## Wildcard Matching

06/26/2016 Dynamic Programming Backtracking Greedy String

## Question

Implement wildcard pattern matching with support for '?' and '*'.

'?' Matches any single character.
'*' Matches any sequence of characters (including the empty sequence).

The matching should cover the entire input string (not partial).

The function prototype should be:
bool isMatch(const char *s, const char *p)

Some examples:
isMatch("aa","a") → false
isMatch("aa","aa") → true
isMatch("aaa","aa") → false
isMatch("aa", "*") → true
isMatch("aa", "a*") → true
isMatch("ab", "?*") → true
isMatch("aab", "c*a*b") → falseexamples


## Solution

Result: Accepted Time: 144ms

Here should be some explanations.

#define MAXN (4096+512)
bool dp[MAXN][MAXN];
bool isMatch(char* s, char* p) {
const int m = strlen(s), n  = strlen(p);
dp[0][0] = true;
for (int j = 1; j <= n; j++)
dp[0][j] = dp[0][j-1] && p[j-1] == '*';
for (int i = 1; i <= m; i++)
dp[i][0] = false;
for (int i = 1; i <= m; i++)
for (int j = 1; j <= n; j++)
if (p[j-1] == '?' || s[i-1] == p[j-1])
dp[i][j] = dp[i-1][j-1];
else if (p[j-1] == '*')
dp[i][j] = dp[i-1][j] || dp[i][j-1];
else
dp[i][j] = false;
return dp[m][n];
}


Complexity Analytics

• Time Complexity: $O(n^2)$
• Space Complexity: $O(n^2)$