377. Combination Sum IV | Leetcode Dynamic Programming

Description

Given an integer array with all positive numbers and no duplicates, find the number of possible combinations that add up to a positive integer target.

Example:

Thinking

用动态规划解决这个问题。用nums中的数字加出target，求共有多少种组合方式。设置一个size为target+1的vector tar用于记录加法总数，假设target为0，则只有一种，不用任何nums中的数字，即tar[0]=1。
求tar[i]时，遍历nums数组，若tar[i]大于nums[j]，则增加tar[i-nums[j]]种方法。状态转移方程如下：
tar[i] += tar[i - nums[j]]；

Solution

class Solution {public:    int combinationSum4(vector<int>& nums, int target) {        vector<int> tar(target + 1, 0);        tar[0] = 1;        for(int i = 1; i <= target; i++){            for(int j = 0; j < nums.size(); j++){                int num = nums[j];                if(i - nums[j] >= 0){                    tar[i] += tar[i - num];                }            }        }        return tar[target];    }};