LeetCode – Perfect Squares (Java)

Given a positive integer n, find the least number of perfect square numbers (for example, 1, 4, 9, 16, ...) which sum to n.

For example, given n = 12, return 3 because 12 = 4 + 4 + 4; given n = 13, return 2 because 13 = 4 + 9.

Java Solution

This is a dp problem. The key is to find the relation which is dp[i] = min(dp[i], dp[i-square]+1). For example, dp[5]=dp[4]+1=1+1=2.

public int numSquares(int n) {
    int max = (int) Math.sqrt(n);
 
    int[] dp = new int[n+1];
    Arrays.fill(dp, Integer.MAX_VALUE);
 
    for(int i=1; i<=n; i++){
        for(int j=1; j<=max; j++){
            if(i==j*j){
                dp[i]=1;
            }else if(i>j*j){
                dp[i]=Math.min(dp[i], dp[i-j*j] + 1);
            }
        }
    }
 
    return dp[n];
}
Category >> Algorithms  
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