668. Kth Smallest Number in Multiplication Table

zibingling777

于 2018-01-16 03:20:07 发布

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分类专栏：刷题笔记文章标签： Binary Search

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本文介绍了一种使用二分搜索算法解决寻找m*n乘法表中第K小元素的问题的方法。通过设定搜索范围从1到m*n，并不断调整中间值来缩小搜索范围，最终找到目标元素。

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1. Description

Given three elements m, n and k. Find the k-th smallest number in the m*n Multiplication Table.

2. Solution

Binary Search.

The left point is 1, and the right point is m*n.

While left is smaller than right,

find the middle of left and right, and then calculate the number of elements not bigger than the middle value.

If the number is smaller than k, then set left to middle+1;

otherwise, set right to middle.

Return the final left point.

3. Code

    int findKthNumber(int m, int n, int k) {
        int l = 1, r=m*n;
        while(l<r){
            int mid = l+(r-l)/2;
            int cnt = count(mid,m,n);
            if(k<=cnt)
                r=mid;
            else
                l=mid+1;
        }
        return r;
    }
    int count(int mid,int m,int n){
        int cnt = 0;
        for(int i=1;i<=m;i++){
            cnt+=min(mid/i,n);
        }
        return cnt;
    }