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.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
|
class {
public int numSquares(int n) {
int[] dp = new int[n+1];
for(int i=1; i<=n; i++){
int j=1;
dp[i] = i;
while( i - j*j >= 0){
dp[i] = Math.min(dp[i], dp[i-j*j]+1);
j++;
}
}
return dp[n];
}
}
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
|
dp[0] = 0
dp[1] = dp[0]+1 = 1
dp[2] = dp[1]+1 = 2
dp[3] = dp[2]+1 = 3
dp[4] = Min{ dp[4-1*1]+1, dp[4-2*2]+1 }
= Min{ dp[3]+1, dp[0]+1 }
= 1
dp[5] = Min{ dp[5-1*1]+1, dp[5-2*2]+1 }
= Min{ dp[4]+1, dp[1]+1 }
= 2
.
.
.
dp[13] = Min{ dp[13-1*1]+1, dp[13-2*2]+1, dp[13-3*3]+1 }
= Min{ dp[12]+1, dp[9]+1, dp[4]+1 }
= 2
.
.
.
dp[n] = Min{ dp[n - i*i] + 1 }, n - i*i >=0 && i >= 1
|
近期评论