <= mid) {
            ans = Math.min(ans, query(root.left, start, end));
        } 
        if (end > mid) {
            ans = Math.min(ans, query(root.right, start, end));
        }
    
        return ans;
    }
 
    SegmentTreeNode root;
    public List intervalMinNumber(int[] A, List queries) {
        root = build(0, A.length - 1, A);
        List list = new ArrayList<>();
        
        for (Interval num : queries) {
            int res = query(root, num.start, num.end);
            list.add(res);
        }
        
        return list;
    }
}

2. 手动拆分区间

class SegmentTreeNode {
    public int start, end, min;
    public SegmentTreeNode left, right;
    public SegmentTreeNode(int start, int end, int min) {
          this.start = start;
          this.end = end;
          this.min = min;
          this.left = this.right = null;
    }
}
public class Solution {
    /**
     *@param A, queries: Given an integer array and an query list
     *@return: The result list
     */
    public SegmentTreeNode build(int start, int end, int[] A) {
        // write your code here
        if(start > end) {  // check core case
            return null;
        }
        
        SegmentTreeNode root = new SegmentTreeNode(start, end, Integer.MAX_VALUE);
        
        if(start != end) {
            int mid = (start + end) / 2;
            root.left = build(start, mid, A);
            root.right = build(mid+1, end, A);
            
            root.min = Math.min(root.left.min, root.right.min);
        } else {
            root.min = A[start];
        }
        return root;
    }
    public int query(SegmentTreeNode root, int start, int end) {
        // write your code here
        if(start == root.start && root.end == end) { // 相等 
            return root.min;
        }
        
        
        int mid = (root.start + root.end)/2;
        int leftmin = Integer.MAX_VALUE, rightmin = Integer.MAX_VALUE;
        // 左子区
        if(start <= mid) {
            if( mid < end) { // 分裂 
                leftmin =  query(root.left, start, mid);
            } else { // 包含 
                leftmin = query(root.left, start, end);
            }
        }
        // 右子区
        if(mid < end) { // 分裂 3
            if(start <= mid) {
                rightmin = query(root.right, mid+1, end);
            } else { //  包含 
                rightmin = query(root.right, start, end);
            } 
        }  
        // else 就是不相交
        return Math.min(leftmin, rightmin);
    }
    
    public List intervalMinNumber(int[] A, 
                                           List queries) {
        // write your code here
        SegmentTreeNode root = build(0, A.length - 1, A);
        List ans = new ArrayList();
        for(Interval in : queries) {
            ans.add(query(root, in.start, in.end));
        }
        return ans;
    }
}