Where is the huge performance difference for the two versions of the code? - palindrome

Question

I am working on a problem that Given a string s, partitions s such that every substring of the partition is a palindrome.
Return the minimum cuts needed for a palindrome partitioning of s. The problem can also be found in here. https://oj.leetcode.com/problems/palindrome-partitioning-ii/
Version 1 is one version of solution I found online.
Version 2 is my code.
They both seem to work in very similar ways. However, with a reasonably large input, version 2 takes more than 6000 milliseconds whereas version 1 takes around 71 milliseconds.
Can anyone provide any idea where the time difference is from?
Version 1:
int minSol(string s) {
int len = s.size();
vector<int> D(len + 1);
vector<vector<int>> P;
for (int i = 0; i < len; i++){
vector<int> t(len);
P.push_back(t);
}
for (int i = 0; i <= len; i++)
D[i] = len - i;
for (int i = 0; i < len; i++)
for (int j = 0; j < len; j++)
P[i][j] = false;
for (int i = len - 1; i >= 0; i--){
for (int j = i; j < len; j++){
if (s[i] == s[j] && (j - i < 2 || P[i + 1][j - 1])){
P[i][j] = true;
D[i] = min(D[i], D[j + 1] + 1);
}
}
}
return D[0] - 1;
}
Version 2:
int minCut(string s) {
int size = s.size();
vector<vector<bool>> map;
for (int i = 0; i < size; i++){
vector<bool> t;
for (int j = 0; j < size; j++){
t.push_back(false);
}
map.push_back(t);
}
vector<int> minCuts;
for (int i = 0; i < size; i++){
map[i][i] = true;
minCuts.push_back(size - i - 1);
}
for (int i = size - 1; i >= 0; i--){
for (int j = size - 1; j >= i; j--){
if (s[i] == s[j] && (j - i <= 1 || map[i + 1][j - 1])){
map[i][j] = true;
if (j == size - 1){
minCuts[i] = 0;
}else if (minCuts[i] > minCuts[j + 1] + 1){
minCuts[i] = minCuts[j + 1] + 1;
}
}
}
}
return minCuts[0];
}

Answer 1

I would guess it's because in the second version you're doing size^2 push_back's, whereas in the first version you're just doing size push_back's.