split-array-largest-sum（参考了discuss）

注意，第一种用法，涉及到一些Java的知识。就是采用Object作为HashMap的key的时候，需要重载这个Class的 equals 和 hashCode 这两个方法。其中equals需要判断一下比较元素的类型，而hashCode 里面可以采用 String.valueOf(val).hashCode() ^ 的方法来处理。

在HashMap里面查找的时候，会调用HashMap里面的元素的equals方法，把待查找的元素作为参数传给这个方法，来进行比较和判断元素是否存在于HashMap中。

// 参考 https://discuss.leetcode.com/topic/61315/java-easy-binary-search-solution-8ms // 开始用类似回溯的方法做，ETL了

public class Solution {

public int splitArray(int[] nums, int m) {
int mlen = nums.length - m;
int minM = 0;
int maxM = 0;
int sum = 0;
for (int k=0; k<nums.length; k++) {
sum += nums[k];
if (k > mlen) {
sum -= nums[k-1-mlen];
}
maxM = Math.max(maxM, sum);
minM = Math.max(minM, nums[k]);
}
System.out.printf("min:%d, max %d\n", minM, maxM);
int result = bsearch(nums, m, minM, maxM);
return result;
}

private int bsearch(int[] nums, int m, int low, int high) {
int mid = 0;
while (low < high) {
mid = low + (high-low) / 2;
if (isValid(nums, m, mid)) {
high = mid;

} else {
low = mid + 1;
}
}
return high;
}

private boolean isValid(int[] nums, int m, int cand) {
int split = 1;
int sum = 0;
for (int i=0; i<nums.length; i++) {
sum += nums[i];
if (sum > cand) {
split++;
if (split > m) {
return false;
}
sum = nums[i];
}
}
return true;
}

/*
class KPair {
public int pos;
public int m;

@Override
public int hashCode() {
int ret = String.valueOf(pos).hashCode() ^ String.valueOf(m).hashCode();
return ret;
}

@Override
public boolean equals(Object obj) {

if (null == obj) {
return false;
}
if (!(obj instanceof KPair)) {
return false;
}
KPair kp = (KPair)obj;
//System.out.printf("kp%d p%d km%d m%d\n", kp.pos, pos, kp.m, m);
return kp.pos == pos && kp.m == m;
}
}

public int splitArray(int[] nums, int m) {
Map mp = new HashMap();

KPair okp = new KPair();
int tmp = 0;
int newval = 0;

KPair kp =  new KPair();
kp.pos = 0;
kp.m = 1;
//System.out.printf("in1 p%d m%d\n", kp.pos, kp.m);
mp.put(kp, nums[0]);

for (int i=1; i<nums.length; i++) {

okp.pos = i-1;
okp.m = 1;
tmp = (int)(mp.get(okp))+nums[i];

KPair kp2 = new KPair();
kp2.pos = i;
kp2.m = 1;
//System.out.printf("in2 p%d m%d\n", kp2.pos, kp2.m);
mp.put(kp2, tmp);

for (int k=0; k<i; k++) {
// tmp is sum of k+1 to i
tmp -= nums[k];
okp.pos = k;

for (int j=2; j<=m && j<=k+2; j++) {
okp.m = j-1;
//System.out.printf("for2 p%d m%d\n", okp.pos, okp.m);
newval = (int)(mp.get(okp));
if (tmp > newval) {
newval = tmp;
}

KPair kp3 = new KPair();
kp3.pos = i;
kp3.m = j;
if (mp.get(kp3) == null || (int)(mp.get(kp3)) > newval) {
//System.out.printf("in3 p%d m%d\n", kp3.pos, kp3.m);
mp.put(kp3, newval);
}
}
}
}

KPair kpr =  new KPair();
kpr.pos = nums.length-1;
kpr.m = m;
return (int)(mp.get(kpr));
}
*/

}