LeetCode 646 Maximum Length of Pair Chain（贪心）

You are given n pairs of numbers. In every pair, the first number is always smaller than the second number.

Now, we define a pair (c, d) can follow another pair (a, b) if and only if b < c. Chain of pairs can be formed in this fashion.

Given a set of pairs, find the length longest chain which can be formed. You needn't use up all the given pairs. You can select pairs in any order.

Example 1:

Input: [[1,2], [2,3], [3,4]]Output: 2Explanation: The longest chain is [1,2] -> [3,4]

Note:

1. The number of given pairs will be in the range [1, 1000].

题目大意：有n对数字，每一对数字中第一个数字总是小于第二个数字。对于数对(a, b)和(c, d)来说，当且仅当c < b时这两个数对才能连在一起。现在给出一堆这样的数对，求出可以连接的最长数对的长度。

解题思路：选择不相交区间问题。可以按照每个数对的第二个数字升序排序，如果第二个数字相等则按照第一个数字升序排序；然后从第二个数对开始遍历，如果当前数对的第一个数大于上一个数对的第二个数，那么这两个数对就可以连在一起，继续遍历并统计数对个数即可。

代码如下：

#define maxn 1005struct Pair{    int begin;    int end;} pair[maxn];int cmp(const void* a, const void* b){    struct Pair* x = (struct Pair*)a;    struct Pair* y = (struct Pair*)b;    if(x->end == y->end) return x->begin - y->begin;    return x->end - y->end;}void matrixToStruct(int** pairs, int row){    for(int i = 0;i < row;i++){        pair[i].begin = pairs[i][0];        pair[i].end = pairs[i][1];    }}int findLongestChain(int** pairs, int pairsRowSize, int pairsColSize) {    int row = pairsRowSize;    int col = pairsColSize;        matrixToStruct(pairs, row);    qsort(pair, row, sizeof(struct Pair), cmp);        int cnt = 1;    for(int i = 1, k= 0;i < row;i++){        if(pair[i].begin > pair[k].end){            cnt++;            k = i;        }    }    return cnt;}