UVA 861: From Backtracking to DP solution - algorithm

Question

Problem: Count the number of ways to place K Bishops on N*N chess board.
https://onlinejudge.org/external/8/861.pdf
I came up with the below backtracking solution but it is not fast enough. I do not understand the DP solution recommended on other sites. Can you please help.
In the below code I am exhaustively searching for all solutions using a recursive backtracking approach.
#include <bits/stdc++.h>
using namespace std;
using Row = vector<bool>;
using Board = vector<Row>;
Board gBoard;
bool isOk(int n, int r, int c) {
for(int i = r-1, j = c-1; i >= 0 && j >= 0; --i, --j) {
if(gBoard[i][j]) {
return false;
}
}
for(int i = r+1, j = c+1; i < n && j < n; ++i, ++j) {
if(gBoard[i][j]) {
return false;
}
}
for(int i = r-1, j = c+1; i >= 0 && j < n; --i, ++j) {
if(gBoard[i][j]) {
return false;
}
}
for(int i = r+1, j = c-1; i < n && j >= 0; ++i, --j) {
if(gBoard[i][j]) {
return false;
}
}
return true;
}
void trace(const string &msg) {
cout << msg << "\n";
for(int i = 0; i < gBoard.size(); ++i) {
for(int j = 0; j < gBoard[i].size(); ++j) {
cout << gBoard[i][j] << " ";
}
cout << "\n";
}
cout << "\n";
}
void dfs(int n, int k, int r, int c, int cnt, int &sum) {
if(cnt == k) {
//trace("OK");
++sum;
return;
}
if(c >= n) {
c = 0;
r += 1;
}
int j = c;
for(int i = r; i < n; ++i) {
for( ; j < n; ++j) {
if(gBoard[i][j]) {
continue;
}
gBoard[i][j] = true;
if(isOk(n, i,j)) {
//trace("tmp");
dfs(n, k, i, j+1, cnt+1, sum);
}
gBoard[i][j] = false;
}
j = 0;
}
}
void solve(int n, int k) {
gBoard.assign(n, Row(n, false));
int sum = 0;
dfs(n, k, 0, 0, 0, sum);
cout << sum << "\n";
}
int main() {
while(true) {
int n,k;
cin >> n >> k;
if(!n && !k) {
break;
}
solve(n, k);
}
return 0;
}
Thank you