This is an extended question for 2 sum and 3 sum, 4 sum, DP problem.
Given n distinct positive integers, integer k (k <= n) and a number target.
Find k numbers where sum is target. Calculate how many solutions there are?
First think about backtracking
#include "header.h"
using namespace std;
void countSum(vector<int>& nums, int pos, int k, int target, int& count, int currSum) {
if((pos > nums.size()) || (target < currSum) || (k < 0)) return;
if((target == currSum) && (k == 0)) {
count = count + 1;
}
for(int i = pos; i < nums.size(); ++i) {
currSum += nums[i];
k = k - 1;
countSum(nums, i + 1, k, target, count, currSum);
k= k + 1;
currSum -= nums[i];
}
}
int countSum(vector<int>& nums, int k, int target) {
int count = 0;
int currSum = 0;
countSum(nums, 0, k, target, count, currSum);
return count;
}
int main(void) {
vector<int> nums{1, 2, 3, 4};
cout << countSum(nums, 2, 5) << endl;
}
Dp way.
int kSum(vector<int> A, int k, int target) {
// wirte your code here
int n = A.size();
vector<vector<vector<int>>> dp(n+1, vector<vector<int>>(k+1, vector<int>(target+1, 0)));
for(int i = 0; i <= n; ++i) {
for(int j = 0; j <= k; ++j) {
for(int t = 0; t <= target; ++t) {
if(j == 0 && t == 0) {
dp[i][j][t] = 1;
} else if(!(i == 0 || j == 0 || t == 0)) {
dp[i][j][t] = dp[i-1][j][t]; // skip the ith value.
if(t - A[i-1] >= 0) {
dp[i][j][t] += dp[i-1][j-1][t-A[i-1]]; // add the ith value in.
}
}
}
}
}
return dp[n][k][target];
}